# problemswithoutfigures

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2 FOR GRADE TO EIGHTH GRADE RTH FOU • fo r Menta l Re views in And • , • SCHOOLS AND NORMAL SC HIGH • S. Y. GILLAN. By ll'HIRD EDITION. ) , • r,;·Vhl./ SHIEO BY S. Y. GILLAN" COMPANY. MILWAUKEE. •

3 re ace. make be taught as can so the pupil familiar Arithmetic to a thc fact that we may use a number in wi problem without th l' l\owing what particular number it is. Some of the funda- thus me of algebra may ntals be taught along with arithmetic. to l.ut, as a rule, whenever any attempt is made do this the degenerates wo soon develops or rk into formal algebra, with a genemlization symbolism, of formulae matter and quota full a which not wholesome pabulum for is child's mind and the reo given '; ult has been that have teachers up rthe effort and have reo standardized t to the use of urncd knowledge put up in separate hay, "arithmetic," another one bale labeled baled pa c kages like - "nl g ebra," etc. CnpiRHlS D'If 190\;. 't', and Every distinct problem in arithmetic calls for two Y. S. GILLAN. "Idel y dlfl'erent kinds of work: first, the solution, which in- the Yo es a comprehension of lY conditions of the problem and another; thei r r e lation to one we second, the operation . First reasoning i;.?:\T\Jlers up to needs a tandard adapted to the s of eighth grade pupils . Ae • •

4 a review high school and normal school classes the problems in be may as in and will be found In ter- taken they order come, pupils in the grades, the teacher stimulating. and esting For ones to omit; this discrimination will be a will which Indicate for the teacher. exercise valuable A few are put in to entrap the unwary. "catch problems" occasionally a pitfall makes a pupil more To stumble into • Prob ems steps his exercise In re- invigorating gives and of watchful ithout 1 ures. his gaining footing. his 'l'he groove runner thus learns to use legitimate the and wits and see difference between a problem an absurdity. is as sight work, exercises used It be recommended that these pupils and. ~eslgnatlng the the teacher band having the in book know you If 1. seven plus times fiye plus times three preparatIOn. prevIOus without solYed be to problems the you the how number? times a number do find GILLAN. Y. S. 2. If you know third much a number with its how WisconSin, Milwaukee, 1910. 21, May • equals, can you find the number? /lllded how To find the number of cubic feet in a box, what 3. you know what must you do? must and • know one-half of how I 4. much John's money IS money is. how one-fourth of much Ned's I'Il d can How find how much money T both have? they boy counted bis money and a;;ked the price 5. A of pair skates, of a pocket 1.-nife and of a sled; he It of knew money much more hen he would have to t how them. before get all of could How did he t'arn he out? finu Helen will how much a box of candy G. cost knows how rind book will cost. How may ;;he much a certain left how she will have money after paying out finu much book and the candy? for the If you told how long a are 7. and how fence post is lind how lligb it is, how can you deep it is set in the roun d? ~ Mary a certain ;;um of money plus one-fourth 8. has much as Lucy ,has. If I tell all how much money you r has, how can you ary how much Lucy has? find -

5 , PROBLEMS WITHOUT FIGURES. 7 FIGURES. WITHOUT PROBLEMS 6 9. If know how sheep. some bought man A you ' to find do you will what and know you how IUU many can bought, he meep how how and paid he much IUllny it contains? cords price sheep? the one of find you American the on star;; the ~re 1~. five-pointed flag A 10. a good man bought time, watch that kept correct or some girls 1906, slx-pomted? On Memorial Day, it but day he traveled one lost time; in what when of one mi;;take by and the stars was dif- flag, a IIIncle direction travel? did he total the you tell I If others. the from nt. r"r number 11. leng and room a of width and th the know I the how or of all the stars, pomts can you find whether the pound of paint of will number square feet that a cover. was o,lcl star five-pointed or six-pointed? many ounces of I find how paint will be required How can Is when Important t~ notice the date the flag was made.] l ~t to room? that of floor the paint three as ,, m 0. time;; many bore orchard an tree One 12. water horse gallons many how know I will a of other all of average the the If you are as l/lples trees. quarts seven horses drink; how I find how many can tree nlcl bushels that one many produced, what how will drink? know and what will you do .lc find how must you to a many how find I times How 13. wagon wheel can orchard? whole bushels the mnny on grew in turn going three miles? will ' long and you a feet many how If know wide 21. . 14. How would you find the dL,tance around a square llar must know and what else you what It'. be, to IS long is? you know ho-;v if two-thirds of one side field do to find how many wagon loads earth of \, ~ll you each oats, 15. wheat and corn A at a differ- man sold be 2 cavation ex the making in out taken III ent price per know If you the price received bushel. ' pickets many how know fence a you If .22. in are of the each, of bushels number the grain, of kind for each must things two what garden, s hlch square a urroun~;; I, the rent amount the and farm of in acres of number be and what will you do to find how know 011 besIdes, cultivating paic1 acre, the cos t of per the crop, how will also feet square IlIlIny garden? the in the net profit on the grain sold? you find 23. horse, and saddle weigh a A certain number rider on some one fed puppies each milk, but A boy 16. man the as much as pounds; 'nineteen weighs of times how tell I If wanted. it you much as half only had as what told you If saddle. h 1 the of are two-thirds find will how them, gave you milk of he gills many the ho find you will how is, the weight weight of have they all them furnished many would pints how !lc1dle? wanted? One 24. long as two-thirds i;; rod iron as another· 17. pickets the of width and you tell I If the the be must and off rod long the of part what cut added fence making in used a pi the between distance ckets make to -length? one same the short the 10 of them and what you must know else lot, square a around what know I If 25. when weighs horse my much how is? the of aide lot long one find to do you will how

