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I 
 
PART II. 
 
 FOURTH AND FIFTH CLASSES. 
 
 f!i 
 
 EXERCISES IN ARITHMETIC. 
 
 , i. 
 
 • i 
 
 '•n 
 
CUTH BERT'S 
 
 C97 
 
 Exercises in ArithiMetk 
 
 FOR USK IN TUB 
 
 SENIOR CLASSES OF F^UIJLIC SCHOOLS. 
 
 PART //. 
 
 il 
 
 A COLLECTION OF PROBLRMS 
 
 SriTABLE FOR 
 
 caxndidatris for thi<: entrance and puelic 
 School Leaving Examinations 
 
 WITH ANSWLSRB. 
 
 SECOND EDITION. 
 
 BY 
 
 W. N. CUTHBERT, 
 
 'I oronto. 
 
 'J'ORONTO : 
 THE COPP, CLARK COMPANY, LIMITED. 
 
 1896. 
 
 
 .1,1 
 
 '■\ i 
 

 I.ntcred accordiriir to Act of the Parliament of CannHa, in the year one thousand 
 eiifht hundred and ninety-four, by Thk Ccpp, (Jlaiik 'Jompant, Limitkd, Toronto, 
 Onti'.rio, in the Office of tiie Miiiisi.r of A^ri'tulture. 
 

 PIIEFACK TO FIRST EDITION. 
 
 Tdr iSec«»inl I'urtof my Kx<ici»t» in Aritlunotic c()ii«ihtH of a co11eo< 
 tion of I'rohlciiiE whii'h urn orvjithi/ ni rmisfnirtion, ninl which were 
 mu(lt) for iiMe in the (lil.rront oIuhhi-h of tli»' I'uliHc SchooU in M'hicl. I 
 have tiiiight. 
 
 Ah alrendy HtiitiMl, the ProlileniH will lie foinnl Hnitahle for vondidaUn 
 preparing fur the Kiitiance Mxaniination to High Schools and < 'ollcgiatt* 
 Institutt'8, and for candidateN pieiiarin^' for the Puhlic School Leaving 
 Examination. 
 
 W. NELSON CUTIIHKRI. 
 
 Vbrschovle, May lut, IS94- 
 
 PREFACE TO SECOND EDITION. 
 
 The anther has much iilcasure in thanking those who have called his 
 attention to the errors which had cropt into the First Edition. These 
 have been corrected ; and in prsscuting the Second Edition he does so, 
 hoping that it will meet with the same marked favor from the profession 
 as did the First. 
 
 At the suggestion of many P. S. Inspectors and leaohers, the Answers 
 have been incorporated, and fourteen new Exorcises (182 Problems) have 
 been added in Fifth Class work, covering the P. S. L. Examination 
 Papers up to date. 
 
 W. NELSON CUTHBERT. 
 
 Toronto, May Ut, 1896. 
 
 -^x5l^ I k 
 
 I 
 
EXERCISES IN ARITIIMEriC. 
 
 PART II. 
 
 FOTJllTII CLASS. 
 
 On the Circls. 
 
 A circle is cnmposod of an indefmito ntnnbor of sectors, the 
 sum of wliicii is Ci[uii\ to tho urea of tliu circle. 
 
 By dividing and sub-dividinj^ tlicso soctora (ho radii como very 
 close t();.^i!tliur, and tlie aru.i of a .small sector ditlbrs very little from 
 the area of a triangle forni'd liy the radii and feho line joining tlieao 
 at the hvso ; and when the radii are indelinitely close together tho 
 haso of tho sector is an inddinitely small arc(\vir:ch niay piactically 
 b.- regarded as a straignt line), and tho uum of uU theso urcu in ut^uul 
 to tho circumference of the circle. 
 
 For the sake of illustration, then, we may regard tho circumfiMence 
 of a circle t > bo composed of an indelinito numlter of straight lines ; 
 and by drawing an indeli!iito luimijer of straight ines (radii) from 
 tho center of tlio circle to its circumference, wo can get an indefinite 
 number ot triangles (sectors). 
 
 Now the area of each of those triangles is equal to half the base 
 multiplied by tho altitude (the radius, or half the diameter, of 
 tho circle) ; therefore, luilf the circnmfcroice of tJie circle (half tho 
 bases of these triangles) mnllipl'u'd by lidlf Uie diameter of the circle 
 (the altitude of these triangles) iseqn d to the nrea of the circle. 
 
 [7J 
 
 r. 
 
 \ 
 
 m 
 
 
■XKKCIMK8 IN AKITII M KTIO. 
 
 Tkll may >>o buttor «xpUinoil hy lofiMoncu to tha following 
 
 Tigs. 
 
 Circlu dividid into u Number of 
 Suutorn. 
 
 ( 'il'.'lt' I i';ili>l()llll<'<l so OS 
 
 tu iiHMiiiiti the Form 
 of a Koctan^'lo. 
 
 Figaro 1 ii.'|trt!.st'iit.s u circle Jividcd into a drfinito mnnl)or of 
 Bt'ctors hy linos dniwn iicr ss tin; circlo tlmtnjih its centro and 
 tonninatin;^' iioar tho cirt'ninfortiu'O, ono lino howovor going the 
 wholo way aomss tho cirolo and dividing it into two semi-circloa. 
 An indctiiiito nunilior of sootors isinipossiMo ; l)nt tho nioro soctors, 
 tho more nonrhj pn-fccl thcf donion-^tration and the better the shape 
 of tho roctangular figuro reprosontod in Fig. 2. 
 
 Figaro 2 ro})resents tho cirolo transforniod into a rectangle wii h 
 tho snrratod odges l»rouL,dit into closo oontaor. so as to form a figure 
 of rectan<j; lar sh.ipo, each half oF tho cirouniforence of the circle 
 having assumed a practically straight line, thas forming the aides 
 of the rectangular ngnro. and oMch half of the diameter of the cirolo 
 
 
 
FOtnTII (LAM. 
 
 fornilnpf tho oiidn of fijo rcctiuiuuliir fi^^uns whirh for tho niirpoKOof 
 illuMti'Htiuii ami ux|iliiiiutioii iiiu)' bu lugiu'tU'il im ii rirctiiii|jlo. 
 
 Now, till) uct'ik of u ri't'ttui^lc is o<|iih1 to tli«> iikiihiiiu of tlio Utnuth 
 niiiUipluil \>y tilt* iiiniMiiK! I f lliii \Mili|i ; itml tla; iiicuHiii'ti of tliO 
 1«iij,mI» .)! iloH ri'rtnii'^U' is Imlt' tln< riii'iiiut'<rri t! of tin- I'iu'li ; nUo 
 the iiiruHiirii of uitiili JM luilr ilii! diuinrti r(iniliiiH)of thu i'lrdo ; 
 tlliirrfofi! liiilf II. c rimimft ifnrt' tij' o ciirlt Viulfijtllnl Inj itih' lh« 
 diiiinrtt-r in t''/u«i^ ^i tht: areti of llu: cii'iU, 
 
 INipilH must iwlmit tlwit tlm cireimiforomo of n cinln In npiil to 
 3| timi-s tlti> iliiiiiuttcr. This, howoviT, may ho )h'ini>iislrii(i'i|, ni u 
 way, hy iihIii'^ u (Miciilar ink Itottlu aii«l \\ piuci) of cord. Tho 
 cirt'iimt'rriiiiLU miy ho .shmvii /<> »mi's •(/•»• thu lUain t^r inme Unn^ 
 ilu*'v Hinci. It iiiuuNiiroH it ^| times, ii.'iuly, whuh in |)nicliiully 
 corri'ct. 
 
 Now, if nf timt'.H nny uivin immhor o<|imlH u ciTtain nmiihi r, 
 thou M) timuM tht> halt' of th/tt given nuutltur uciuuIh tht) halt' ot the 
 certain nuiulu'r, hm for I'xamplu : 
 
 :]}y\i Jh 
 
 Aiul 3) X (liatiiotor of a cirolo = circtimforonco. 
 /. 3| X J «liamut«r of a circle = A ciriumft'rinco. 
 
 Ititt ^ I'lrnnitt'i'i'i'iii'r x \ ilUtmclct' of a circle = itrai, therefore, hy 
 BUh»titiitim.% ui) hav«> : 
 
 (Ilj X h iliamotiM) x h <lianu!tor = area. 
 
 But lialf thu diamutur (^ diauiuLur; :-= the radius (r.). 
 
 Sulistitiitu a;{ain, and : 
 
 [i\ X r. X r. = arc'u. 
 That is 3}^ r.^ = urea. 
 
 Now, ropri'soiitin'4 '^] liy tt . we have, Trr.^ = nroa of i\ circle. 
 
 Sec Kx(irri;u? f^XIl'. for c'X;imiilfs on tin- ci'ch'. Other uxanipU'.H 
 are interspersed On. u,'h the I-'oiiith aiiil i'inh class wurk. 
 
 \Vi:i<;Mrs of VAiuofs AiiTici.iis K.staui.i.su' u uY Custom. 
 
 Aharrel of ll-iir - I'.Mi Ihs. (net). 
 
 " heef =--200 Ihs. (net). 
 
 ** I ork -^ 1:00 Ihs (net). 
 
 " white fsh — L'lMJ Ihs. (not). 
 
 " trout . L>00 Ihs. (net). 
 
 " salt = 280 Ihs. (net). 
 
 ♦' lime = 220 lbs. (net). 
 
 
 I k 
 
 
 . b 
 
 
 i( 
 
 
 «t 
 
 
 
 
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 • ) ., 
 
 1 
 
10 
 
 EXRKCISRS IN ARITHMETIC. 
 
 Hay well settled 4^ lbs. to the cubic foot. 
 Corn on cob, in bin 22 lbs. to tlio cubic foot. 
 Corn slielled 45 lbs. to the cubic foot. 
 Wiioat 48 lbs. to tho cubic foot. 
 Oats '2bl lbs. to tho cubic foot. 
 Potatoes ,')Sh lbs. to tlie cubic foot. 
 Sand (dry) 95 Dw. to the cubic foot. 
 Clay (coni{)actj lo5 lbs. to the cubic foot. 
 Marble 1G9 lbs. to the cubic foot. 
 
 Anthracite (stone or liard) coal = 33 cub. feet per ton. 
 Bituminous (lignite or soft) coal = 42 cub. feet ])cr ton. 
 
 A Surveyor's chain is 66 feet long. 
 
 22 yards long. 
 
 it 
 
 
 *' 4 rod.s long. 
 •♦ 100 links long. 
 
 \ 
 
 Exercise I. 
 
 1. Divide $990 among A Ji and C, giving B twice as much as C, 
 
 and A ^^0 mure than | of t!io remainder. 
 
 2. A can walk 4 miles, 80 rods, an hour, and B can walk 110 yds. 
 in a minute, liow long will it take A to oveitako B if the latter 
 has 2 minutes the start ? 
 
 3. A can do a piece of work in 6 days, B in 9 days and C in ten 
 days. A and B work together at it for "J days, then B and C work 
 together at it for k a day. How long will it take a boy, who does ^ 
 a« much in a day as C, to finish it? 
 
 ' A has half as nnich money as B, and B has one-fourth as 
 Ui\x,.'(>. /.gain as C. What per cent, of A's }iionoy is ^ of C's ? 
 
 6. Two men carry a weight of o cwt. 41 lbs. between them, and 
 ■Mi'ii iis-ads are to one another as 0:5. By how much does one 
 K dd exceed the other '{ 
 
 6. A man sold a horse which cost him $154, losing by the sale 
 10 per cent, of the proceeds. Find the price at which he sold the 
 horse. 
 
 7. Find the cost of paving a square court-yard 24 yds. to a side, at 
 3 cents a sq. foot. 
 
 
 > 
 
Fourth class. 
 
 11 
 
 • 
 
 
 8. The Province of Manitoba coiitiiiiis IIGOOO sq. miles. What 
 is tlie Province worth at $2.50 an acre ? 
 
 9. If 7 pears buy 5 peacliea, and 8 peaches buy 15 ai)ples, and 
 there are 90 api)le.s i i a peck, how many doz. pears will 100 
 quarts of apples buy ? 
 
 10. A man mixed 14 bualiels of clover seed with 20 bushels of 
 timothy scud, and sold 30 biisliels of the mixture. What was tlio 
 value of the chjver seed sold at $♦) a bus) i el i 
 
 11. A farmer sowed 21 bushels, 5.5J11)S. of wheat on 7 acres, 40 sq. 
 rods of land. How many ounces was that to the sq. fuoti 
 
 12. Simplify yf7 + rr^jj + ^. 
 
 13. The lari^or wheel of a bicycle is 4^ yds. in circuinfcrenoe, 
 and the smaller wheel is 24 feet in c rcumforence. IIdw often will 
 the same points in the wheels como in contact with the ground, 
 .simultanoou.sly, in going 5 miles, 950 yards ? 
 
 Exercise 11. 
 
 y 
 
 1. Find the cost of a tract of land 75 chains long by 15 chains 
 wide at $00 an acre. 
 
 2. Multiply 6 1 acres, 121 rods, 30 yds., 2 ft., 90 inches by 8 ; 
 divide the result by 9 ; and roduce the quotient, thus obtained, to 
 square inches. 
 
 3. A man walked 25 miles on Monrl.iy, IfiOO rods n Tuesday, 
 36900 ft. on We<lnesday 7010 yds. on Tliur.sday, 500 chains on 
 Friday, and G40 perches on Saturday. {<i) M w many miles did he 
 walk during the week ? (6) How many inclies ? 
 
 4. In 41080 inches of wire, how many rods, yards, feet and 
 inches are there ? 
 
 ^ 5. A and B owned a flock of G42 sheep. A's share of the flock 
 .was 5 times B's ; but when they divided the sheep, A gor 500 .sheep 
 and $210 in money for his share. At this rate wliat was the value 
 of the whole flock ? 
 
 6. A man owns a horse 16.V hands hii,di ; how much less in height 
 is he than his owner who is 5 ft. 8 hiclies high ? 
 
 7. Bought 84000 grains of tea. Paid 5 cents an ounce for J of 
 it, and 85 cents a lb. for the remainder. What did the tea cost mejJ 
 
 8. Show, by a diagram that 10 chains square is ten acres. 
 
 !'• 
 
 u 
 
 
 ■U! 
 