7 • " • • FIGURES. 11 PROBLEMS WITHOUT WITHOUT PROBLEMS FIGURES 10 hi of [Find purcha&e? s several amount the IIUS It I not see do more? Answer: The latter, 14 more. If you rs.] answe I('ct I diagram a it. plainly, tIus to illustrate make milk of pints of number certain a uses family ,0. A pound; the by sugar dozen, the by sold are Eggs 42. find I of number the gallons you will how day; they farmer bought , price of each is given in cents. A the week? .~ . I n a it for paid you sugar some and must What egg5. in A 1 [J • boy · knows at what rate he can walk and at pounds you will what and do to find how many of know bicycle, t far how rate also it a he is on ride I can sugar got? he can How repairs. bicycle his left he where town for the from t erec stands pond. pole A . a of bottom 43 it and to to take will town long how linu return walk the the water also Jepth of If I know the total length, bicycle? It is may I find how water, above hight the and thc how deep If .J~. you know the per pound and the weight price earth? the in set ia it how r II ham, can you find how much it will cost, if many 44. how and dimes many how you tell I If fat 1\ eitY hth of the weight is and one-eighth bone? amount a nickels boy has, how can you find the of his I inches how know .:1. long sheet 3i many and wide money? feet is, i Il and how many how long and wide a roof is; i r of a tower , surmounted by a flag pole The top 45. It I find how many sheet~ will cover the roof? I know you reached many how of by 1f "tail's. means is zero, ;,1 above was temperature the day one On . the how many high ste p is, inches many there are, and how a find the uay difference below in t I . How can you distance feet pole ~s, how can you find the the from long IJiperatu re between days? two these the top the pole? the ba5e of the tower to of Mi. you a know the If for each day for temperature the store; 46. man what A bought several articles at you of IIl1h I' days, how can find the average temper- you must how find to do much will what and know you days? those for rn I t receive? change he should table has two leaves know equal size. I how .!Ii. A of sticks of dIe bun a have how long; foot a each 47. I the of the also i;;, width table the long inches "IllY can ;;hall I find how many separate one-foot squares I leaves when I' width the you tell I If down. are both rectangles with them? How many two feet long enclose find I square of number the inches you will how leaf, Oil f foot will the sticks enclose? wide and a up? are both when top It t II rods you 48. how tell I If many many how and long ;.7. thousandths seven hundred two larger, the is Which field you will how is, feet rectangular a wide find how J [Ans. wo latter.] The thousandths? six and hundred I it a many field? the around is yard numbers, . consecutive three of sum the Knowing ;, boy and handed 49. A made a purchase at the store of lull' ran vo u find each the nnmbers? the change received he payment; in bill as a merchant • how If yo u know the ,ID. of a barrel of apples, cost of the same value. four silver coins no two of them ,

8 • S. FIGURE WITHOU'£ PROBLE!1S 13 12 WITHOUT FIGURES. PROBLEMS of length the I know liH. width the and rods in a field will can at sold when bring three ihey profit the find you can it acred many how find I t, how fl' I contains? cents? for :five dealer has anum ber Ii!!. small baskets of the A of feed pounds of oats, how you a hor1'e several 60. If bushel into II ,' f,ize, which he puts a of apples. W11en cent. per you a bushel of feed him? find you what will "old make to wants he ,11"' will How profit. certain a harrow you is, a wide If 61. inches how know many finel many apples to put how each, and at what into distance the harrowing in traveled an will you how :find sell to " p r basket them? ground? of acre O. just years many as older brother is John his than the ceiling painted is blue, half 62. If ana-third of a the younger is than his sister. If you know age and surface remaining red the remainder is unpainted, and John's find you can how sister of his brother I can how length, the I if ceiling the of area know the :find 'J the room? width and hight of • 11. diameter know the weight and the grind- a of I a has grocer A 63. number sackil each of the same of t also the size of the hole in the center of it. How Ilf', :filled size, potatoes; he knows the weight of one with I the weight of another of the ute same dimen- It amp the total number of bushels in :find he may How sack. which large? but material Ilnd as has twice 111 a hole all sacks? the gave the merchant 72. boy made a purchase A and of 64. grew a certain number A inches in a night; vine each coins, three change bill, receiving in differ.mt a of how we find the average growth per hour? can was the amount /I his purchase? f nl. [Find What of on a snow the weigh you If 65. square lies foot that answers.] correct teen "ix 1f'llst t of ground, how can you :find the weight of snow on an room, the :I. Knowing length, width and hight of a acre of ground? and number of the • and windows and size the doors a 66. A boy has fragment of stone of irregular shape. how ,.tIlt the base-board, can you find how many square of it He wantil to know how many cubic contains. inches ,'I. ceiling? wall" the and on plastering of I, allowing and water of full brim cup a in it Immersing What - I. iil the easiest way to find the sum the all of overflow a the water to cup into saucer, he removes the bel'S printed on a 11 January calendar? I III it and weighs the saucer and the water which contains. . 76 tract - square a around of of number The rods the empty out saucer. the pouring Then waleI' he weighs number large it acres of contains; how I'm l equals the weight of a how water, can foot cubic If he knows the of It? he :find the volume of the 1'tone? found was 76 coin . A C. B. 420 inacription the bearing told are If you eyes, 67. the total number of feet, was it? Ilow old number a of boys and three fingers and wings certain • standing 7. Some boys are row, a In equal at times find you can how how many haye, chickens many as dis- • the know you If apart. 1H'(,5 length of are? boys the line there and