 )X 
 
u 
 
 RXEKCISES IN ARITHMETIO. 
 
 9. Bought 072000 grains of tea at 87^ cents a 11). and sold it for 
 $105; find my gain per cent. 
 
 10. What will 40 chains, 40 rods of fencing cost at 40 cents a rod ? 
 
 11. If a five-cent register stamp be 2^ inches lont,' and | of an 
 inch broad, what wonhl it cost to paper a wall 20 ft. long by 9 ft. 
 high with 5-cent rct^ister stamps? 
 
 12. A scud merchant mixes 15 Um. Htmt^arian seed worth •>_ HO 
 a bushel with 12 bushels of inillt't worth $3.20 a Imshel. Find the 
 value of 11 bu lels of the mixture. 
 
 13. (a) What i.s the value of 1 mile 18 » rods of rope at 5 cents for 
 10 yards 1 (b) How often is the G.C.M. of 155 and ISl^''^ contained 
 in their sum ? 
 
 Exercise III. 
 
 1. A railway train going 15 miles n hour takes 3 minutes to 
 cross a bridge OGO yds. long. Find the length of the train. 
 
 2. The simple interest on $800 for a certain time at 5^ per 
 cent, is $264. Kind the time. 
 
 3. A boy sold a coat which cost him $24 losing 20 per cent, of 
 the proceeds. Find the price at which he sold it. 
 
 4. The total cost of G6 lbs., 10? ozs. butter ;it 2}.\ cents an oz., 
 and a certain number of bushels of wheat at 87^ cents a bushel, 
 was $58.60. Find the number of bushels of wheat. 
 
 5. A manufacturer sold his goods ^o a wholesale merchant, 
 gaining 20 per cent. The wholesale merchant sold to the retailer 
 at an advance of 8J per cent. What would the manufacturer 
 have gained on the sale of 6G0O dollars' worth of goods, had he 
 sold direct to the retailer at wliolesale prices ? 
 
 6. Simplify (a) (3i + 2i)x3i-(l^-U) ; (6) (3^ 2^) x (3^ - H) 
 
 7 If f of a car-load of cheese cost $540, what would be the 
 value of ten such car-loads ? 
 
 8. If 9620 lbs. of wheat at 75 cents a bushel, 480 His. apples 
 (undried) at 90 cents a bag, and 4 tons of bran cost $183.85, what 
 was bran a cwt.? 
 
 9. If 9 oxen or 12 sheep can feed on a certain field for 6 days, 
 how many days could 20 slieep and as many oxen feed on a field 
 8^ times as large ? 
 
 ^ 
 
POUKTH CLASS. 
 
 1.". 
 
 
 < 
 
 X 
 
 10. By sellin!? an article for 4 shillings, Od., I lose 5 per cent. 
 At what price, in Canadian currency, must I sell it in order to gain 
 140 per cent. ? 
 
 11. From 45 miles, 80 rods, 4 yds., 2 ft., 6 inches subtract 13 
 miles ISO rods, 6 yds., 2 ft., 8 inches. 
 
 12. At what time are the hands of a watch equidistant from the 
 Hgure VI? 
 
 13. (a) A cheese-monger sold 2184 cheeses at $.'30 each. On one- 
 half of them ho gained 130 i)er cent., and on the other half he lost 
 .'{0 per cent. How nuich did lie \i!\'u\ or lose on tlitj whole lot? (6) 
 The difference in weight of two chests of tea is 12 lbs. 8 ozs., and 
 the value of both at 54 cents a lb. is .$47.25. How many lbs. are 
 there in each chest? (o) Find the value ot 4G bushels, 15 lbs., 17 
 bubhcls, IG lbs., 47 bushel, 20 lbs., 10 ozs., 75 bushels, 30 lbs., (i 
 ozs., 57 bushels, 18 lbs., 20 ozs., 1 > bushels, 10 lbs., 12 ozs., and 
 14 lbs. 8 ozs. of wh(!at at 72 cents a bushel. 
 
 Exercise IV. 
 
 1. If a man walk 41 miles. 725 yds. during a week as follows, — G 
 miles on M(mday, G50 rods on Tuesday, 18270 y Is. on Wednesday, 
 26400 feet on Thursday, 800 chains o"u Friday, 443520 imihes on 
 Saturday, and the remainder of the distance the next day, tind the 
 length of the Sabbath day's journey. 
 
 2. A rectangular farm cost $10980 at $45 an acre. It was 122 
 c lains long. How wide was it in rods ? 
 
 3. If 5 doz. bananas or 3 doz. pine-apples are worth $1.20, what 
 would 15 doz. of each kind cost ? 
 
 4. A bought 6 stacks of hay of 16400 lbs. each at $15 a ton. He 
 sold § of it at $17 a ton, and the rest at $16 a ton. How much 
 did he gain or lose ? 
 
 5. Seven men engage to dig a ditch in 42 days, but owing to 
 sickness one man is unable to work. II -^^ long will it take the 
 rest of the men to dig the ditch ? 
 
 6. A mixture of 50 gallo is of liquid is 70 per cent, alcohol. 
 How much alcoiiol must ))e added to make it 80 per cent, alcohol 1 
 
 7. If l'^ of a lottery ticket is worth 13 florins, and a florin is 
 worth 2 sh. Sterling, what is the value, in Canadian money, of g of 
 a lottery ticket ? 
 
 8. Find the H.C.F. of 1 rod, | of a yard, and 2 feet ; and the 
 L.C.M. of 4716, 3930, and 9170. 
 
 \in 
 
 I 
 
 fi 
 
 t 1 
 
 '' i 
 
 i ii 
 
 i ■ ' 
 
 ll J 
 
u 
 
 EXRRCISB9 IN AIUTIIMBTIC. 
 
 9. If, by soiling an articlo for $7)1 a mercliauL lose 15 [)er cent., 
 what per cent, would hu gain, should he reccivo $,b for the article? 
 
 10. A miner after losing J of \'^\ par cent, of his money has } of 
 90 per cent, of it k-ft, and the <lill'L'ronco heLwecn the amount lost 
 and the amount left is $81.00. What was he worth at tirst V 
 
 11. A, B and C, have together $700. A has 3 timca as much as 
 B, and C has $20 m(j:e tiian 7^ times as much as A and B together. 
 How much money has ? 
 
 12. A glazier cuts 48 panes of glass, each 12 inches long, out of a 
 plate of glass 12' 0" x{V4". Row many feet in length will thtt 
 edges of all these panes of glass measure ? 
 
 13. A fruiter divided a basket of 40 doz. and 8 peaches, equally, 
 among 8 of his customers. One of thest^ customers then divided 
 his share among his three boys in the following manner: To Tom ho 
 gave 2 for Will's 3, and to Will 4 for Sam's 6 What per cent, of 
 the original basket of peaches have Tom and Will, together, then ? 
 
 Exercise V. 
 
 ■^ 1. How many lbs. of cofTee worth 35 cents a lb. must a grocer 
 mix with 6 lbs. of chicory at 40 cents a lb. to make a mixture 
 worth 38 cents alb.? 
 
 ^ 2. How many yds. of paper 2 feet wide will be required for a 
 hall-way 72 feet long and 14 feet high ? 
 
 ^ 3. A man earning .^1.80 a day works from 1 o'clock p.m. till 4.30 
 o'clock p.m. What does he earn, 8 hours being a day's work ? 
 
 4. After taking 10 gallons from a barrel of vinegar, and then ^ 
 of the remainder, it was found to still contain 25 gallons. How 
 many gallons were there in the cask at first ? 
 
 5. A man buys a farm for $0250, pays taxes $32, insurance o i 
 building $30.75. What does he make per cent, on his investment, 
 if he rent the farm for .$350 per annum ? 
 
 6. What is the duty, at 15 per cent., on 320 boxes raisina, 
 each containing 50 lbs. at 8 cents a lb. ? 
 
 7. Find (a) the volume of a cube whose edge is 13 feet, 8 inches, 
 (6) the surface of the cube. 
 
 8. A wholesale and retail man deducts 33,^ per cent, from his 
 retail price in serving a wholesale customer. Wh'it per cent, will 
 the retailer now make by selling to compete with the whol sala 
 man at retail prices ? 
 
FOURTH CLASS. 
 
 10 
 
 0. Divide 91460 among A, B and C, bo that 3J times A's, 
 twice B'b, or 4 times C's simll uU bo e'lual. 
 
 10. If the carriage of IG tons, 200 lbs. o? ^oods for 70 niilos cost 
 $13, what weight, ut the hhiuo rate, should be carried 210 miles for 
 $135? 
 
 11. If 9 horses require as many oats as 15 ponies, and 20 ponies 
 are fed 3U days on 240 bushels of oats, how li>ng woald 0:10 dollars* 
 worth of oats feed 27 horst-s, when oats are 37^ cents a bushel ? 
 
 12. A pile of wood is 60 feet long, 25 feot wide, and G feet high. 
 How many cords of fifteen-inch wood are there in the pile? 
 
 13. (a) A sold ahorse toB, losing 8J per cent. ; B sold it to C for 
 $240, gaining thorel)y 9j^^ per cent. What did the horse cost A ? 
 (6) Find the auioinit of ib720 for 3 years, 2 niontlis at 8% per 
 annum, (c) Had 5 times 70 bushels, 1 ])eck, 1 gallon, 3 quarts, 1 
 pint cf wheat; S(»ld 303 bushels, 10 ll)s., 5 oz.s. of it; find thd 
 valuo of the remainder of my wheat at $1.20 a bushel. 
 
 n 
 
 Exercise VI. 
 
 1. Afc what time after 5 o'clock are the hands of a clock 
 eciuidistant from the tigui e V ? 
 
 2. At what time after 11 o'clock are the hands 3 min. more 
 than half an hour apart ? 
 
 3. At what time after 9 o'clock are the hands of a watch opposite 
 to each other ? 
 
 4. At what times after 7 o'clock are thj hands of a watch (o) 
 first at right angles? {b) coincident? (c) at right angles the 
 second time ? 
 
 5. What time after 11 o'clock are the hands of a watch equidis- 
 tant from the figure XL2 
 
 6. At what time past 11 o'clock are the hands of a watch 11 min. 
 apart the second time ? 
 
 7. A watch which loses 5 seconds in every 2 minutes is set 
 right at 8 o'clock a.m. What will be the true time when its hands 
 are together between 4 and 5 p.m.? 
 
 8. At what time after 10 o'clock will the hands of a watch be 
 together ? 
 
 9. By the clock it is VII. How far will the hands be apart 
 when the minute hand has gained 11 minutes on the hour liand ? 
 
 
16 
 
 EXUltCISKS IN AillTllMUTIC. 
 
 10. At whftt time aftor TIT o'clock hii« tlus IuuuIh of a wjitdi 40 
 minutes upait ? 
 
 11. At what time after 4 o'clock will the haiuls of a watch bo 
 equidistant from the fij^uio IV? 
 
 12. It is 3 o'clock. By th(( time the minute hand has f.^aino(l 11 
 minutes on the Ikhu' hand, how many minutes will there !)■• 
 b(:tw(.en the hands? 
 
 I'.i. By the clock it is 12 o'clock. In what time Avill the hands 
 bo ((t) f) min., 41 soconds apait V (/>) at li^dit aii'^lcs to each olIut 
 for the first time 'i (c) 22 min. ai)art ? ((/) opposite oach other i* («) 
 at rij^ht angles tho second limo^ \f) 5 min. apart .second time/ 
 ((/) equidistant fvon» the liguro XII? 
 
 Exercise VII. 
 
 1. A, B and C entjaged an opuri hf)Uso for a certain concert. 
 B contributed 317*\ •*!:'-o(), ami A secufc I i he sri'\ kh-s (»t a rxni'iily 
 company to "^dvo thcj conrert. The total receipts frinu the concert. 
 were .SL'iiO, of which A's share was ^rjOit. Find t arh aitisL's fee, 
 piven that the conqumy consisted of 21 artists iuckuling the leader, 
 whose fee was $50. 
 
 2, A laborer ayreod to dig a certain ditch at 12 cents a rod. 
 The first week ho dug 25 rods more than tho halt of it, and the 
 next week he finished the remaining 21.") rods of the ditch, 
 
 {(}) What was the 
 
 on an average 
 
 (d) \Vliat \V(M'.' his daily wa^es 
 
 diiTerenco between his daily wages each week ? 
 
 3. If a farmer can keep 20 cows, that each makes 73 dollars' 
 worth of butter a year, on 45 acres, tiO scp i-ods of pasture-land fcjr 
 which he pays an annual rent of J?)], 20 per acre, what is ids yearly 
 gain from the cows, supposing him to put aside $374. ttO for losses 
 and expenses during the year I 
 
 \ 
 
 I i 
 
 4. Re uce 2f lbs. Avoirdupois to the fraction of lbs. 
 
 Troy. S of | 
 
 5. By how much is ^ greater than '714285 ? 
 
 6. Oats are worth § of 7 sh., Od. (ISterling) a bushel, and hay is 
 worth $15 a ton. IIow many bushela of oats ought to be given for 
 730 lbs. of hay ? 
 
 7. What is I of 5 acres, 80 sq. rods, 4 srp yds. ? 
 
 8. How many cows must a person buy at .^34 each, so tliat, after 
 allowing 73 J cents for the food of each f<jr a week, ho may then, by 
 selling each of th. lot at $3G.91|, gain $172. 48^ i 
 
KoUKTH CLAH8. 
 
 17 
 
 
 0. A stack of liny will koop 30 cows or 27 horsos for a vrmAi ; 
 li(»\v 111 .ny (lays will it keop 10 cows iiiitl six horsos ? 
 
 10. Find tlu'suMi of rho ij iminl.ui.s wliicli follow XCDCCCLXXX, 
 and oxpruss your ariswur in Koiuati rniiiifrals t 
 
 11. A h.itl.'ilioii, coiuint^ hnmo fntm hattlf. lias only J of its 
 oriyin.il nmiiltT of incii. If lias lost ,\, in kiilcil, J in prisoinr.s, 
 and !-5 in dosurturs. Find tliu uiiLjiniil nuni' or of men in tlio Ijattlel 
 
 12. A man liaviii'^' i of 810 >, L,'avo away '» of his inonoy and tlicn 
 lust !?S at l.illi:irds. \Vli;it has he still loft? 
 
 V<). {(i) What is the valuo of 7 times ^ of 4 acres, 40 s(]. rods, 10 
 s(p yds. of land at !?;{8 7- an •.i-vv.'. (h) Bought ICi crates of o;^'}.;s of 
 ■10 do/. (sK'li at 15 cents a do/. ; two out of every dcore wore l>ad ; 
 Muld the remainiU'v jit 25 cents n do/. ; what did I gain, after i>aying 
 a enmiasion m^ reliant iii'7.70 for selling the eggs? 
 
 Exercise VIII. 
 
 1. What is the value of 2;=i of t':5i^ divided by 3g ? 
 
 2. At wli.it time after \) o'clock will the hands of a clock be 
 one minute a[»art i 
 
 3. Our, nf a heap of C inadian cent pie -es, weighing 57 lbs. 8 
 o/s., 4 15') cent pieces are taken «,ud the hea;. then weighs 13 Iba. 
 How many cent [lieces were lu the hea[) at first? 
 
 4. Fin 1 L.C.i\r. of : (a.; 7 feet, inches, and 4 fee , inches; and 
 
 5. If f, of 2 lbs. of sugar cost as much as 2 lbs., 8 ozs. of rice, and 
 if 3^* 11)3. of rice cost 15 cents, what is the value of a barrel of su ,far 
 wei-hing 300 lbs. ? 
 
 0. If (dophants eat 50000 lbs. of hay in 20 days, how many 
 tons wduld last 5(5 elephants 33 days? 
 
 7. A field GO chains long and 80 rods wide will produce 21000 
 bushels (jf potatoes, What is the rate per acre ? 
 
 8. A goldsmith earned £3 Sterling in 5 days of 2 hours each ; 
 what were his daily wagis in dollars and cents? 
 
 9. What will it cost to pave a court-yard 50 yds. long and 60 
 feet wide with square paving-stones 9 inches to a side, at 5 cents 
 each stone ? 
 
 h 
 
1 
 
 18 
 
 KXKKCISKS IN Alt! I IIM C TIO. 
 
 10. If tho true diHcount on 81078, for n oertain time at B per 
 cent, bo i<'JbS, on wluit huiii hIiouUI tlio truu discount, fur tho hhiiiu 
 time, at 8 por cunt, bu ^4 U ? 
 
 11. A fruit <b'iil(!r boiiylit 24 ba.skotH of gnipos at $3 a basket. 
 If each basket huUl 40 II>m. and Iio sold tliu hjt at 15 cunts alb., 
 tind bis ^iiin ur \oh» pur cent. 
 
 12. A man r<»]lin;^a wheel barrow takes 90 Htoi).s, each 2 foot, 
 inches lon<^. in a niinuto. How often will thu whuul of the bairovv, 
 which is 14 inches in dianuiter, revolve in an honr ? 
 
 13. (a) Mnd the cost of catpeting a room, 'J I fi- 1, 10 inches \ou^, 
 by 10 feet, H inches wide, witli carpeting,' *J7 inches wide, nnniin^ 
 lengthwise of tho room, and .dlowin^ 8 im Ins per strip for waste, 
 tho carpet costing ii^l.'-.';") |)er yd. (h) A deah;r boui^ht bro nis at 
 $24 a jzroHS, and sold them out at LT) cents I'.aeh ; find liis gain per 
 doz. (c) The sum of three numbers is liL'aH, and ^ of thu lirst in ^ 
 of the second ; also ^ of tho second i.i ^ of tho third ; tind the 
 numbers. 
 
 Exercise IX. 
 
 1. A man draws wood to supply a contract of 700 cords of 
 twenty-inch wood. His sleigli-l ox is 14 ft. long, and he puts on 2 
 tiers, each 2 ft. in. high, the length of his sleigh-box, at each load. 
 How many loads vill ho recpiire to draw to fill the c(»ntract i 
 
 2. How many bushels of pease at 80 cents a bushel must be 
 mixed with 00 l)ushels of oats at oO cents a busho', to make a 
 mixture on which may l)e gained 0}J per cent., by selling the 
 mixture at 55 cents a bushel i 
 
 3. Find the value of ten rectangular plots of ground, each 55 by 
 40 yards, at $110 an acre. 
 
 4. The selling price of a pair of boots is Ih times the cost price 
 and the gain at which they were sold is ^2. Fnid the cost price of 
 the boots. 
 
 6. A sold a farm to B, gaining 5|} per cent, ot the cost. B then 
 sold it to C for $3010, losing thereby 5 per cent Find A's cost price. 
 
 6. Divide $040 among A, B and C, so that B may have 6 times 
 as much A, and that C may have Ik times as much as B. 
 
 7. If i of i^^j of a farm be worth ^5800, find the value of 80 per 
 cent, of it. 
 
 8. If a lb. of tea is worth 3 lbs. of coffee, and 12 lbs, of coflTee are 
 worth 15 lbs. of rice, what is the vabie of a chest of tea weighing 70 
 lbs., when rice i» worth 28 cents a lb.? 
 
 ai 
 T 
 
 1" 
 
 A 
 
 m 
 
 Fi 
 
FOUHTH CLASS. 
 
 19 
 
 9. Find the cost of papering the walls of a room, 20 ft. l'»nj{ by 
 in ft. wiclo, with paper '21 inches wido, worth 12]^ cunta a 
 single roll, allowing 12 ft. for doors and windows. 
 
 10. A man aft«!r .spunding 82 inori' than ^^n *'f J^*** money found 
 that ho had still left 40 per cent, of what ho had spent. Ilow niiich 
 did ho spend ? 
 
 11. A proiliico dealer paid .*80 for butter, $t for hoof and 8120 
 forchoeae. Ho tluiii sold tho wlu)lo for .S.'!:.'"), u'.iinini^ 20 percent, on 
 thy butter and 11 jj per cent, on tho beef. What percent, did he 
 gain on tho chceso ( 
 
 12. Totn and Will receive 34 A per cent, of a basket of 78 dozen 
 and 4 oran'^'es, dividinl among throe boys Tom, Will and Sam. If 
 Tom got 4 for Sam's 5, and Sam got 'A for Will's 4, what fractional 
 part of tho basket of oranges was divided among tlie tluoo boys i 
 
 13. Sold a horso for 8180 which was ^-'io more than he cost m(». 
 Allowing 815 for his k«!ep whilo I owned liim, what per cent, did I 
 make by tho transaction ? 
 
 Exercise X. 
 Find the prime factors of : 
 
 1. 340, 2800 and 2940. 
 
 2. 48G0, 5904 and 4500. 
 
 3. 8400, 3824 and 1380. 
 
 4. 4400, 8G4 and 5400. 
 
 5. 280, G40 and 7722. 
 
 6. 900, 1800 and 2500. 
 
 7. 45045, 8778 and 15400. 
 s. 1280, 7200 and 8100. 
 9. 3300, 0500 and 3900. 
 
 10. 1800, 5200 and 7500. 
 
 11. 1150, 5040 and 1820. 
 
 12. 2100, 8700 and 3500. 
 
 13. 1340. 4050 and 5887. 
 
 4 
 
 * 
 
20 
 
 BXERCI8KS IN AUITIIMICTir. 
 
 Exernise XI. 
 I'liul \]w L.C.Isr. of: 
 
 1. :j, !», IH. \n, 4r,, 21. 
 
 2. All the fnlnif niiiiil>*>i'H hctv^Meii 7 Htid 23 iiiclusivti. 
 
 .'i. Ml lilt' > r, II iiiiiiilierM bittWfiMi 8 .iiid .'lU iucliiMivu. 
 
 4. 12, 14, 21, .'(2, 48 nw\ 50. 
 
 5 2, 4. 1>, IH. 10, ;{(), IHi). 
 
 «, 4, y, 7, H, (i, 12, 14, 28, und uO. 
 
 7. «, 2, 18, 10, 17, 51, \). 
 
 8. 3, K), 28, 14, m, 20, 1200, KIHO, 1008 imd 720 
 t). 4, 7, 14. :tO, 21 iiiul 100. 
 
 10. All tlu' odil niiiubirM l)i;t\vi'«}ii 7 nnil 25 iiiclii,>Hivu. 
 
 11. All the nnn/ioitite hotwtt'ii 8 uml 28 luclnsivt'. 
 
 12. All th« I'l'en iiiiinlKa's Ix'twiuu M2 iiud 42 iiicliisive. 
 
 13. 740, 15.")4, 1054, 4278 iiiul 1035. 
 
 Exercise XII. 
 
 1. Find tlieL.C.M. of all tlio prime nuinlxsr.s butwouii 2 and 17 
 iiulusivo. 
 
 2. Find the L.C.M. of all the even ninnbors l»otwoon 7 and 21. 
 
 3. Find the L.C.M. of 3U, 42, 48, 70, 75, GO, 120, 7, 4, 36, 25, 
 10 and 5. 
 
 4. Find the L.C.M. of 8, 3, 1(1. 48, 2iN 50, and 75. 
 .^^. Find the L.C.M. of 2, 9, 18, 45. 63, 70 and 72. 
 
 6. Find the L.C.M. of all the odd nuuihers butwuon 8 and 28. 
 
 7. Find the L.C.M. of all the e(»niposite numbers between 15 
 and 25 inclusive. 
 
 . 8. Find the L.C.M. of 8, 19, 27, 50, 54, 57 ftnd 7182. 
 
 9. Find the L.C.M. of 11, 2, 22, 75, 150, 00 and 20. 
 
 10. Find the L.C.M. of 3, 28, 50, 15, 45, 00, 27, 30, 48, 90, 125 
 and 420. 
 
 11. Find the L.C.M. of 6, 9, 18, 24, 30, 103, 90 and 4;i2. 
 
 12. Find the L.C.M. of 34, 170, 95 152, 62, 117 and 00. 
 
 13. (a) Find the L.C.M. of 41, 39, 123, 40, 75, 110. (6) Find 
 the L.C.M. of 5i, 41i«i, 4g and 11^. 
 
POITIITII <'i.\sn. 
 
 31 
 
 Exercise XIII 
 Fiii.l tlio n.r.F. of: 
 
 1. l!»:.r»7 hikI \ts\\\r.\:\. 
 
 2. KVJI4 1111(1 lO.'I'JL'H. 
 
 a i:ni aixi ir>.'Ui. 
 
 4. :J:iHt. H'J72. 70(17 himI 2ii()i>. 
 
 5. lolU, 1177 Htul I<;hi. 
 
 n. ft'j77. io!>47Hti(l ii::o3. 
 
 7. 5187. 5850 1111(1 ]:VM). 
 
 8. Cr.'n. r)'.M;7 and i(;n2. 
 0. 8i8r>7;{»» hikI t.'o:.7H7i>2. 
 
 10. 15(10, 1.VM)/vu.l 2'J'J'A. 
 
 11. 8541, 2'JI(;i iin.l liO:U87. 
 
 12. 1247. 1505. 1720 uiid :{8ii7. 
 
 13. 370G5, 701G7 and (iliOl. 
 
 .14 
 
 m 
 
 • r 
 
 :\ 
 
 j L 
 
 .7 
 
 Exercise XIV. 
 
 Find the O.C.M <.f 
 
 1. 225, 1575, 001)0 Mild 0225 
 
 2. 10287 and (>7818. 
 
 3. (;0()2 and 82(55. 
 
 4. 428108 and 58(;740. 
 
 6. 040, 724, 9(^.8 and 3S28. 
 
 6. 1470, 4007 and 507. 
 
 7. 4100, ^282, 12:U1 and :52.W. 
 
 8. 1800, 3000 and 5208. 
 
 9. 444, 1480, 10()5, and l.'IOO. 
 
 10. 984,1470, 2952, and 241572. 
 
 11. 14.m5, 20.391, and 49287. 
 
 12. 107G7, 9409, and 20:!(»21. 
 
 13. 7029, (-.0.39 and 9999. 
 
 I 
 
 : 
 I 
 
 i 
 
 !^l 
 
S3 
 
 EXKnciuM ly AiiinniKTia 
 
 Exercise XV. 
 1. Find tho L CM. ..f li, 8, 'U, 42, HS. Ort. 170 am? ftrtif). 
 
 II r'fc'^'f 'r im" ''/Vr?.."^ ^' ''^*' '*'*' "^'"^' ''•*' '*'"' **» ''-^ ^'»« 
 U.L. t of JilUi luid it'.Ki.tt. 
 
 3. Divi.l.j fl... LC.M. of 8. 20. 10, IS. ICvn.l 108 hy Uio II C.P. 
 
 [. Divi.l.. tl... L.riNT. ofO, 10. 21. «'2. 8'. fin.1 117 hy tho If.r.F. 
 of l!L'o7 III 1(1 Jim',). 
 
 n,J: 'V''i" ^i'" ^'^^^ "^ "• "^ •'' ^-' I''' ^i- '« »'y f^»« " o.F. of 
 
 n(H):» liiid <i7()i»7. 
 t ri\.^''''''? I''" ''•/'•''^'' *^^ 2i;, 28, ;{o, ;{2. ;u, .'k;. ;{ii, i.y tho ll.c F. 
 
 of 51051 nil. 14(18741. 
 
 7. Kind tho product nf tho II. OF. and L.C.M. <.f 128, 084. 708. 
 and 'JOOt. • 
 
 8. What Is tho iuisf nninhur vvhiih will loivvo a nnuundor whm 
 dividul l.y luiy niMiil.ur Lotw.-on II and 10 im;lii.sivo| 
 
 9. Divide tho L.C.M. of ft, I 'j ,md ;| l.y tlu, a.O.M. of ft, fl, ,9- 
 and lh\. • w «• 
 
 10. Find tho L.C.M. of ,•>„ ,7,, .|^\^ ^„,i ^4^, 
 
 11. Find tho L C..M. of (Oli-5-0,*;) nnd (,••, x Ig). 
 
 12. Fin.l tho L.C.M. of (8i7jxl.'^,) and 12^ - llJ + 4,\- *J. 
 
 13. (a) Find tho G.C.M.of 
 
 
 
 and 
 
 8 X t") X ? 
 
 (6) Find tho O.C.M. nnd L.C.M. of + h of 22 and (;^-r;|) of 
 
 ^ -7- 4 
 § + M^-il + 3- ('•) Sold 8184 Il).s. wluwit ntOlJ cents a bushol, and 
 with tho procouds bought 220.t'^y yds. carpot. What was tho caiuot 
 worth T)or yd. 'i 
 
 Exercise XVI. 
 