9 PROBLEMS FIGURES. WITHOUT FIGURES. WITHOUT PROBLEMS 15 1~ and Rli. Given the length of a straight line of fence number find boys, how of you the be- distance the can can how posts, the the distance III' find you between boys? the tween r of h 11111 posts? length 78. fence of line a of and the know u yo If the of liven the number pastil 'e sts and the distance betwee n of number' in it, how can you find the distanc po I the fence? of line of length the find you can how l'lll, posts? between the the length of the (, and the number of posts, iven fence 79. the snme number of If boys are standing at equal you are? POilts the apart far how find an IW intervals of lengt the circle a of circumference the on h the mental habit of vis- acquired have pupils Unless NOTE. I known, is which distance the find you how between can they things the 11l~ I II problems, arithmetical in with deal on circle? the of arc an measuring boys, two foregoing 1111 flounder hopelessly In trying w ill to answer the who num- the me told melons -some raised boy A 80. Illg 11< t problems.] of how vines and ber number of melons on each vine; the The . a certain bu square orchard are planted in trees vine? can I find the average number of melons per row apart they far how JOu tell I If * fashion. 1'1- times as old as three Henry; what must is 81. John outer from r' Ilnd how far the boundary the trees are, will what and know you many you do to find how ran orchard the tract land IIW the you find the size of of as old times certain any be as John Henry number will II pi s ? later? of years Lay or desk on the three matches toothpicks of On a street railway the price a ride is cheaper 82. equilatcral ow N triangle. form the of an arrange for those who buy ticket", but some passengers pay two of kind ilame siue. 'each on a the make t figure, cash. At the end of the run one indi ca tor shows how " . cconu how many times is large as the triangle as many another how many c8.sh fare s were and tickets l? ciphering. any without this Show the total how mpute co you can collected; taken amount H . (a) There "ide the of one along road public a is on the trip? in of of certain a r1l1east quarter the southwest quarter and be known must that things four State 83. three '1iO with his fences joins owner the If land. of ll finding to be done in things the length of a railroad train he st mu fence of many I j. lIbors maintain? how rod,; rtain pile move of coa1. ce a to required (b) has If he a "spite fence" and "devil'" lane" on one 1. pounds) In the pile. (or tons of Number (a) Answer: (' how he does e maintain? much of his forty, fenc Average (c) car. a of capaclty Average (b) car, a of length Some a field corn are men in ,9. a certain husk ing at (d) couplings. Length of engine and tender. Including will ric-· farmer the cost it for much How bushel. per • d. add and c by multiply b, by a Divide 2. trees so Is. "That make are es sid whose square a adjacent tour that make 84. cubic feet of coal 37 a ton, - how many If might they which In way r he anot Show tract. the of I 1 with the sides the trees be trees Lll ",tod so that no tract would hold more yet the would tons a bin in sides perpendicular a base has in and which to the ' r tOll'et h er n or nearer tor the boun da ry. See Glllan's Ourlosltlel ~4, Ila('.o room, hool right the forrn of a triangle?

10 • FIGURE S. PROBLEMS WITHOUT IG FIGURES. WITHOUT PROBLEMS 17 be What must this known the of field of husking corn? cornered square a long rods III)' how also is, n garde answer? the and what done to find that is walk half wide leet 11\ the round way a run a • flag, how 90. If you know the width of an American can in II'd\ 11, how you find the number of square feet the stripe, find blue the of and field? one of width the can you the walk? by t 11 I I occupied 91. room, a of length and width hight, the Knowing cheese !IH. Knowing how many ounces in the a and the of from northeast corner how can y ou find the distance I . the the of price I find can how pound, pcr II' cheese? the ceiling to the floor? southweiit corner of the I !l!). made a purchase at the store and gave the of I the Knowing 92. a bushel of ca.n how oats, cost ' . five receiving bill, t a ('han in I pieces of silver change a gIven from eat will horses my oats the of cost the find of the what purchaae? the II was amount the same value; of date February? in the to January in date correaponding them.] 1,1\ sev eral answers, and verify must What be done? what and known can How 10. water the of weight the com- you find a. at A 93. farmer sold a grocer a cake of beeswax a gallon from escapea which steam the III I of in water price pound. It was afterward found per that certain n time? a give IIlillg I the a large cake know of center was in cavity. If you the wide 101. A board has a and a you if end; narrow cavity volume of the the weight in cubic inches, and the board, the . width of each end and the length of the 0\\ trana- adjust you would how beeswax, of inch a cubic of the find inches of number the square you an \I surface of farmer action fairly, between the and the grocer? II of side it? onc a If you know the length and width of sidewalk 94. stands If I tell you a pond. in A pole upright 102. and nnrober the and underneath stringers the of size l length part of fractional lota the it, of is that it the boards of board the do how find total number you part fractional the earth, h t that and water, the in feet of of thickne.5S the build it? lu~.ber required to Is I I' I and blue painted is water the above part the of ird It the boards taken into account in problems of solving of the t find length you can how white, the of I it this kind? I It tha t is in the air? in know how many acres are 95. a field and you If 10:1. If the diameter of a wheel is known in how feet, long find how many you can how is, it rods many how of III (he any in makes it revolutions number number of it iil? . wide feet d. I be fonnd? 96. red, a box of marbles some are some whIte, In turned furrow the a of width the Knowing 104. by blue. the and others If you are told the total number, you how find how '"w, I can plow- in wal.ks team a far also the the of sum the red white, and and the sum of acre," square "a about anything say [Don't acre? on r white, you can how find the and blue the the Dllrober t mathematician tell t r can hnt is an impossible unit; no color? each of I I I ngth of its side.] . are you If 97. , how wide rods many and how told cents 101i. the number of Given whi ch a certain num- •

11 • HOUT LE: :' lS ,n T J3 FIG UR ES . P UO 19 FIGURES. UT PUOBLEMS WITHO 18 price cost, how can you find the es ch e s pint of ber rri of y m ore James has than Robert? How many times I lI of a bushel at the same rate? must give many How ? each that so Robert James you 1£ 106. know what fractional his of marbles part same number? the ave h a boy how left, has he can many you lost find and how 117. in trees of rows an how know you Ii many bushels hn ru , h ow many tree::; in a row, how many many he lost? how acreage of total the Knowing 107. each of several fields on per how and average, the much the to !lples II , tree can each in acres of number the and them but of one, how how he the find ;you an c value for, sold h ' I t y a re you that find the acrea one? ge of tho crop ? a holds can depth A equals its gallon; 108. cylindrical . in boy living I I the country left his bicycle in A diameter. its What are can? dimen sions of the the dis- I . t o be repaired. Ii you know how many miles It number of trees s row of a the know I Ii 109. in the s boy can p er mile many hour III is, n ow t the how number and th e total orchard of treei!, how can I square distance, whole the ride to him takes it long how nd a dk, each find the number in row? \ • to walk to him take will it long bow find you can can how 1£ one hors e 110. walk three hour, an in miles nd II ride back? • a far can four horse::; walk the same time? in V. II many how you t ell I If white sheep and how of 111. I know a third Ii the sellin g price and half per bl k ones in a flock, how c an you tell what ac lIy how c the or profit the find I an loss? price, cost the blaak:? are em th of l. sheaves in a "hock 112. Ii you know t he number of a cup; he then quart 1"0 . A boy carefully weighed and of wheat, the number the of acre, e th to cks sho clean it d s it and .. weighed ith w pebble after again; width and length you can how s, rod in field the of as th Iri ng in as much water I the cup would hold wi t h e field? the in sheave::; of number total the find weighed then h e time; third a it poured , he it in s l hh you find the number gallons in a box 113. do How of water that would run off weighed and once I n 11 t he it • and inches? in known are depth who width length, se he the pebbles, the of weight the find can IIow IIII'{'. mules the A man took some 114. and some oxen to the and off, poured was that water of t Ivh the weight sh op and you must What "hod. them had t r blacksmith pebbles? he water wet the to clung that number of what will and you do to find the total know day tell 1. On a certain '> inches of rain fell; if I I pounds many ow h '11 how weighs, water of foot cubic a required? shoes a The 115. le ngth of of c hain in feet and the number II fell on an acre? u find how yo many tons links you can how known; it are in a length the of find knife, A paper. some and book a a bougbt boy . "2 1 I find you can how article, each of price the you tell J in link inches? number certain a marbles, has James 116. of and if receive will merchant the he change gives he 10 much • can find has a smaner number, how Robert you how f wo-c l o llar bill?