 1. Find tho value of lj{ + 2j4-3J + 4J. 
 
 2. Find tho 8um of O^V, r„ m U- 
 
 3. Whati8i%+iVa + ir/j? 
 ^- 4. Add 5i^^„ S^^f, 5i| and f ^ 
 
 6. Find tho sum of 5^%, 2,V ^g and J J. 
 
 0. Find the value of liV+5i| + .'3i^ + 4^. 
 
FOURTH (LAMt. 
 
 S3 
 
 
 7. WlmtU(.0 03-23l (^)U^j-8,"y1 (>')l2^-^,\^ 
 
 8. Subtmot 18 1 J trom 25/,,, miil 18] ) from 'J1|V 
 0, Siihtnict 12|;} from "JO,",, iiii-l rtO from 10^. 
 
 11. SuhLmct (<tj 8^ from D^:*, ; {b) 7j\ fri>m lOi'V- 
 
 409 
 
 mi 
 
 12. Sul>truct §} from 
 
 13. (a) Subtract — from .'J| of 10},^. (6) Add | of u iq rod, 
 I of a sq. yd., ^ of n m<i. foot H of a nq. inch. 
 
 Exercise XVII. 
 
 1. Multiply (a) 8f by Ij*, ; (/>) 14,\ by 7^. 
 
 2. NVhtttia33xl|5x^!|,x|J1 
 
 ^ 3. Simplify 7ix5'VxAx8x«x68x3iV 
 
 4. Multiply 2J, y, IJ, i\, g together. 
 
 5. Simplify Ijj x 'Ji'a x33"5 x43il x i?. 
 
 0. What i8 8 ,\ X i} J X 2^ X 3g X ,7^ x 10 ? 
 
 7. Divide (a) VJ^^i by 1,^^ ; and (h) 131 by 4^. 
 
 8. What is (a) 62+3i ? and (6) SJ-rTi? 
 
 I; Hud I --+9gof 4|V I 
 
 I 10] if 
 9. Simplify \ -i-5S3 
 
 10. What is (a) 22^8^2} jg? and (6) 133254-8,^? 
 
 11. Divide 21i by 4^ ; ll,>t by 24 of 1^ ; 7^ by 43^0^. 
 
 5A 
 
 12. What is —^-(^5 of 3^)? 
 4J 
 
 7 (U of ^) 
 la Divide (a) 
 
 I 
 
 (sT"} 
 
 hy.^iih) \ (lSof5,S)}.by4, 
 
 \ 
 
 ^^ 
 
 ] 
 
24 
 
 EXEliCIbES IN AUrillMKTK 
 
 Exercise XVIII. 
 
 1. AdcU, 3|, 2J, ^u.d^. 
 
 2. Simplify I of fj + i of ? + 13, of ?^ + ^}^ of 11. 
 
 3. Simplify Jiii-(^^+M)^ +(^+i + > + i)+15| 
 
 4 Simplify '{(^ + hk-fi)^{4'i-'Sa + ^\,)y +^i. 
 
 - c- If 7,', of ryi +2 104 
 o. Simplify " ^ ' 
 
 * ^ Hi, of L\\-] M)r> 
 
 6. Simplify § of ^liV "f ^'H7(t-iAt. 
 
 - c ^■t lof Ux'J?; of 4aof 1> 
 
 7. Simplify ^' 7 :• ° i! y li 
 
 8. Simplify 
 
 7 -''21 J I 
 
 1 7 
 
 ^+ — 
 
 V • 
 
 3H2iV + -{{^T-7AUi^8 
 9. Simplify l§ + ji 10 7^ 
 
 fof2^ 3' -H 
 
 3 5 3 
 
 + + 1 + 
 
 iO. Simplify 7 5 3 
 
 8- 
 
 ()• 
 
 1 + 
 
 11. Simplify 
 
 2-1 2-t 1+h 
 
 Hi of Hi 
 
 ^jof (l + 5^) + t of 2^ of (7-2i)-i 
 
 4 1.5 
 
 -rl7 
 
 12. Simplify 24^ 
 
 + 5 of I -r- - 2(y. 
 
 30 
 
 13. Simplify 
 
 .f of } 
 
 ni 
 
 o- 
 
 of 
 
 40 
 
FOURTH Cr.ASS. 
 
 Exercise XIX. 
 
 36 
 
 1. \Vliat fraction divided by 3 of 12 will give ^ for quotient 1 
 
 2. ITow in;iny vests, each containing J of a yard, can bo made 
 out of 24 yards of cloth? 
 
 y. liow many |)«)or ptioplo can bo supplied with ^ of a lb. of 
 meat each, out of a basket containing lT) lbs., \)'i o/.h.I 
 
 4. A lady boie^dit three pioct s of cloth ; tin* tirxt contained 30^ 
 ydfl.; tlie secoml 28] yds.; the third 25^ yds. How may yards, iii 
 all, did she l)uy i 
 
 r>. If § of a mill is worth §5225, what is | of the remainder 
 worth? 
 
 0. Ex])ress tlu; following in fractions with the least common 
 ilenf)min;itor, and lind the ditference between the greatest and the 
 least .7, ifj, 7, 1 and t^^. 
 
 7. If 27;^ miles are travelled in 2f^ hours, how long will be 
 required for llj;;;\ miles? 
 
 8. A man lias ,'^7.; of an acre in one plot ; f of an acre in another; 
 l^Vj acres in another ; and 4;^ acres in a fourth. How many acres 
 has he altogether 1 
 
 9. A dairyman sells ('),5 lbs. of cheese from a piece weighing 20 
 lbs., 4 ozs. How much of the piece has he left? 
 
 10. A man who owns ^^ of a ship, sells J of his share ; what 
 fraction of the whole ship does he still possess? 
 
 11. The sum of throe nunibers is >'5 ; the least is ^ and the 
 greaiest ^J ; what is the prodiict of the three numbers ? 
 
 12. A house and lot together cost 82400 ; the lot cost \ of what 
 the house cost ; find the cost of each. 
 
 13. (a) The remainder 9 is 1 of the divisor and § of the quotient ; 
 what is the dividend ? {h) A cistern loses, by leakage, 4 gallons 
 .3 quarts, 1 pint, in 7 hours, 48 minutes ; what is its hourly rate of 
 
 loss ? 
 
 
 \m 
 
 I 
 
 Exercise XX. 
 
 1. What is the value of 2| of 3| divided by 3|? 
 
 2. Add together |, {;}, ^f , and ^l^j , and divide the sura by the 
 ditference between ^| and ^^. 
 
 Ml; 
 
 I, '.I 
 
 I ' 
 
 I 
 
2fi 
 
 BXRRCISES IN ARITHMETIC. 
 
 3, Arrange the following fractions in order of magnitude |, |, 
 3 + 4 
 
 and 
 
 4 + 5 
 4. (rt) Find the L.O.M. of 1547, 1729 and 4199 ; (6) Add y/- 
 
 ^"tt 
 
 antl i|3^. 
 
 215T» 
 
 5. The numerator of a fraction is 3, and the fraction becomes yl, 
 when divided by 2. What is the fraction ? 
 
 6. The numerator of a fraction is 16, and tho fraction becomes 
 144 when multiplied by 40. What is the fraction? 
 
 7. Simplify 
 
 ^of7,\ 40 8;^ 11/j 
 
 ^fHf 7 20 '"hT 
 
 8. Simplify 
 
 and their difference is 
 
 5^ + 5J (4S - 4,7^) of f J 
 
 5f-5i* 4§ + 4,7jof §J * 
 
 54J 
 
 9. The less of two numbers is 
 
 If iof8| 
 
 — ; what is the greater number ? 
 
 10. Simplify (a) | of Klf + A ^f "7-^1? of 3; (6) 
 
 1 ^ ) HI 
 i+ + 7 >of of $210. 
 
 n 2; J- ) Hu 
 
 11. Di\ iilc yIjt by the difference between the greatest and least 
 of the following fractions : |^, \l and ^^. 
 
 12. W!i;it number added to f + ^ will give that number which, 
 yrhen subuucted from 3^^, leaves 1^ ? 
 
 HHi)-; 
 
 la (a) Simplify 
 
 Hi 
 If 
 
 1 + 
 
 (6) Multiply the sum of ^, ^, and f by 
 
 2-i 
 
 the difforoMce between 4 and |. (c) 
 
 J of ^. ('/) If a plot of ground f of 
 
 750 lots of equal size, what part of an acre will each lot contiun ? 
 
 Illustrate ^ of f , ^ of ^, f of ^, 
 square 
 
 be divided into 
 
 (e) Simplify |(§ • |) of ^^ 
 
 H 
 
rOUIlTH CLASS. 
 
 Exercise XXI. 
 
 27 
 
 I. Reduce the diU'orence beLwoen 14 tons, 1(5 cwt., 11 lbs. jind 
 li{ tons, 18 cwt., 20 lbs., to ounces. 
 
 •J. \ boy, having a basket of oranges, <ftiVii awjiy a certain num- 
 ber of tlicui, and tlieii ho bought ut a fruiter's times us many as 
 he gave away, after which ho had 2O5 (h)zen or twice as many as ho 
 had at tirst. How many nioro did ho buy than ho gave away ? 
 
 3. A lias a fiehl GOJi rods s(juare, around wliich, on tlio inside, 
 he makes a roadway 10 rods wide. How many acres and square 
 rods does the roadway contain 1 
 
 4. Wlien apples are 'o2 cents a bushel, a barrel costs $1.27 ; at 
 this rati;, what will a barrel cost when apples are 40 cents a bushel, 
 the cost of packing being lo cents a barrel ? 
 
 5. A does g of a piece of work in Ij days, when he is joined by 
 B, and together they iiniwh the work in 5 days from the time when 
 A began the work. How many days would the work have occupied 
 each alone ? 
 
 G. There are 917 square yards in a path which surrounds a plot 
 containing I acre, 80 mi rods and whose length is 80 rods ; lind the 
 width of tlie path. 
 
 7. How far may a man row down a river at the rate of l'-* miles 
 an hour, so that he may walk back at the rate of 2^ miles an hour 
 and be occu[)ied 7 hou s, 15 minutes in travelling? 
 
 8. From 2 acres, 140 sq. rods, take 1 acre, 150 sq. rods, and 
 reduce the dill'ereuce to inches. 
 
 9. A man, having 75 acre-i, 130 sq, rods of land, sold 13 acres, 
 150 sq. rods, 30 sq. yards. What is the remainder worth at H cents 
 for every 5 square yards ? 
 
 10. From a square stick of timber, 15 inches to the side, and 
 containing 3 cubic yards, 8 cuiiic ft., a piece 4 ft. long is cut. How 
 many cubic inches are still left 1 
 
 II. A man buys 50 busliels, 1 peck and one pint of wheat for 
 $04.34, and sells 10 bushels, 2 gals, and 1 (juart of it for $iG.45 ; 
 what per cent, is he clearing '{ 
 
 12. Mr. C has 40 bushels, 5 lbs of barley on his wagon, and Mr. 
 D has 30 bushels, 25 lbs. of wheat on his wagon ; what fraction of 
 C'a load is D's / 
 
 13. How many small boxes, each 3 ' x 2" x |", can a traveller pack 
 into a box 3' X 2' G"x 2' 2"? 
 
 i 1! 
 
 I' 
 
28 
 
 KXEKOLSKS IN AKlTiiMKTIC. 
 
 Exercise XXII. 
 
 J. If 2 of a house is wortli $250, what is tlio vuluo of two such 
 houses i 
 
 2. Ff ^j of a boat is worth $1200, what is tho vahie of /^ of it / 
 
 3. If 7 of 'A^ of a farm oust $4D0(>, what is thn farm worth ? 
 
 4. If 1*^ of a bushol of potatoes cost $2, what is 23 pocks worth 
 at tho siiino rate ? 
 
 5. What is H of an aero of land worth, if j^ of an aero is worth 
 $18 '{ 
 
 6. If J of a coal mine is wortli $0000, what is the value of ^^ of 
 it? 
 
 7. If I of I of an estate is worth $900, what is the value of thi; 
 estate ? 
 
 8. What is ^ of ^-t-yjj of i''" orchard worth, when f of it is worth 
 $500 ? 
 
 9. A man sold threo quarters of beef for $.''0, and one quarter of 
 mutton for $3. At that rate, what was the value of the whole of 
 his beef and mutton '( 
 
 10. When ^ of a gross of lead pencils cost $4, what will half a 
 gross cost 'i What is that apiece ? 
 
 11. If I of ,^ of a wiigon-load of turf will cover <I0 square feet of 
 ground, what will 50 such wagon-loads cover ] 
 
 12. How many carrots will grow on nine acres, if 180 bushels 
 grow on j'(y of an acre ? 
 
 13. (a) If I of a stack of hay is worth $28, what is the value of 
 i\ of 2'j of it ? (b) Find a uuiltiplior which will give the amount of 
 any sum of money at sinqtle interest for 5 years at 4 per cent. 
 Use the multiplier to tind tiie amount of $5U0 for the said time at 
 tho said rate. 
 
 Exercise XXIII. 
 
 1. A and B do a work in 8 days, H and in 10 days, A and C 
 in 15 days ; all throe work togethei- at it f(jr 4. da} s and then A 
 leaves j the other two go on foi 2 tlays longer and, then, 13 leaves. 
 In how many days will C linisli ihe work alone i 
 
 2. At what price per yard must a mcrclumt mark silk which 
 cost him $3.20 a yard, so tluit lie may thrcnv oil 20 per cent, and 
 still be making a profit of 25 per cent, on cost ? 
 
roURTIf CLASS. 
 