12 S WITHOUT FIGUR ES . PROBLEM 'r FIGURES. WITHou PROBLE1>£S 20 21 how of work in a week; piece a d o 123. One man can cent. per given a realize 10 til. his on year each profit men take se can hor long will it three Ona to do it? run t? 1\\1 lruen long will it four minute~; in how around a race course :12. I and bushel the by seed grass buys merchant A it? do to horsas four take quart What Illd i t up in packages for the retail trade. a square field; 124. I know the number of rods around his profit will you do what and know u yo Ulll to find on field? in acres of number the find I an tha c how e? kag pac C'!I men a certain village the do of shoes 125. How many driving market; to grain of a load took farroer A . :13 I of half three per cent. if them are one-legged and waar It II t sca l es the weight of the team and the loaded wagon s and t of weight t he he afterward team , found II and the others go bare-footed? 126. price If you know the weight of a book and the be done to find mply value wag on. What remain s to the d of per paper wrapping the of weight the also postage, ( t ounce he loa grain? a on put to can used, how you tell how many red stamps certain is from it long how tell you can How L. 1:1 a the a certain 11110 in the forenoon to afternoon? time in books? the a number of containing package 127. a post and the the langth of its know hight of I cloth with 1 :1 ~. A flat-topped desk is covered except a shadow the how tree; a of can the of length also shadow, number the know you If width. unifol1n of of wood 1' ' 11'<1 tree? I find the hight of the in the finches of the table, also in the length and width horse 128. If I tell you how many bushels of oats my in inch es, how II' you find widt h of how the border can in February , how can you tell how many pecks he will ate with cloth? square covered are feet n ny eat in the first week of :March? :lG hor s es, c ow- s, and sheep, and some sold man A . 1 of tha Given 129. a board and its width at one length the Ilh money bought hogs. If you know the number it, number of square inches in and one side of the end, the horses, of one of price f alw sheep, of and cows, find other end? n you ca the width at the how I'nch of animals, how can you find how many r kind statement of il\: easy, process is The [NOTE: but a concise I he bought?

14 • \ WITHOUT FIGURES. PROBLEMS 24 • FIGIJRES. WITHOUT PROBLEMS you walk:;, how can which find and a walks a boy man make to necessary be ()uld II I amount the pay people the meet how ,soon they will the and if A one starts at other hs ? Ii· mont opposite in walk directions? at B and they liZ. I half between strike clock a do~ times many How of 154. amI feet in floor a the length the know you If nd past I I fi Vt3 a half twelve? From half past twelve width yards in inches, how can you find how many square way a such solving of huH past short a Find ? seven , contains? it the is one: this to What Apply m. ,hI the method tooth-picks enclose to a square 155.. If you have enough of in 11\ all the numbers printed tha calendar for certain a of to need you will more many how ~ize, enclose one, (Thirty '11 t? -one plus I divide by two, multiply by , square large? as times four III Why?) . II/),-one 156. United of coins of s kind different many How number 1/i3. How can you find rails required of the be would value total the States money have you seen? What railroad a mile of lay track? of one coin these of ach e of kinds? boy and paint some bought a brush, A painted I. IIi and wheat; man and corn oats, A farm his on grows 157. II squara the by him paid father His wood-shed. rother's how many farm, if you know tha number of acres in the what must What you know and I'd. will . you do to find are acres planted and the and wheat, in many how n cor in day a much I job? the on cleared boy the else per and know you must what yield of oats what acre, yards is stove-wood IIi:;. A of __ and pila long do will you to find the value of the oats? does cords many contain? How it h high. 158. If you are told the width of a barn, th 'a hight IliG. , a square straight line ii' a land of township In to eaves can how roof, the of hight slant the and the you corner 1\ from the southwest 11 of section seven to the the to ground if the from hight the find ridge the ridge, many co u(h rner of

15 • • • WITHOU'r PROBLEMS FIGURES. PROBLEMS WITHOUT FIGURE S. 26 27 to be a town, tha amount of certain money property in turns small than mile a in the one the more timas lIy !!llI taxation Dr. value assessment of the and by raised Irge one? Brovm's tha amount of ta.'( property, how can you find O. 1 and earn~, man a a week much how know you If pay? must he which can month ow much a he spends, how you find how much wholesale at avoir- "old by and bought are Drugs 171. ar htl .y , saves? weight, dupois If weight. apothacaries' retailed but a by and pile in logs of number the If 1. I a length the druggist which at ounca per price same the at sell should can If length total the be how known, are log found profit would ha buys, have? he what per cent. of How, they if length? equal artl all are they -se ea 11 load certain a in bushelo many how know you If 172. langths? rent dilIe ,I' can the of find bushd, how weight you and potatoes of a of 1 2. A basket of apples was given to a number and known equally; sharing - all . , Ito what what be must the of weight the load? 173. boy had some money, -tlarned some more, and · A IUllc recaived? each apples many how find to spent have? then then he did much How some. how If . 183 will a cer- day" many it know you take dividtld girl A 174. among equally nuts of quart a number a fin you can how fitlld, plow to men of d ,in you must What herself. and sisters and brothers her men number larger a take will of days ny ma 11\\ to it each many one find to do you will what and how know the low same fitlld? rectlived? em, paid is Type-setting 184. for that a hori- is, the by the If I tell you the thickness of a brick and of 175. the width the to 'aqual measure l unla of II m. letter the hight seam, also the of mortar wall, how can you find to many how know ems 1111 the line, and lines to the thtl number of courses of brick in the wall? a co lumn and columns number 11('h, al;;o the of inche s in of 176. had you if have you would sum What one each what what you 10 It page, else must you know and will of different coins now issued the by the Unittld States cost page? a setting of the find 10 It) government? know 1 5. block If yo u , the distance around a city bronztl eagle on should top of a clock the If 177. al street, tbe of enter c line a the in the so '1I('asured on hears strike, clock the time it wings its every spread measured at the curbstone, bow around lance can you II it it sp pa~t half from them many timas woul!1 read how . street? width of the the I lid eight? twelve to half pa,st several differen 186. How do you find the average of t a distance square field you If 178. around the know bers III II II ? how in rods, of can you find the numbar it acres bought it ld so and a A 187. farm certain a at man co ntains? invasted I . of profit; in rcnt the proceeds of the sale he and the lar ge circumference the If of 17 you know 9. farm loss. of t. cen per ;;ame the at it ld so lilt hcr Did and how find you wagon, a of wheel small the how can of i' 01' lose as the \\lake of the two transactionf; result

16 PROBLEMS wrrHOUT FIGURE S. FIGURES. WITHOUT PROBLE1IS 29 28 you e with IJ'Illcd can gum, tell how how far th such length end weight of a know steel you 188. the If shoot? can 'Iliad required how can you find how many tons are rail, to as how peail many times as large is a of peck . A 99 1 of mile track? lay a cider? of rt 'I" u a of capacity the Given 189. in and the car pound;;, 0: you find how much a pan of dough loses can 20 H~w in find yield acre of wheat per bushels, how can you how baking? III of we III process the Ight many crop cars will hold the from a section of land? • The freezing the above was day one temperature :>0 1. know ditch, width and depth the of you If 190. a are was you If zero. told I'OIDt; the next day it below a the workman can and number dig of cubic feet which t find you how day, many each how lip temperature on can of ditch he how many rods in find can how day, a you dl'grces the mercury fell? in dig can a week? • are what . Two town;; ~02 in the northern hemisphere; you and the dimen- a walk of width the know If 191. you and t you know what will IIllt do to differ- the find it how ;;urrounds, flower-bed which rectangular a of sions them? What, if has one t in 1I('e latitude between north c you find area of the an walk? the latitude? other the .IlIel south of cubical box, outside a hight the know you If 192. 203. were pigs and an geese equal of number Some the how the of ckness thi can and find you walls, measure, were so half out II a barnyard; enough pigs that taken how it will hold? many gallon;; ileveral It· removed. were feet of number total Find eren ce of two 193. If you know th e s um and diff the II IT re nt groups of which thi s could be true. numbers, how can you fin d the s ? number length the know you 'Wi If .. and bridge a of width and bushel can how , wheat of a ce of pri the Knowing 194. you hI' kness of the planks th Ic used in flooring it, how can you the price of a pound? nnd lid t he nnmber of board floor? the in feet depth know If 195. the you of a cellar, the total number know you If value of . '!05 the the grain destroyed by the walls, of s cknes and the thi of , feet excavated cubic mouse each and average ileason--the a in cc I i for the al;;o how find you an c sions, how many side in dimen till' number of mice an owl eats each day during the e so s ? wall nry ar the in feet ma of cubic n, ·.IBo the also the by killed chickens the of value total the 196. you know all If inside dim ensions of a cellar II the same time, how can you compute the commercial in I how t thi ckne ss total the find you an c of wall;;, he the d an owl? tiuc an of amo of unt on? ati excav "06 of the Given . hight IUSO a round the chimney, Given st eps in the y, and a stairwa of mber nlol the 197. how you can how wall, the of lC'kneilS , find cubic many step c t and wid th of each gh in inc find you an he how s, hi know onry ~ diameter imide its of mas you if contains it t'l arpet c of ny . yardil w ho it ? er ov c will ma if ow II diameter? outside the know you a a t w oo sh n ca man ith far h ow w kno If 198. you tax of amount the ven Gi . "07 an.il pays t~e man a and ad a s in are n me y man how qu rifle er ~t he c n \ Yi •

17 PROBLEMS FIGURES. WITHOUT F 1G Ut ES . 31 PROBLEUS lJT WITHO 30 ars \lI in an office at How certain price per thousand. a ' find the his of value assessed property, can how you rate you find how long it took him to earn the money for l'un district? of taxation in that cent. per he t bought? he goods beef, the price per pound of eggs 208. If you are told 215. you If in walks far how team an a plowing know represent numbers three given are and oheese, and which of the furrow? how ground, of re Ilc can you find the width comparative nutrition of the three foods, what the value is 216. Wheat bushel oats. than alwaYd per more worth elae you will know you must and do to find which what of mixture a, is box one n, r equal an oats, and wheat Remember the three is the most economical to buy? of an w )ght of ~ each; III another box a similar mixture , that each. ' ~ Iual bulk of Which mixture is worth more per land who He buys many stones, buys und? po buys beef buys also He bones, who , He shells, buy must eggs buys who Augus- ,2 17. ~hich would be a longer journey, from St. who else. nothing buys cheese good buys he But l lll FlOrIda, boundary to Hudilon the around of or Bay e, lifornia? 'n ( behind a 209, If you know how many rods a dog is 218. Knowing price the a of ton of coal and the number and how minute, a in runs each rods many how rabbit month a for furnace a fire keep to required of pounds up to dog the take will overtake it long can you find how cost day? per average find you can how ' the the rabbit? 219. from many how know is mile A to B you If it s 210 , If you lmow the age of a boy and of father, his hour and walk-s, man a that al~ per miles of number he I find their combined ages a certain number of how can you you how bicycle, a on goes boy a which at rate lhe can hence? years nd starts how far from fi they will meet if the man B of number the can man a which in days 211. Given at I L A and the boy directiond B and they go in oppo s ite in days of number the and work of piece a a which do meet? II ntil they how it you can how it, do will take find long boy can deep hole post a square in inches cubic many How 0. 22 do to them both the same piece of work? .. water? of a barrel hold to nough 212, Given of the temperature each day in January A has vari- the book bank hid of stubs the on man 221. will average February of this year, how and you find the ous amounts which bank. from the had He drawn he has two months? the temperature for at htl deposited 0 different of record a the amounts ill you saw How a board would ao as to make 213. the find can How imed. l in he now he much how has at nailed and overlapped are they if box a square of sides ho bank? th~ are the if How way? usual the corners in Corner., If earn- man a wtlek a much how you 2 22. tell I was larger r Which would be box? the mitered out was he weeks many how on Il g, employment of bought some 2M. A boy and a sled, a book paper, gamblers' stock the of his ount 'c I much how panic, to cir- by for pay folding money the earlled atiU them