 29 
 
 c 
 
 A 
 Is. 
 
 
 3. Find the simple intoiust on 8Hr>.r)0 for 4 yours at 7 per cent, 
 per niniiuii 
 
 4. KxprcsH ('27 of 13s. 4d.) + (-lU4 of £2 10s.; as the ilociniai ot 
 i'IH2s. (kl. 
 
 5. What is the value of (.^ (.f -lO-r •.S7r>)- of ^UO ( 
 
 6. On what smii is )?ir»7.50 tho true discount for 2 years, (> 
 
 iiioiitlis, at 7 per eont. per aiiiiMm ] 
 
 7. A dealer can well 7!>U bushels of ))arlev foi JS4H0 cash, or tor 
 i^ollO due in 1 yeai" (5 iiionMis heiiei;. Whii-h olVcr iiad he better 
 !ieee[)t, money briiiLj uorili 8 [ter ueiit. per annum ? 
 
 71 
 
 ». Simplify (rj;!;!-:,-, "f 4! 
 
 ^-^ 
 
 I"" 
 
 f 7.," 
 
 ^•1 
 
 I'V 
 
 21.*.".". > \ 
 
 r.40()f "" 
 
 9. What time after I'J o'clock will the liamls of a watch be Jird 
 at an anifle »»f i'_'0 decrees ? 
 
 10. An a'4ent sold 215 bushels of apples at 82. MO a barrel on 
 a conunissidn of 4 per cent. , tiiid the anumnt of his eommi.ssiim. 
 
 11. A and B own | of <i [iit of apples, and C the rest. A's share 
 is 3 times li's and tho diilerence between B's and C's shares is 58 
 bushel.'-;, 1 i)erk, 2 (juarts, 1.'. pints. How many bushels of apples 
 does the pit contain ? 
 
 12. A man exch;;ngos 20 [>ecks of clover seed at $o a bushel for 
 hay at 80 cents a cwt. Itow many tons and lbs. does he get? 
 
 13. (a) Find the value ot 4 barrels of ei^gs, of 96 doz. each, at 35 
 cents a score, (h) A can m(jv; .'j of a field in 3 days, and Bean mow 
 1 of the same field in 3 days. In what time could both, working 
 together, mow -^r, of the field ? 
 
 Exercise XXIV. 
 
 1. A line X is one-third as long again as a line Y, and Y is three- 
 fourths as long again as a line Z. VVhat fraetiijn of AT is ^ of Z ? 
 
 2. Divide 8225 between A and B, giving A 1| times as much 
 asB. 
 
 3. A man sold a lot, losing thereby 25 per cent, of the cost of 
 the lot, and Avith the proeee(l.s he bought a bankrupt stock of 
 grt)ceries which he innnediately .sold for 8":5500, thereby gaining 16| 
 per cent ; find the cost price ui the lot and his total gain or loss 
 per cent, by his transactions. * 
 
 i' 
 
30 
 
 SXliROISES IN ARITHMBTIO. 
 
 pure Bilvor bo worth $15 a lb., find the value of 102 
 ounces of Eimliah standard silver. 
 
 4. If 
 
 P 
 
 5. A'a jiGjo i.s 6f>lj per cent, of B'a, and 7 years ago tlie half of 
 tlio sum of their ng(!H was 13 years ; timl tlieir ages. 
 
 0. Dividt) $',(>ir) anioin,' A, 11, C, D and E, Riving A $30 less timn 
 C, C 810 more than I'., li $100 Iohh than E, E siO'moru than A and 
 B toL,'otht'r, and D half as much as all the <ithur.s together. 
 
 7. The wheels of a road-cart are each 14 feet, 8 inches in 
 circumference, and together make 14400 revolutions in going 2 
 hours'. How fa.st does it go per hour '/ 
 
 8. A cistern C(mtains 8000 tralions of water, hut when .3^0 cubic 
 feet are withdrawn, the ci.stuni is foinid to still coiitiiin (il^OO Ujh. tif 
 water. How many gallons of water are tliere in a cubic foot / 
 
 9. The sum of $135 wa« ])aid as a weelc's wages to an e({ual 
 nuiid)er of men, women and l)i)ys ; the men received $1.25, the 
 women 75 cents, and the boys 50 cents a day. How many men 
 were there ? 
 
 10. IIow many chains is it from Winnipeg to Calgary, a distance 
 (by railway) of 955 miles ? 
 
 11. At 30 cents a load, it cost $6G to gravel a walk, 80 rods long, 
 by 9 feet wide, with gravel (5 inchas deep. How many cubic feeb 
 make a load V 
 
 12. For every 2 ounces of green tea in a mixture there are 5 
 ounces of black tea. How many lbs. of each are there in 14 lbs. 
 of the mixture 'i 
 
 13. How much heavier would 12 barrels of pork be than 1 cu bio- 
 yard, 2 cubic feet of water 1 
 
 Exercir^ XXV. 
 
 T^Vof 9;\of 3jof OfV 
 1. Simplify of $100. 
 
 TT 
 
 of 3.^of 12} of 21^ ot ^^^ 
 
 2. If 9 hats cost as much as 25 silk ties worth 99 cents each, 
 how many hats could be bought with $330 ? 
 
 3. A whaler, n\ pursuit of a whale, lost ^ of his wli;ile-line ; he 
 then added 500 feet to the rcrnauider, when he found it to bo } 
 longer than it was at first ; find the cost of the original whale-line 
 at 25 cents a yard. 
 
 Bi 
 
FOURTH OLASfl. 
 
 81 
 
 4. A man soM a horse fi^i i'OO, tliorul)y losing' KJ^ per cent, cf 
 Ills purcluiHo. Wli.'if per ci nt. of his salo woulil lie have gained, 
 hud ho Hold the horwo for .*?2t)0 ? 
 
 6. Divide isJtT.nO uinoiiu A, B and C so that, B shall have f of 
 A's share and (/ ij or IJ's share. 
 
 6. A persnii a^roo.s to complete a pieco of work in ."30 days, (a) 
 What part of it ouj^'ht to he done in 2-4 days? (/>) How niiidi Itss 
 than § of it will ho done '{ 
 
 7. A bill of 55 Ihs. of nnjtton and 45 lbs. of veal amounted to 
 .':i«l.'<.35. The veal cost \i cents a lb. more than the mutton. What 
 i.s the vahie, at this rate, (.t onecwt. of mutton? 
 
 8. A person who paid away ,'| of the contents of his purse, and 
 was r()bl»ed of \l <>f tliu i-oMiaiuder, found that ho had atill left 
 i^LSO. Jlow much luiM lu^ at Jirst 'if 
 
 0. Two h()rsc.'^ are worth as much as 5 oxen, and 3 oxen as much 
 a.s IG sheei). What will Ije the value of a horse, if the price of a 
 MU(jre of sheep is iJiSJJOl) ? 
 
 10. A buys 75 tons, 2 cwt. of hay at $14 a ton ; B buys 64 cords 
 
 of wood itt !ir').75 a (!(jrd, and (v l)U}stt piijs o.ich weij^hio'^ 115 lbs. 
 at ^3.26 a cwt. IJow much ^locis A [jay moi-e than B and C together? 
 
 11. In mavldntj quest i'lis one is the maximum, and six the 
 miidnmm. What per cent, does a candidate make who receives 4 
 marks) 
 
 12. If S8 be allowed as the interest on $160 for a certain time, 
 what will be tJie interest on the same sum for twice that time at 
 half the rate ? 
 
 13. A man owning a section and a. half of land in Manitoba sold 
 (wo rectangular lots out of it . the lirst, 50 by 40 rods at $150 an 
 acre, and the second 90 by 70 rttds at $80 an acre. What was his 
 average selling price per acre 1 
 
 Exercise XXVI. 
 
 1. A and B start from iMontreal for Ottawa at the same time that 
 G starts from (.)ttawa for Mi'Utieal, a di.'^tance of 100 miles. A and 
 B travel, res[)Gcrively, 10 and 8 mile.s an hour, and C 11 miles an 
 hour, (a) In how many hours will (J be midway between A and 
 B i (b) How far will G be distant from A ? 
 
 2. A rectangle contains !)600 .square yards of area, and its sides 
 are to one anothor as 3 : 2. Find the number of yards in a side 
 and an end of t!ie rectangle. 
 
 i 
 
 :iJ 
 
 I- <! 
 
 ■■!' 
 
 
 ^f 
 
;i2 
 
 BXKHCIHKH IN AKITUUI TIO. 
 
 .'J. Su[t|t<.se tluit "8 i8 ruprcBonted by unity, wluit number will 
 
 I. Ii<»n^lit>4 liiiul iiMil !i foi'iHjii.'irtnrnf h.-.-f wiM'^Imm'^ 'J.'t'J |M>iin<lH, 
 |i;iyiii^ 7] cents a lb. for t ho liiiid quarter and 5^ ctiits .i lb. tor I lie 
 fore (lu.iiter, Hud tound tliiit i h;id juiid L'U cuntH uiure for it tlitiu I 
 would, liiid 1 bought both at the average prici- per lb Kind i)und)er 
 of lbs. ill the hind (piarter. 
 
 5. liought \'3 horses at li'j percent, below their real value. I 
 then sold tiieni at 20 per cent, less than they cost me, which was 
 $286 below their real value. Find tht; cout pi ice of a horse. 
 
 6. The ditrerence between 2 per cent, of a number multiplied 
 by 6 and 3 per cent, of it nmltiplied by 7 is 22. VVlmt is the 
 number i 
 
 7. A farm is 391 rods long and 345 rods wide, and it is divided 
 up into square fields of the largest possible size, ilow many acres 
 and sq. rods are there in 32 of these fields t 
 
 8. Bought 70 gals, wine at $3.20 a gallon. How much water 
 must I add so that I may gain $9.75, by selling the mixture at $2.75 
 a gallon ? 
 
 9. A safe and its contents are, together, worth $189, and the 
 safe is worth 'j of its contents. Find the value of each. 
 
 10. How far from the end must I cut a board, 14 inches wide, to 
 have a piece containing 14 hi{. feet? 
 
 11. Divide $000 among A, B and in the ratio of 3:4:6. 
 
 12. A man has a certain sum of money of which he spends |, 
 then J of the remainder, and lastly ^ of what still remains, when 
 he finds he has $;!00. How mncli money had he at tirsL ? 
 
 13. A man buys horses at an average price of $90 each, feeds 
 them it a co.st of 90 cents each, and then sells them at $125 each, 
 gaining on the lot $1I9.'<.50. How many iiorses did he handle ^ 
 
 Exercise XXVII. 
 
 1. What time between 8 and 9 o'clock are the hands of a clock 7 
 minutes apart? 
 
 2. A and B run a mile race. A gains one rod on B in every 176 
 yards. How far will B be from the winning-post when A arrives 
 ther«1 
 
FOURTH OLASR. 
 
 33 
 
 .'{. A Hnoculiitor hnyj^ a tr.-i.'t of l.iiid at !!^IR nn nrro, muI by hiII- 
 iii'4 it off m I(»tH tn.iki'H HO por otiit. on nil ho sells : so that, aftt'i- 
 iT^nrviri'^ h " <|ii,iilt'r rttclion" fni* h farm. In- I'mkI-- flwif Ik^ hrtH 
 H'ali/,i'-<l, i>n what, lio hiis soM, ."?110|() iiimic ^mm tin; \vliol«» truct 
 iMHfc him. How iii.iny hcwh wcro there in the tract hoiittht? 
 
 4. A cwt. (.f herf in Kiii,'l(iii(l is worth 8*{('>.n() Cati.ulinn ciir- 
 renoy. At iiow many ponce por Ih. must it ho sold to y.iin 40 pel" 
 r((nt. ? 
 
 6. A niillor rocoivod .S2nr).12', for flour at ft7.'io. tv hni;. ITow 
 many hiirrels an<1 poiuHls of flmr ilid In; soil, and wliiif dirl a ha^; 
 jiold, givon that Hour is worth !?.'{. 50 a, cwt.? 
 
 6. At 11 cents a rod, what will 4 niilos 110 rods of fencing cost '/ 
 
 7. r.ou^lit 20 Ihs. hlaek toa and 15 lbs. ijreen tea for $20.60. 
 Tho black ti ,i co.'^t 28 (tents a lb. more than tho i^recn tea. Find 
 the cost prieo of a ton-pound "caddio" of groon tea. 
 
 8. From 21 acres take 10 acres, 3 roods, 30^ S(|. yards. 
 
 0. A man spent 1 of a certain sum of inonoy. thei\ .St more than 
 ii of the r(Oiianidor, then ^ of what still remained all but $6, when 
 ho had yet loft .SU>. What was the original sum ? 
 
 10. Wliat time after 9 o'clock are the hands of a wateh 
 ofpiidistant from the liL,'uro IX ? 
 
 11. Sixteen men can do a i)ioce of work in 10 days. How long 
 will it take them when assisted by 4 men ? 
 
 12. A fruit dealer bmv^dif barnd.s of ;ipples at $2.45 a barrel. 
 The six barrels contained 83 doz. each, and he sold them out at 5 for 
 .3 cents. Find iiis gain per cent. 
 
 13. (a) If a quart contain 78 i'n])ic inches, how many })nshels of 
 grain will a uniform circular elevator, 42 feet in diameter and 01 
 foot hisxh. hold ? (/>) How often does the L.C..M. of 10},, 4i and 40Jt 
 contain tlnnr H.C.F.? (c) A has twice as much money as P>. A 
 receives !$70, and B receives 30/^ less money than A. but tlnds that 
 his jnoney is increased by 1101% of what it was Ht Hrat. Ho'.t^ much 
 money had A and B (together) at first ? 
 
 Exercise XXVIII. 
 
 1. Find the total cost of putting a board fence, 4 boards high, 
 round a lot, 81 rods. 4 yds., 2 feet long, by o9 rods, 2 yds., C inches 
 wide, with inch-lumber 7 in(ynes wide at §12 a thousand, the posts 
 being 7 foet apart, and costing 7 cents each, and the labor of making 
 the fence being at the rate of $33 a mile. 
 