19 FIGURES. PROBLEMS WITHOUT 34 FIGURES. PROBLEMS WITHOUT 35 each multiply his weekly you week, number what by should If 250. water, the sand, the of weight the wow you savings? his find to wages yearly the making in used lime the ond a pla~ter to mortar cup 240. from filled be a pail a can times many How can months , plaster the of wtlight the find you room how six water? of put is r afle it on? find at- How do you 241. the average number of pupils 25 y 1. If each pupil receives a new pen tlvery Monda a month? for tending school and will and know you must else what Thursday, what also marks in the usual way and clock . A strikes 242 find you do pens of gross great a wtlek5 many how to the hours half times How it one by many does stroke. last? \I'ill and the of strike between noon anniversary sumet on the can How 2. 25 from seconds of nmuber the find you Hill? of Bunker battle 1 he end of President Roosevtllt's administration until miles many If you know how 243. it is from A to B to-day? on r:o and how distance, the in how many minutes a train runs . What between difference thtl to give we do name 253 train you find hour? the speed of the can in miles per llie cost price and the thoughtfully, se lling price? Amwer 244. you wheel hind the of diamtlter the know If of if you can answer right the first see time. linu the wagon how wheel, front can of circumference the and It water of depth the and width the know you If . 254 in the find shortest distance you which they will both make feet speed in the and ute ch irrigation cornered a square ill a whole number of rotations? which at r minute can how pe , it through flows water the that the largest l5quare find you can How 245. can be . ground of acre an :;upply to must it long how find u ·o run inscribed in a circle? an of equivalent the th wi inch rainfall? of adding after gallon; the by 246. A vinegar bought man . can know how brick a of dimensions thtl you If 255 a quart to of each water same the at it retailed he gallon surface? its of area yo u find the price per What gallon. per paid he quart per which cent. and . a of 256 brick If you know the thickness of a profit make? he did 1lI0rta r seam, also how many cour:;es of brick in a wall, how bought sold farmer potatoes to a merchant and A 247. of the hight the find you ('an wall? sug ar you calico; one of them paid some cash. If and the Given . 257 the and a window in panes of number pound know price,; per bushel, the and yard and the amount of each pane, dimensions how can you find the total area commodity, of each one which find you can how paid money of glass, the s if ize, uniform of are (b) the if (a) panes how much? and are :;izes? different they of the 248. a given of cost number find you can How of 258 ,,'orkinz . A boy earned a certain sum of money of a certain price bushels per ton? wheat at nol by the day during the month of February, 1900, How find number of Thanks- days from the you do 249. he earn ing on any work How much more could holidays. Washington's birthday? to giving Oil the same terms during tllis month?

20 .,~ vi PROBLEMS Wl'.rHOUT FIGURE S. WITHOUT PROBLEMS FIGURES. 36 price per pound, what must you know and what will else 259. blue, painted is pole flag a of part upper The you ham? the of cost the find to do in portion the If part red and a middle white. the lower sheep field. are boys some and in Some . 266 The a of the white the and blue the of sum the you tell I also ers fing of number le who number the equals thumbs and the can pole, the of length how and white, the and you red heads. and many sheep and how many boys? feet 01 How much is painted white? how find answer. correct smallest the Give a land, B owm three of 260. A owns half section width the know you If 267. inches in mower a lawn of three section of a tracts quarters all section; a 0 and cuts how it lawn of yards square many find you can how form, square quarter the section compact usual, the in are feet? of number certain a running in build to How much fence must each one unit. being the 268. pipes two If of you know how long it takes each enclose land? his to fill a tank, how both? can will it long how find you take enclose 261. How much to fence must man the build box, a from cherries of number a eating After 269. the his southeast the of half west is which farm quarter the divided remainder equally among girl her brothers a the section, if there is a a road on of section line public as then had as share many left for her she herself; and and neighbors? hid with fences joins he the number had .,he her already eaten. If you know of 262. liquid of displaces an object floating A amount the in cherries of find can and how box, you thers, bro full equal to its own weight. of cubic foot wood is A how many one received? each in water; if know the weight of a cubic you floating If . 270 the know the clothes, of suit a of price you wood the of part fractional what and water of foot used amount tbe material in making them, and of t the cos find above the surface of is water, how can you the can to the journeyman tailor for making the suit, how paid the of the wood? weight tailor's u merchant the yo find profit? 263. price the know you If number the and cigars of man A the 1. sheep some with and 27 proceeds .;old adding week, conSllmt'lS man per the to nothing of them a I tell the land. ght bou If you how many sheep he sold and injury incurred subtracting nothing and account for any land he bought, also price per head, the number of acres of the pleasure enjoyed, how can you compute much how for per price how you find can acre? the annually? him costs habit the . many dollars a thousand feet 272 If I tell you how 264. of If you know the width a barn, also the hight and how many on tax a lumber, as pay we imported peak the and eaves the to to of the gable, can you how timber land, how can you an leet of lumber on acre of cord that length ' of a the will reach from ground find • acres the ('o mpute mJmber of of trees a "lumber king" must grOllDd the roof, crossing the eaves and ridge at over to uestr tbe to make through oy a operation him millionaire right angles? • forests? of this premium on the destruction of our is bone, per Ten 265. cent. of the weight of a ham five . measured 273 llar ce a of dimensions the know you If and know rind. cent. per one If fat, cent. per the you