 M 
 
 ;h 
 
 
H 
 
 ^XV.nr.l^KH IN AMITIlMKTtr. 
 
 2. Find the ooHt prioo nt clieoHo, |)or cwt., it' li salu of 50 owt. 
 for <J'J5(), ^iv^!H a pp-lit, of ,', of tlio •»ri;^iMi»I o<i>,t. 
 
 l], Fiml tlio v.iliuj of tliij Hynip 'niiliiiiiDd in u vussol, wlilili i» 
 exiifily illlcd liy Hiii|ityiii^ into it tlio uotitiMitH of 2( du/.oii tiiiiform 
 on't'iilar tin jtiils, o;ioh II iirluis in di.inj 'ttM* and I'i iiiclun ilt'i![», 
 wlnii ;i j^'.illun of syrup w-' 'Iim i'A^ [Ua., worth H\ ii'iitM h Ih. 
 
 4. If n <Mi','it ho :),',, ^r.iiiis. how iiiiiny chimIh would a diHtiioiid 
 bo, which \vi i-hs ^'^'^W-^ ot u 11). ? 
 
 5. A, T^ iiu<] ;uo purtnorK in n business. A 1ms in it 87000, B 
 i?lO()0, ;in 1 ii^nooO. V\u y -.liri in B yo.irs. .SH10i)i>. A thon ret..'jH 
 from tliu biisinosH : wli;it ;(U 'ull ho tiikf with iiini? 
 
 6. Sixty conts will buy 1 cocouiuts, 12 "Imm^'os, or *J0 biinjinas ; 
 how iiiuny do/^uu ImuiinaH urn worth im much na 'J ilu/.un orungnH und 
 4 C()co;inutH ? 
 
 7. A nuwsboy bought a certain nnnibor of naptrH ut 3 conts 
 each. Ilo sold thoni, i^aininf,' ^'.\, which was O^j pur cent, of IiIh 
 Halos. Find tho nuinbiT of papers bought. 
 
 8. Fintl tho number of acres, an. rods, etc., in a tract of Ian I 
 oonsistin*,' of 50 s(piaro fields, each 14 chains 40 lin1<ft to a side. 
 
 9. BoULfht .'3l> dozen oran'_^es and leujons for i;^l«j.80, the lemons 
 at 3 cents oacli, and the oritiiL^'es at 5 ceJits each. How many do/on 
 more lemons were there than ranj^es ? 
 
 U „ 2i-lj{ 8j^ 
 
 10. By wliat fraction must j-jT of f + i • in~H4 be divided in 
 
 order to give a quotient of ij ? 
 
 11. A boy's homo is situated one-third of the way from N to TNI, 
 two villages on the bank of a river. The boy can row from home 
 to M and back in 2 hours, 8 minutes, and ho can row from home to 
 N in 40 ii)inutes. He leav(js homo n 8 a.m., and rows to N, thon, 
 from N to M, wher.! ho stays 48 minutes, after which ho rows home. 
 What time dues he reach hfjme ? 
 
 12. Divide the number 1089 in tho proportions of J, ^ and yg- 
 
 13. In Winnipeg, a man paid $55 a foot frontage for a store site. 
 What was laud, an acre, in Winnipeg? 
 
 Exercise XXIX. 
 
 1. A man invested $1540 in sheep ; he then sold a certain 
 number for $297 at $4.95 a head, losing thereby 11^ per cent, of his 
 sales. Row many sheep did he buy ? 
 
FOURTir CLAfm. 
 
 30 
 
 2. A pornon borrowH a roifuin suiii nf inmu'y fnr 4 yr.irM, 6 
 itiontliH, fitfi^ por ci nt. and iriiirns, at thuunil of tliut tiinu, lefii'JJJD. 
 Wlmt w/iH tliu Niiiii l)urr()Wi)(t ? 
 
 3. A gtiitluhiaiii from London (Kii};.) [)iii^ £'2'iO Sterling for n 
 **<jimr(or Hucfion' df Imid in Alburt^i, N.W.T. \V|»,tt wub land 
 pur iioru tliuru i 
 
 4. If tho import diUinii on hn<tn into Oan.td.i h<» HO conU a ••wt. 
 in<>r<< timn 25 por cent, of tlm cost pec (;wt. in Illinois, uimI tli> [KirUur 
 pays l!(|Mi;() duly on u Cfvr-ltiiid of lo()0 Ijo-h fiNcnigmg IhO 11>8. uucli, 
 what is pork [hm' uwt. in Illinoiti ? 
 
 6. If a twiintylivt) ctmt pioco weiji;li 3 dwtH., 18 ^'rs., h(»w many 
 flve-cen^ pii-ces wonM wii'^li IVi Ib.s. Avoi'liipois / ll^w much is tlie 
 puru Hilvur in thorn worth at i|5l8.'J8) a ll>.V 
 
 <V Two hoiMt'8 uru londtMl, onu with .i <;uliic;il t.mk, 3 foot to a 
 ■ido, tilh'd with H;uid winch is l,V^' tinius us houvy as water, and tho 
 otiusr with 1) harrcis tlour. It' tho tauU woi'^h "0 Ihs. and oiioh 
 barn 1 \2 Ihs. ; which hortie is drawing tho greater h>iid, otiior things 
 bcini{ uipuil i 
 
 7. F'ind tho cost of wiro, at 8 conts p'r 5 y<lH., to onch)Su a tiold 
 SO by 45 roils, tlio fluid I uini( roolaii;^'idar in form, and tliu fouco 6 
 wires lii^l'- 
 
 8. How many foot of luml»rr, inoh ni' iisuro, will ho rcfpiirod t<» 
 plank a play-ground, IGli foot long hy 0<i foot wido, with plank 2^ 
 mchos thick/ 
 
 9. The moan hoight of 6 trcos is 91 foot. What must bo the 
 height of a ui\th trou, wl^li brings tho avorago up to 9-4 foot? 
 
 10. Simplify (a) 5;! ..f ,\M(i\-r,) + 'f!i i (6) [ ^ 2^ -r f J ). ^ 
 
 11. A man owns a farm, divided into liil j>lots of rectanijular 
 8hai)0, each !)0 by 80 yds., which ho has plaiiit^d with potatctos. 
 Find tho value of the crop, supposing iioO bushels to grow on an 
 acio, and potatoes to be worth 00 cents a bushel. 
 
 12. A drover paid l?18595.50, in Toront.), for 200 head of i)rime 
 cattle, avera,t,'ing 1771 lbs. o.icli. llo shii pod thoiu to ljivor[Hiol at 
 a cost of .SlO.Ot) a head, and sold them in the Kngli-sh market at 9 
 pence a lb. Find his gain. 
 
 13. The larger wheel, of a hie vole, which is 16 feet in circum- 
 
 fe 
 
 g 
 
 ence 
 ng 2 
 mailer wheel 
 
 makes 0.'J90ii rovolulioiis hjss than tho smaller wheel in 
 
 20 miles, 60 rods, 15 feet. Find tho circumference of the 
 
 i1 
 
 'M 
 
 I 
 
 m 
 
 
36 
 
 KXKIUiNKN IN AKiniMITIO. 
 
 EX«T<IM« XXX. 
 
 1. Il«>w ofti'ii (IniH iIm 1<. C. M. of :i, 0, 17, IH, 42 lUid (it 
 n.iiluiii Ihr <;. i\ M of IM-i'MmiimI I'MJKiL'V 
 
 2. ('«) l{« si.lvo iHtJ, •l.'M> Hh"! TJ^'-''^ »»»••» tlu'lr iuinn' fiu'r<>rH. (/») 
 
 UmO tlll'HU flU'tiiK to |>l'(»Vl) till* tiutli of null of tito fo||oS\tliU Mtiitu* 
 
 nit'tilH ; — 
 
 I. "Till) (J. C. M. of twoorni"r«» iiimil>t'rH is i>oiii|m)n«><I <•( 
 
 nil tin (iti'hii'K lihuh ilfH rnmninn t«' I Im)Hi' liUliitifrs." 
 
 II. " Tliu ]s. (-. M. of tMoor more nuinl)i*rH in cuinpoHnl nt 
 tlif Hnatll'-d .if.hrtlioi >>/ fartorn tliut iiidliiduN tliy tuotorH 
 of uHcli uiviii iiiiiiilit'r." 
 
 3. {(i) |{i«Molv(' l.'KirMUitl irMii iiiti. tlii'irpriiiu- fiu'toVM. (/») Fium 
 tlio fiiiturs ihiiH ol(t,iiii(i| K«'li I I ih«'si' tucinrs uiiu'h t'nnn (i.)tlii' 
 (i.e. M.; iirxl dr.; ihou! whi«li »oiiii llic Ij.C.M. {< , Show (i.) 
 timt tlu> (i.e. M. iumI L. C M. ur»^ i;oiii)»oisr«l of nil tliu fiictois of 
 tln'Hi5 tiro niimlMis ; ainl (ll ) tli.it tlio (».('.M. in cnnnMisiul of all flu» 
 fact" ri'jtcd'd liv tliti jj. (' M,, iiml »'/V» cms,;; m.) tlmt Llit! 
 (1.0. ..'. X L. (J. M. III.' iM'HJiul of tho iiihiiImi>>. (Why /); iv.) 
 thur till) G. C. IM. X L. <'. M. :- ono of tho nmiiluTM - tho othrr 
 iiuiiiIhv, m\>\ I'ii'r (vml ; him! (v.) that \\w \i. C M. of tho two num- 
 boiH — tht ir product -r tlhir (i. ('. M., ainl oice aiad. 
 
 4. Fiiiil 'ho [i. C. M. of j>„, ^, ,»^ iitid T^. 
 
 5. "'I'lio priicif)!*) of liiiditi'^ tho <}. 0. M. of two nninht'iK 
 d('iu>ndH upon tho following axioms;" (i) ''AnnM>iiro of any 
 iiiiiiiImt is als(» u ino.isiin' of any mM////</»M>f that nuiiibur." (2) "A 
 inc.tHure of oiioh of two nn nl' ih is tjso a moisiiro of thoir .sum or 
 di/rnnce." \N ith tho miiiiW 'is 'jr. I ami .'ll'J piov Ihcso axions to 
 1)0 true. 
 
 i\. Tho H. 0. F. of two numbors is 74, and thoir L. C. li. is 
 15,540 ; ono of the innnbirs is ir)54 ; tiiid tho other. 
 
 7. The H. 0. F. of two uuinbois is 240, ami thuir L. 0. M. is 
 2880. Find tho nmnbors. 
 
 H. Find tho L. (J. M. of jJ, § »"it^l ilny ""^^ divido it by the hist 
 fraction. 
 
 0. Fiu.l the 11. C. F. and L. 0. M of (8}? ^ Hi;) and (IJ x I] 
 X 2i X :{,!). 
 
 10. (a) Find tho II. (!. F. and L. (.'. ISl. of ( | of " ■- .,\ x g) ami 
 (i X i <»f M "J" ^)- (''.' "*^^^' "f'^ " '"^ f'l'*J "• ^'^ '*• cniitaiiifd in each / 
 
 11. Fin.l tho L. C. M. of AiMVJ, 7175, 7770, U'.'OIi, and 01)70. ' 
 
 21 .1^ 
 
 12. Find the L. 0. M. and II. ('. F. of ji of 5, 9, 
 
 and 
 
 1} 
 
ftMiTII C'I,AJI'<. 
 
 37 
 
 |M Pin«l thrt Kr*»rtfrt>if »»mimI)»t wliu'h will ilivi<l« '27'X\ aii<l 5101, 
 
 Mxnrolno XXXI. 
 
 1. If 1*10 hii««ln>ls of Milts nrv \y<>rt\x lA Nhoo|>, in «lnMip worth 2 
 i»XOt», 7 >'"!<•) «)f MXttii wnifli 'JoH Imv^s, IH |»o.{H vvxifit II t'tiis l>i'uii ; 
 how imuiy hiiNlioU c»f cutH lnu^r hi* ^ivni for l.'l Imiim of hrun / 
 
 2. 8im|)h"fy: | [ : ' I Ij .)f :\'j}. 
 
 'I. A fruitor hnyH iipph's ;it 2 for 3 ooiitH, Aii<i ns many pours at 
 'J for n oi>nt.s. How iii.iiiy niti hn Mull Hull for #1, un uiiuiil iiumliur 
 of I'ueli, ill ordur iiuithrr to ^niii nor I<>ho1 
 
 4. A hoy •••in iif« i 10 (MHily.MtickK at a confiu-tioijor'K oaoh 8 
 iiii-lii'N loi)^, for 'JO (jt'iitH ; or liu fun t<ot a <l<)/,uii Mti<ks of tht; Ndine 
 kind. «'fifh 7 inclus loii;^. for IM ccnfM, (n) In wlmli Uiul had lu> 
 lu'tttsr iiivitnt i (/») If, on II iicitiiin occii.sioii, ho j^.uKud 10 conta hy 
 tlio lu'ttor invostiiuMit, how iimiiy stifkn <lld ho buy i 
 
 tl 
 tl 
 
 5. (^f two nmnhorH .'{ tiiiMs oim in oipi.il to twioo tho other, and 
 m of three timt's the < 
 
 Ul 
 
 11) iiiiin 
 
 an 
 
 'ICi' 
 
 are 
 
 hiTM / 
 
 6. How often will a Imrrow, 1:} feet hy 15 foot, move thoiun^^th 
 of itself in hurrowinj? ;i tithl of 20 nrros ? 
 
 7. A cnhical block of iron, 4 iiuihus to a Hide, woi^dis 40 lbs. ; 
 find tho wci'^ht of n circid.ir disk of iron whoso diunuittT is .'U inches 
 and whoso thiokncsf* is .'U iin'ho.s. 
 
 8. How much sM^ai' at 4, <>, 8 .ind 15 cents a lb. will bo ro(piirod 
 to form u niixturo o* l.S bainls of '270 lbs. oacih, woi-th 10 cts. ;i ll>.< 
 
 '.>. How much pt)r cent, will a grocer s^uin who sells a mixture of 
 If) lbs, tea at 55 cmts a lb., lbs. of which cost <»0 cents a lb., and 
 tho balanco 40 cents a lb. ? 
 
 10. Find the co.st of p.iintiui; a hall-way, OO foot lonj^, JO feet 
 wide, and 12 fitet hi;^h, at 51 cents per sf(. yard, allowing for two 
 doors, each foot by 3 foot, and oiih wimlow 10 fout by 4 foeb. 
 
 11. The cost, gain, and sollin'4 price of an article, together 
 amount to )?5t) ; and the gain, at which it was sold, is 40 per cent. ; 
 find tho cost price. 
 
 i 
 
 n 
 
38 
 
 ■XERCISES IN AUITriMKTia 
 
 ■A 
 
 12. A man sows 10 lbs. tnillct, sood on every 212 sq. yards of 
 Ills moiiiul. Find tho cost of set ding 20acro8wilh millet seed nt 
 81.80 H hiishol. 
 
 13. (fi) TTow n^.'vny hush(>ls .sludled orn are tlioro in a bin 8 feet 
 sijiiuro a(, tho l>?isc, and 10 f(M't high 'i (1)) Divide the L.C.M. of 
 
 r)-25, 25 aii.l 10-d by th.'ir II.U.F (r) Tf boarders (in a certain 
 h()anliiii!,-ho\iso) consipno ^ of a bariolof flour per wei^k, and the 
 liost, at the end of 8 .' 'cks, admits 3 ni;w boarders, what will be tln". 
 amount of the flour bill at i lie end of a period of 13 weeks, tlour 
 being worth $4.41 per barrel ? 
 
 Exercise XXXII. 
 
 1. A stationer bought 138 reams of paper at .1?2 a roam, of which he 
 kept 18 ream.s for his own use. At what price per quire must he 
 Sell th') remainder that he may have his own for nothing? 
 
 2. Soap is bought and made up into uniform cakes, the selling 
 r-Tce p"r cako being the same as the busing ]»rice per 4 ozs. What 
 n ' at be the weight of each cake so as to insure a gain of 6| por 
 ueut.? 
 
 3. Divide $199.36 between AandB in the ratio of '2 : '34. 
 
 4. A grocer buys somo tea at Osh. a lb. and so.uti at 4sh. a lb. 
 In what pro])orti(ui must he mix them, so that, by selling the mix- 
 ture at 5sh, 3d. a lb., he may gain at the rate of 20 per cent. ? 
 
 5. If §of a mine be worth $198,000, find the value of 8'3 of 
 
 the mine. 
 
 6. How many square foot are there in the surface of a cube, one 
 of whose edges measures 8ft. , 4 inches ? 
 
 7. A sold a house for a certain sum, losing thereby 8,^ per cent. ; 
 B sold it to lor 8240, gaining O^y per cent. What did the house 
 cost A 1 
 
 8. A farmer weighed 5 loads of hay on tho market and received 
 a ticket, niaiked 10950 lbs. Tf his wagons weighed 1250 lbs each, 
 and he got .^18 a ton for his liay, how much of his hay ntoney 
 would ho have loft, after buying 661bs. of sugar at lllbs. for a dollar, 
 5Clbs. 2| ozs. tou at 52^ cents a lb., and 80 yards of cotton at 12^ 
 cents a yard 1 
 
 3. A can do a piece of work in 16 days, B can do | of it in 9 
 days, and C can do ;^ of it in Ij days. Ifow long will it take C, 
 alone, to finish the work after A and B have worked together at; it 
 for 3^ days 1 
 
 
FOUKTH CLASS. 
 
 39 
 
 10. A man paid $20100 for a farm at $24 an acre. What will it 
 cost to piiL u foiicu aii'imd it, at 80 cents a rod, and two cross ftiioi'S, 
 niiu lcnL;tli\vi.so and tlie dther <;rossinj^ it at right-angles, <,'ivrn that 
 it is 200 rods wide and thu cross fences cost 65 cents a rod less than 
 the outside fence? 
 
 11. A tradesman earns 40^ cents an hour. IIow many £, Sterlinj^, 
 does he earn in a month, at this rate, workini? 8 hours a day/ (a 
 month = 4 weeks). 
 
 12. A salt merchant sells 500 bhls. salt at $1.40 a barrel, on a com- 
 mission of If per cent. How much does he remit? 
 
 13. (a) Find the average cost jiricv' of HO lbs tea at 60 cents a lb., 
 40 lbs. at 50 cents a lb., and ^0 lbs. at blV. cents a lb. (b) Find tlie 
 L.C.M. of 2^, Sj and 11| ; how often does it contain all these 
 numbers] 
 
 Exercise XXXIII. 
 
 1. A can do a pieco of work in 4 days, B in 9 days, and C in 10 
 days. If §8.30 is paid for the work, how much of this does each 
 one receive ? 
 
 2. A drover marketed ^ of his herd at M. at $80 a head, ^ of the 
 remainder at N. at $100 a head, and the remainder at R. at $90 a 
 head. If he had markotiMl twice as many at N. and half as many 
 at M., he would have gained $800. How many cattle did he 
 market at R. ? 
 
 3. A and B have each a flock of sheep. A lost J of his flock 
 
 \v;tvth $5 each, and B soUl ■^^^ of his flock valued at the same rate as 
 A valued liis, one man losing what the other man realized. If A 
 liad sold his slieej) instead of losing them, they would both have 
 realized, for tlie sheep sold, $300 cash. Find the value of both 
 flocks at this rate. 
 
 4. Bought a quarter-section of land in Manitoba; but land having 
 risen, I sold ^ of my land f<»r what the whole of it cost me. What 
 per cent, did land rise in value ? 
 
 „_5. Simplify f of i^ + i-Hf of lJ + |of fKAxf. 
 
 6. A farmer laid out $2940 in purchasing an equal number of 
 sheep, hogs and cows. Each sheep cost $8, each hog | as much as 
 a sheep, and eacli cow as much as 2 sheep and 2 hogs together. 
 Find the number bought altogether. 
 
 7. Along a certain street, one mile long, there is a house every 
 40 yards, and a tree every 16 yards. How many houses will have 
 a tree in front? 
 
 I; 
 
 M'i 
 
 ;■! 
 
 Hi 
 
 J 
 
 !!i:!i! 
 
 :il 
 
'i! 
 
 40 
 
 RXERCISKS IN ARITHMKI'lO. 
 
 8. The product of two numbers is 5103, and thoir G.C.M. is 9. 
 Find tlieir L.C.M. 
 
 9. Divide 493 into two parts such that } of the greater is equal 
 to ^ of the less. 
 
 10. A grocer tsuld two kinds of tea, the deurer kind at 90 cents a 
 lb. and the chi'uptir kind at 50 cents a lb. lie received $204 for 
 280 lbs., sdld. How many lbs. of each kind did he sell? 
 
 11. A man and a boy, working together, earn as much in 21 days 
 as the boy alone can earn in ()9 days. If the mans daily wages jiiu 
 $1.60, what are the boy "a daily wages ? 
 
 12. Seven-eighths of the selling price of certain goods is ten per 
 cent, less than the goods cost. Find the gain per cent, at which 
 the goods are sold. 
 
 13. (ft) A man wishing to sell his farm asked 141^ per cent, more 
 than it cost hiui, but finally sold it for 6^ per cent, less than his 
 asking price, gaining thL'i'ol)y 11'500. How much did the farm cost? 
 What was his asking price, and for wJiat did ho sell it ? (h) Bought 
 5000 lbs. of coal in Scrantoii at J^O a ^^ung " ton, and sold it in Wood- 
 stock, Ont., at 86 cents a cwt. per " short " ton. What did I gain ? 
 
 Exercise XXXIV. 
 
 1. A can do a work in 12 dayH, B in 15 days, and C in 20 days, 
 
 working alone. If A and C work together at it for 7 days, what 
 should be paid B, who finishes it, given that A, B and C can earn 
 $6 a day when working together ? 
 
 2. A man borrowed $560 at the Ontario Bank on February 1st, 
 1888, at 8 per cent, per annum. He paid back, at a certain'date, 
 $695.84. Find the date on which he returned the money, allowing 
 305 days to a year. 
 
 3. A fifty-gallon cask is | full of wine, which is 83i^ per cent, 
 pure. Twenty per cent, of the contents is then withdrawn, and 
 the cask is filled with water. What percentage of the contents is 
 pure wine now 1 
 
 4. A has 11 times ai^d B 13 times as much money as C, and 25 
 per cent, of the ditference between A's money and B's money is $4. 
 How much money have they all ? 
 
 5. A hatter sold two hats, getting 20 per cent, less for the 
 second than for the first. He lost 1 2^ per cent, on the first, but 
 gained 40 per cent, on the second, which made his total gain, on 
 both hats, 30 cents. Find the cost price of each hat. 
 
 
FOURTH CLAaS. 
 
 41 
 
 6 Wliafc is tho fUfforenco in cost, at 50 cents a square yard, of 
 
 l-iviiig a .S(|iiari' |)l<)t, of L^rniiiul ."»."> yanU to a .si<le, and out; in i\\v 
 f(jnii of a oirclo, .">5 yards in diaiiietei' ? 
 
 7. A and 15 sold potatoes, oaeh niakitii; the same rati' y)(3r C(^nt. 
 profit. A'.s cost 40 cents a l)iisli(d and Ik; sold at 45 cents. IJ's 
 cost 24 cunts a l)uslicl, and a nujrchant hDiii^ht 54 dollars' wortli of 
 j»otatoes from him. How many biisiiels did iie ^et for tliat money { 
 
 8. The interest is ^ of tlie principal, and half the ditl'orence 
 between the interest and tho principal is $.'100. If the timt; is H 
 years, 3 months, what is the rate per cent. ? 
 
 9. If coifee is mixed with 40 per C3nt. of its own weight of 
 cocoa, and 10 percent, of its weii;ht of chicory, wliat percent, of 
 the whole mixture is the coffee ? 
 
 10. What is the value, at $70 an acre, of a semi-circular tract of 
 land whose radius is JOO rods? 
 
 11. Simplify: (u) m + 4h)-^-p, oi .'Prr-l + l^ i%^^ ot ^ I ('>) 
 3H4Ki'V of t^iV-i + l-i'^x fir of 1^ 
 
 12. A boy's ai^e now is one-third of his fatlier's a'jje, but six years 
 ago he was one-ninth of his father's present age. How old is the 
 boy? 
 
 13. (a) A stick, placed vertically down in water, a])pears, owing 
 to refraction, only | of its real length ; find the de|)th of a T)ond in 
 which a stick, placed vertically down, appears to be 14 fe I long, 
 and which exactly measures its depth, (b) A man being asked how 
 old he was, answered : " Tf I were as old again as I am, and half as 
 old again, and 9 years older, I would then be 99 years old." Hcjw 
 old was he ? 
 
 Exercise XXXV. 
 
 1. Paid 1235.20 for the use of $840 at 8 per cent. For what 
 length of time did I use it ? 
 
 2. If, to 6 cwt., 72 lbs. of sugar, 448 ounces of sand be added, 
 what percentage of the w) le mixture is sand ? 
 
 3. A man speculates with i of his income, gives away y^ of the 
 remainder in charity, and banks the remaining $1200, after spend- 
 ing $150 for clothes. Find the amount of his income. 
 
 4. If 28 barrels of sugar and 420 boxes of cheese fill a car, and 
 16 barrels of sugar and 32 boxes of cheese fill I of a car, how many 
 barrels of sugar and boxes of cheese can I ship in two such cars, 
 filling a car with eacli ? 
 
 1:'! 
 
 11 
 
 
 
 -' • i 
 1 
 
49 
 
 BXKRCISFS IN ARITHMETIC. 
 
 5. The sum of tlireo numlicrs is 200 ; and eight times the firat, 
 twice thu HoconJ, and once the third are all equ:il. Find the 
 nuniber.s. 
 
 6. A rectangiiljir court coTitaiiiiiig 2 acros 13 closidy paved with 
 flng-Htnnoa, inches in tliickntss. How in.uiy cords of stone are 
 thero in tlio pavement ? 
 
 7. Multiply 47 acres, 134 sq. rods, 13 sq. yds., 2 sq. ft., by 108, 
 using the factors 9 and 1 2. 
 
 8. A man, owning ^ of a section of land in Shoal Lake District, 
 sold I or his share at $15 an acre. How much did he realize on 
 his sale ? 
 
 9. What is 95 times $ 
 
 3 
 4-f 
 
 ■4+^ 
 
 10. A pile of SO-inch wood is 80 ft. long, 20 ft. wide, and 14 ft. 
 high. What is it worth at $1.80 a cord ? (Sidf nicasurennnt.) 
 
 11. The sum of two numbers is 7fij, and their difference is 46, 
 The larger ninnber is how many times the .smaller ? 
 
 12. By selling a mixture of 300 lbs. of black and green tea at 42 
 cen':a a lb., a merchant lost 142- per cent, of the cost price of the 
 mixture. If the black tea cost 55 cents a lb. and the green tea 40 
 cents a lb., in what ratio were they mixed ? 
 
 13. (a) Find a fourth propoirional in the ratio as 7! 147! '.10; 
 (6) Bought G.'O bags of flour at 81-50 a b;\g ; kept out 40 b.^gs for 
 my own use, and sold J of the remainder at ,$1.25 a bag. For l»ow 
 much, per bag, must I sell the rest in order to gain $120 on the 
 whole lot ? 
 
 Exercise XXXVI. 
 
 1. Find the amount of $450 lent out for 7 years at 5 per cent. 
 
 2. A man put $1(500 into a grocery business, and at the end of 5 
 years witlulrew $2000. What rate per cent, did he realize on his 
 investment ? 
 
 3. In what time will $800 amount to $1600 at 8 per cent. ? 
 
 4. A person can buy a farm for $20000 payable in 4 years with 
 Interest at 5 per cent., or he can buy it for $10000 cash. Which is 
 the better bargain for the buyer provided he can get money at 4 
 per cent. ? 
 
POUKTII CLASd. 
 