21 PROBLEMS WITHOUT FIGURES. 38 WITHOUT FIGURES. PROllLE.l>fS 39 to so as enclose the in them re-arrange now square; a on wall, outilide the the on of also the inside, how can you of form the a diamond. larger, the square or the Which is compute the of masonry in the feet number cubic of walls, diamond? making and no deduction for doors windows? how can you If you know the weight of a brick 282. 274. A spends per \$ and day per \$ earns man find ? brick of foot cubic a weight the of much he saveil per year? month. How how find you can 283. A farmer sold by by potatoes dozen, the eggil of 275. is the diameter What passing auger an hole bought he pound; cloth the by and bushel, the butter remove half the cube? through a cube, that will straight yard. by If you know each of the four prices and the A stream 276. outlet; flows has no which lake a into dozen, bushels number and ponnds, of also how much the and a across iil the stream dam all the water runs built cas the find you can how cloth, the buying after left was h a chute. through are If you a told the area of cross- number ? bought yards of of ion sect hour chute and the per inflow thl3 of the speed right string at brick a around tied angles is 284. A evaporation in feet, how can you find the daily from • string? corners it crosses; how long is the which the to lake? the three correct anilwers. Give several thtl add you If the for paid amonnts 277. man 285. in small packages of a bushel up A put wheat Leacher's janitor fuel, for wages, and repairs, ~ervice, size. equal of how can know thtl number of packages, you If supplies of s the divide and kinds, all the by um number of of the ? weight each you find pupils enrolled, what will the quotient be? how many steps boy a iLl. If you know takes 286. 278. A some fruit bought gave the ~tore­ girl and a walking length average how the mile, find you can he the change in four htlr gave bill; bank a keeper of step;;? the coins, each one silver the value. of a What was different row straight a uniform in 287. are Some trees dis- at the of fruit and bill? the denomination price the of row the of length and know you If the apart. tances and hat a for pencil, 279. boy bought a book , a A number the far how find you can how trees, of apart week's wages which he paid his le sil his expense for trees are? the bo ard . article each bought, price the know you If of of the cost and harveilting planting, of seed, Given 288. his wages, weekly and how can you find the price per week threshing straw, wheat, also the value of the of acre an board? for pays he which per rent you can how acre, per yield the and acre, find the on 280. A man measured the length of cast a ;;hadow cost of bushel a producing of the whMt? the ground by a factory chimney; then he sct a stake in gallons you the number of find in a. 289. How do the ground. What oth er measurements must en tak be tank whoi!e dimensions are known? cubical of the how will they be l;s ed to find the hight and rainy with 290. On a a can night a boy set out straight chimney? er the numb compute From the result he was able to sides. the on table or matches 281. Lay some toothpicks • •

22 40 FIGURES. WITHOUT PROBLEMS PROBLEMS WITHOUT FIGURES. 41 • tona of on farm during fallen had that water of his father's know many of plumes the hats how an you If 299. How? night. the starve to decorate, will egret how many young birds you 291. If know the elevation of a mountain peak an because of the egret, also of death how many killing line, find what fractional how timber you can and of the in the:;e wear plume church fashionable women certain a s, part of the hight is bald? mountain's lives many e e<; th adorn to costs it how you tell how can of depth the width 292. an irrigation Knowing and hats? men's wo per the can how hour, flumtl, current the of speed also t on another to station one from rides man A h~ 300. flow on an many hours' acre ground of will you how find walh back. and If I tell :rou the rate per hour of train equal a amount given of rainfall? the and of the man's gait, and the sp'eed total train's a 293. A mine is at the base of mountain; if you know trip, the find you the round can how taken make to time thtl depth of the mine, how and mountain the of hight the the between distance stations? of difference the them? altitude between find can you at Water much how costs gallon 301. price a certain per of subtracted! vest boy's a on buttons 294. number The gill ? Per ton? per shoea his on number the his on number the equals from send 302. How much a is required to number postage on and shoes the on buttons of number the told if coat; cards, weighing-- book a postal many as letters, of on vest, the how can you find the total number coat, package a and ounce:;, same the of merchandise of weight woes? and vest the book? as a water of bottom The 295. __ contains tank square older and Tom of age of know you If his 303. the many the water is feet deep; how and feet pounds' when how old his brother was brother, how can you find on pressure thtl bottom? born? was Tom flock A 296. sheep of sum before worth a was certain price the know 304. you and shoes, of pair If a of :;maller sheared; were they after sum they a and sheared, were how the price was added muoh account of the on of the if know these and you expense of shearing, how sums much you can how how cost would find they tariff, can you find the the of value wool? system free of a under trade? 297. A got drunk and man and had to pay disorderly, 305. heavier, a pound the or silver of a pound is IVhich how much liquor, for paid he the know you If fine. a of feather , How s? heavier? much and wasted, time the value the htl fine the of amount of some the on boys, 306. On one side of a fence are other which he incurred? the money loss compute can how you side some horses; ys is the smallest number of bo what length of an engine and tender 298. If you know the the es s, ey that will make finger sum of the of horses and of cll!ra of uniform length and of the caboo:;e, the number equal and s on the one side nose the sum of the feet and each, how can you find the in a train, and the length af the other? ears on length of the train? sand 307 Lay some grains of . as close as you can place

23 WITHOUT FIGURES. PROBLEUS FIGURES. Wl'fHOU'f PROBLE1>1S 42 43 of 'eighth an inch long and count them. a around extends width usual the of road them in a rowan 317. A section Tell does section the of acres many land; of how of how from tbis you can compute the number grains the occupy? road a of sand? pint in 318. of small the of tire the faster, out wears Which 308. length If you know the a cubical bin and the coal, number feet in a ton of <:ubic how can you find of wheel a wagon? of wheel large the Why? or of will bin the toni! hold? many how a of quantity paper 309. If you know the weight of of diameter 319. If you know the and the depth a before and weight the find you can how printing, after find how tank, it gallons many how can you cylindrical ink? of the hold? will times many hand How long the 310. does day per very like solving [For a problems short, practical rule for carefully befora clock? a of hand [Think pass the w.ort one, see Gillan's this Arithmetic School, Common the in 96.] page one.] you answer this hogs, coal a of of base If drove a of one each of weight the Given 320. triangle. right a is bin The 311. find how may you aggrega the average te The weight? and the you know the length of each side of the base, weight? of a in feet cubic of ton the also bin, the hight number Three 321. men of the number the compute you can how coal, of tons bin for them office; same the one ran of received more votes other two. What majority than the will hold? have? did he the 312. If you know average per capittli of wealth are days many How 322. in many paupers the a country, how between can you find how and Ohristmas Washington'iS birthday? produce? will millionaire one of making as Henry. How will their 323. John is twice as old If you know how pupils were at school many 313. iii now? old as John is Henry when compare ages as each day a month, how for you find the average can 3240. George bought a dog; then he bought some lumber attendance? daily furrow a wide inches many how know you If 314. is, for nails he Later dog. the paid house a built and and team will walk compute number you can how of the milas a a tax him, and then took a prize at on dog show. the If an plowing in acre? a fair pleasure to the expenee of having the dog was set-off 315. To find the average population per square mile dog the sell he should price what at him, feeding of make to know must what state, a in and do? you the tax? much profit as the amount of as If 316. combined weight of the a man and a know you Given how find you may bushel, per price the 325. and neither when weight combined their dressed, both hog, per the Of oats? Of corn? price shelled of pound wheat? his and was dre8Sed, also of weight of the man the bushel per Given the price per ton, how find the price how clothes, the hog weighed can you find how much of coal? 326. "on the hoof?" Given d diameter of a the how can you fin log,

24 44 WITHOUT FIGURES. PROBLEMS • WITHOUT FIGURES. PROBLEMS 45 to be removed in order to make thickness the ·of slabs the and length a of width the city the know you If 333. ber tim ? the largest stick of square 8treet, the how can you tind the block, also the of width 327. area the finding of method shortest the is What around the of middle the in street? measured it distance [Answer: known? of a square field whose diagonal i;; same boy 334. A had ;;ome dimes and the number of by Square by Show two.] a divide and diagonal the the he quarters; spent quarters the and sled a for dimes is that this square paper a folding by or diagram of price book with the of compare the doe,; How a book. for correct. sled? the that of by ship to more costs It from freight Chi- gooda 328. 335. A per much for lot city a square sold man as could you compute How cago to Spokane than to Seattle. per as he had paid per square rod; what cent. yard total the de- are Spokane of people the which of amount profit did he make? railroads? the by frauded each 336. A boy earned a certain wage working day 329. uniform of logs of or pencils, round of number A from His father then Christma,; until July 4, 1908. sloping way, the pile both on the in usual size are piled made present of a certain sum, and him he a deposited many how know you if houae; the sides like roof of a in a amount the wa,; I .. mey savings bank. What all his the total you bottom how find layer, are in the can deposit? his of Multiply the number in the pile? [Answer: in number If an you know the width of the blue field on 337. bottom the number the half by one plus layer bottom the in can of the find you width how flag, American stripe? a correct. is this that layer.] by a diagram Show ~nator States United a of salary the know you If 338. book, many 330. If I tell you how pages in a what how for amount that times many it and tenn full his by the part of book i;; taken up pictures and fractional to how tell you can much elected, get costs him how • print on a full page, how can you find of many how lines to even crooked by make must method;; out come he in the book? nllm total the lines of ber financially? 331. number equals in a pile The number of bricks the would of pOllnds How 339. of number the compute you brick; edges number the is what of a on edges of total you if hold of will jug thickness the knew water a gallon in of Total pile? number bricks the corners? the on all jug? of the the walls faces? Of water find III the of weight the in 340. How can you bought girl A 332. each pencil some cost pencils; as a;; of you if peck sand, are a moist given a pint of it whole bought. which pencil;; number she the as cents many of sample? the change in She gave coin dealer a bill and received one a have quart a and water pure of of quart 341. If you tes g Sta United overn- the by made denomination each of you can weight of the find ways in what two brine, pencils she received that no gold. How many ment, except the the heavier cargo salt in a brine? Will a ship carry what at price? aud did she buy, in the ocean or in a river?

25 46 WITHOUT FIGURES. PROBLEMS FIGURES. WITHOUT PROBLEMS 47 dis- standing row a uniform a in 342. Some boys are length average the know you If 348. .;tep, man's a of to required be apart; how many more boy.:; will tance you find how walking in takes he steps many how can mile? a row, the distances apart re- uouble the length of the This used be may problem as [Note: same? the ning mai number and 349. Knowing the of miles traveled the and a test to di;;cover which pupil s speak think first number from going in of wheel a buggy by made revolutions after ward.] how the diameter the you can of B to wheel? find A lumber are needed of to feet inch 3403 . How many 350. a board If I tell you the width of in inches at the box foot? cubic a contain will that lid) (with each end, length in feet, al.;o the thickness in inches make a one-eighteenth.] sw er, seven and [A n it how you tell can the llllmber of board feet which contains? thimble g A 3-14. and some a pencil, a bought irl is circle the area the largest that can of 351. What the each of Ii you know the price and olates. choc is of land? area VVhat section quarter a in drawn be the the find you can how back, received value change of amount the of pieces corner the of each circle? of outside the merchant? of the bill or coin which she gave cow. She died next day· he bought 352. A man a flower square I wish a around border a make to 345. the you tallow. and hide What sO.ld know and ~hat must shall border the of equal area the that bed such width of his do to you WIll loss? compute of that border? the of width the be must VVhat bed. the 353. a skates; of bought pair he and sled a old John ~ to It must be equal the differen ce between [Ans wer: marbles. the know Ii a you If book, ",orne and kmfe . the square.] Prove that diagonal of the side and the find pnce how of each of the fiVe articles, how can you is correct. this much more, or less, had he transactions the after money . A 346 sold sheep farmer at a certain price per head before? than How at find a different price. hogs the total can you and you can How 354. of between minutes number the find both? amount received for two dates are more apart? that a year than a 347. bought a pup, boy A chain and collar, and some of pole 355. Equal parts a flag are painted blue and he the for nai18 with which house built a lumber and yellow. the of rest The painted is green, pole white and pup. How can he compute the month per much how you If color. each whole of part equal an the know keeping of the dog cost him pleasure and satisfaction can portio length sum the find you the how ns pole the of of the year dog tax) not the counting first (including for are green? and yellow painted that anything the for dog's food? ~56. a s dimension given of paper of sheet From So there [In making your computation did you remember that sides both .of off ". end and cut is width uniform st np are to account? into taken Pre- some "inventory" item s be (possibly) and chain, size and collar the dog, the sumably paper the of house the Knowmg the width of the strip and value. have some items, again.] consider these you try If did not how can you find the dimensions of the resulting sheet?

26 48 PROBLEMS WITHOUT FIGURES. have same "hape (proportion of dimensions) as it Will the sheet? the original the a of the base and side slant hight of 357. Given square pyramid, how can you find the total area of all a s faces, it base? including the cherries you the If of know per bushel, how 358. price you find the price per quart? can John has a certain number of cents, Henry 359. the same number of dimes, Peter the same number of quarter~; lunch if their money for a all and share it spend they among them, how much will each of the other equally • Peter? boys owe The number of yards in the length of a floor equals 360. you number in its width; if feet know the area in of the feet, how can yOU find the length and the width? square • • • • • •