 43 
 
 6. A mixture of brandy ami wutor is as 4: 1. How much of the 
 niixtun' must ho drawn dll" and wafor [ml in its place that the mix- 
 ture may contain hiandy and water as 3: 2 i 
 
 (I. A feed nier(!'iant ' ii()|is a mixture of 20 hiishels of pease at 
 70 cents, .'»2 hiislicls of oats at .''5 ci-nts, and 8 Imshels of barley at 
 GO cents a bushel ; tin; mixture increases, in tim ciio[)j.ing, 15 per 
 cent., and he then sells it, by measuro, at 50 c^nts a bushel. What 
 does he gain 'i 
 
 7. One-fifth of the time a man works afc a jol) ho gets 82.75 a 
 day, ^ of the tinu; iirlj,25 a day, and for the remaining threo days, 
 which the job lasts, he gets •'?4 a day. What does he receive for 
 the job i 
 
 8. If a skein of linon nuvkes 16 knots of 110 threads each, and 
 each thread is 2 foot 9 inches long, how many miles and yards of 
 thread will 13 lb.s. of linen make, given tiiat a slu-in weighs 14 
 grains ? 
 
 9. I[ow many tons of bran at $16 a ton should I receive for 
 4500 ivut of lumber at $18 a thousand feet, G480 Ihs. of wheat at 
 $1.05 a busliel, 1720 lbs. hay at $15 a ton, and a pile of wood 100 
 feet long and 5 feet high at $2.50 a cord, the length of the wood 
 being 22 inches ? 
 
 10. Divide 882 acres, 101 sq. rods, 19 sq. yds. , 4 sq. feet, 72 sq. 
 inches l)y 03, using the factors 7 and 9. 
 
 11. If 10 turkeys and 4 ducks are worth $11.20, and 4 turk- 73 
 and 10 ducks ari worth $8.20, what is the value of 30 ducks ? 
 
 12. If a hiborer earns $1.50 a day when wheat is $1.10 a bushel, 
 what should he receive when wheat is $1.10 a cental ? 
 
 13. If a train travel 203 miles in 6 hours, including on an average 
 2 minutes per hour for stoppages, how far will it travel in 9!) hours 
 when 5 minutes per hour, on an average, are lost by delays ? 
 
 B> 
 
 Exercise XXXVII. 
 
 1. At what rate per cent., simple interest, will $1170 bear 
 $31.20 interest in 8 montlis' time ? 
 
 2. A man exchanged 11 t<ms of hay, which cost him $88, for 15 
 sheep at $0 each and 2 pigs at $10 e; ch. What per cent, did he 
 gain by the exchange 'i 
 
 3. A garrison of 7200 men had provisions for 9 months. How 
 many men must vacate the garrison at the enl of six months that 
 the provisions may last till the end of the year ? 
 
 4. If 4| ounces of tea cost 60 cents, what will 29 lbs. cost ? 
 
II 
 
 44 
 
 EXEKOISRS IN AUITn>!KTIO. 
 
 5. A cart, wlieel is 84 iiichoH iti dijiiiititcr ; liow oftoti will it ttiin 
 In gojnjf J I iiiil(!,s ? 
 
 6. Tf fiO Iba. of cutnje, m\d for i?27, K'.iins 12.\ per cent, of t\w 
 cost |»rio(!, find Mincttst prico prr ll». 
 
 7. If 15 men or 'M> wouumi c.ui r»;jip a ficM of whc.it in 'M) diiys, 
 in liovv many dayhi conid (5 men and onu woman ntap ten .sncii 
 liulds / 
 
 8. Sold ])arl<*y at 80 cents a bushel, p[ainiiiL^ 14^ per cent. Find 
 the cost, at tliis rate, ui L'oOO l)\ishels of barley. 
 
 )^f\ 
 
 I 
 
 9. How many lbs. of tea at 4<'i, 50, 75 and 80 cents per 11). 
 respectively, will make a mixture worLli (JO cents a U). ? 
 
 10. Sold a lot for $'.>., 0, Idsini? ^ of the proceeds. Find my 
 ain per cent., had I sold the lot for $1500. 
 
 11. If 10^ lbs. of milk make a lb. of cheese, which sells at 12}, 
 cents a lb., find the value of the cheese made from 5(iO tons of 
 milk. 
 
 12. A salt merchant bouL>ht 5(5 tons of salt at !?8 a ton ; put it into 
 barrels, at a cost of 15 cents a barrel, and then sold it all at Jii^l.oO a 
 barrel ; find his gain. 
 
 13. (a) Find the cost of carpeting a room DO feet 10 inclics, by 
 24 feet 8 inches, with carpetinj,' 30 inches wide, at |1.H0 a yard, tin; 
 carpet to run len^'th wise of the room and 4 inches to bo allowed, 
 per strip, for waste. (6) An agent char Lfcd $15 for selling a sewing- 
 machine worth $76 ; what per cent, on the cost prico did he collect 'i 
 
 Exercise XXXVIII. 
 
 1. What principal will produce $370 interest in four years at 5 
 per cent.? 
 
 2. What will it cost to put a board fence, 5 boards high, round 
 a lot 60 rods long by 220 yards wide, tlie luml)er used being inch 
 boards, 10^ feet long and 1 ft. wide, worth $18 a thousand feet ; 
 the posts 10^ feet apart, from centre to centre, and costing .$50 a 
 tliousand ; and the cost of lal)or, in building the fence, 10 cents a 
 rodf 
 
 3. A can do a piece of work in 10 days, B can do | of it in 9 
 days, and C can do ^ of it in Ij days. How long will it take C to 
 finish the work, after A and B have worked together at it for half a 
 day? 
 
pouuTH rr.Asfl. 
 
 40 
 
 Y 
 
 \. If ii (luiii lost 6 iiiiniit(;s per hour in purfiiniiiiit; n joiinitiy of 
 154 inile.s in 4 hours, lu)\v nmny iMiiiutcs »in hour wouKl it lose when 
 it |Mrt<ituir(l ii journuy of 957(5 niilos in lOchiy.s, iU rutoof travollin;^ 
 ht'iiiL; uiiif<»iiu ( 
 
 5. How much w.itcr must be juMrd fo a mixture of 240 "^mnona 
 of hrundy and wiitcr \ pure, ho 'liul Iho hriuidy may bo 7^ per 
 cfut. of tho whole luixturo ] 
 
 0. How mivuy seconds will tlu-ie be in tho year 1000? 
 
 7. A morchant fails in business, owini^ ^.'{(KlOO. His assets aro 
 827000. What will a creditor lose to whom he is indebted $720 ; 
 
 8. Six persona on a journey of three mouths spenil §.'i<)5 ; how 
 long, at this rate, may persons journey on four times half that 
 sum ? 
 
 0. A pile of 22-inch wood cost 8727.05 at JBl.OG a cor.l. It was 
 180 ft. lour?, 20 ft 2 inches wide, ami 6 ft. high, (a) How was it 
 measured i (h) Which way was it piled 1 
 
 10. At $120 an acre, a plot of ground is worth 84500. Tt is 
 75 rods wide ; what will it cost to enclose it with a fence at 87A 
 cents a rod i 
 
 11. How much tea at 50 and 70 cents per lb., respectively, will 
 make a mixture of 13 lbs. worth $7.50 ? 
 
 12. Pure wine is worth $4.6G§ a gallon. How much w^ater is 
 there in a mixture of 100 gallons worth $382.66|? 
 
 13. (a) A had $17 less than B, and $21 less than 0. He then 
 gave B $5 and C $11. How much money had C more than B then '( 
 (b) If 40 oranges be sold for $1.20, and the gain thereby be 20 per 
 cent., find the cost price per dozen. 
 
 !!•] 
 
 Ii 
 
 I,. 
 
 ■r.it 
 i.if 
 
 
 Exercise 1XXIX. 
 
 1. A boy walks from A to B, a distance of 15 miles. For the 
 first quarter of his journey he goes at an average rate of 120 yards 
 a minute, and for the rest of tlu; way at 90 yards a minute. How 
 long will it take him to perform the journey ? 
 
 2. Bought oranges at 3 for 5 cents, and sold them at 50 cents a 
 dozen ; what per cent, did T gain ? 
 
 3. If § of a herring cost § of a dime, how many herrings will $1.80 
 buy? 
 
 ,1 
 
4d 
 
 ■ZKKCI8B8 IN ARlTmfRTIO. 
 
 4. A taMe, 4ft. Sin. \(>nK^ ''y 2ft. 11 in wide, in covonul witli 
 Canjuli.iti corit |»ioco8 nlucod in rows contimidiis to on«i anotlmr, ami 
 nono toiichinj? nioro than four others. Il each rout pitce iwan irth 
 in diaiimtor, fin«l tlio surface o* thn table that rouiainn unt'ovund 
 by coins. 
 
 6. Sold /tj of my goods at a Iohh of 3.3\ \H)r cent. Hy what in- 
 crease, ])t'r (.xdt., ujiist, I r.iist! thn H((lliii*j prico of the rtMnaindiir to 
 gain 5 percent, on tho entire cost of my ^oods? 
 
 ({. A spcoidator hom^Iit .'VJOO dollars' worth of land at $12.50 an 
 aero. Ho Hold 200 acres of the land at 8'{ an acre, and 5tO acres at 
 ^5.00 an a(;re. At what price per aero must ho sell the remaindi-r 
 HO that his total receipts may be lijual to r)'2l<'»2r) times the cost of 
 his land ? 
 
 7. Simplify: nVx[-! (4J 2^) x(7H2A)-(8i- 3J) + (2,V-V^) 
 
 8. Find the least number that may bo exactly divided by 9, 11, 
 51 and liCt. Find tho sum of the mivend qnolif.nts. 
 
 9. Had a certain sum of money ; spent \ of it, then ^ more than 
 ^ of the remainder, and had still left $2 ; Hnd tho original sum. 
 
 10. An ocrof dealer buys ey^'S at 40 cents a score, aiid sella them at 
 30 cents a dozen. On a certain day, he received $21 for eggs ; how 
 much of this was profit ? 
 
 11. A man lost \ of his money and 15 more, then ^j of the re- 
 mainder all but ."^■5, and still had money enoui^h left to buy OOlbs. 
 lO^uzs. of butter at 37 3t cents a lb. How much money had he at 
 first? 
 
 12. A farmer bought 30 sheep at $8 a head due in six months. 
 He sold ^ of them, immediately, for S12.S cash, and the rest at -^9 a 
 head due in four months. What did lie gain, <! per cent, per 
 annum being allowed off a debt f<)r innnodiate payment in cash ? 
 
 13 (a) A paid $840 dollars for hay, and sold i^art of it for l?405 at 
 
 $15 a ton, uaining, on what he sold, .^81. How many tons did he 
 
 • buy? (h) If 8 bushels of wheat sow 4 acres 80 sq. rods of land, 
 
 what will the wheat cost, for a "quarter-section" of land, when 
 
 wheat is $1.35 a bushel ? 
 
 Exercise XL. 
 
 1. Bought 20 tons 3 cwt. oat hulls at $3.87i a ton, and «old the 
 whole of it out at 20 cents a cwt. Find my gam. 
 
rOUHTII CLAM. 
 
 47 
 
 2. iHvido 270 cocoa nuis jimntj;^ tliroo ))o3'8, giviti'4 tho first half 
 lis many an Ihe Hcuond, und thu third L'O itioro thtin K of tliu re- 
 niniii(h r. 
 
 /V 
 
 ;{. Mow offnn does tho L. 0. M. of 3, 0, 18, 17, 42 and fit con- 
 ain ihu 11. C. F. (.f 18!»!)i; »ind '2Wsi'2 { 
 
 I. Twclvo doll.ii'.s ar»! |tiii(l down for a suit of dot-hos, nnd thi« 
 Ih i of tho pi'icu «»t it. IJi'W many Ija^^.s of ai^ilus, at oO ct'tjls a \y,v^, 
 will pay thu bahmco duo oii it i 
 
 5. A hoii<,dit iMilutoL'S ill 75 ctntn a bushel, and li bou'^dir ajiploH 
 Jit 7- «i!nt.s a bai^. How m.ny bushols of apploH should L5 givo A 
 for 121)0 bu.shilH of potatoes i 
 
 (}. A coitaiu numlx.T (li\ ided by 2, 3 or 0, loaves ronpoctivoly 
 lemainders of 1, I and •!, and thu sum of tho tlir>'(^ quoiicntsU 
 7'.>3. Find till) numl»i»r. 
 
 7 A c(!ttain kind of <,'raiu is $l.f ^ a cwt., or $.70 a bu»hel. 
 flow m.iny ll).s. in a Imshcl of that grain? 
 
 8. Divide !?i.'H.80 anion;; A, B. C and D, ho that A's sliaro sliall 
 bo 8^.70 more than IVs, ami (hut C'.'o'iuro shall bo !:rl0.40 lus.s than 
 
 \'s and ll's toLjcthor, and tiiat D shall havo^o.OD loss than tho com- 
 bined .shari's of A, ii and 0. 
 
 9. 'riio Slim of §12.50 i.s made u[) of fivo-centand ton-cent pieces, 
 thore being JO more livo-eent than ton-cent pioi-cs. How many are 
 there of each? 
 
 10. Find the cost of 208 100 shingles at ^4.80 a thousand. 
 
 11. Find tho cost of 1022 lbs. of oatmeal at fifty cents a stone. 
 
 •G -24 
 
 12. What i.s 40 «( — -f — -I- '325 - '150 
 
 •25 -W 
 
 ■? 
 
 13. (a) 1 buy an article for .1?280 a ton. At what price per lb. 
 must 1 stll it in order to gain 14= iter cent. ? (h) Divide $1150 among 
 A, B and C, so that A may receive /j of tho whole, and that B may 
 receive } an much as C. 
 
 Exercise XLI. 
 
 1. A man after selling •:375 of his farm, had still loft '8 of the 
 remainder, having lo.st, in sjiuculation, 12^ acres worth $70 an acre. 
 How much was his farm w(jrth ? 
 
 2, Simplify : 
 
 (a) H^of ^xg. 
 
 (b) IxKi^crof 'i- 
 (c)lof fxfjj-i-it. 
 
 ^Bfi 
 
 I 
 
 ii.- 
 
48 
 
 BZRKCIHKH IN AKITMMKTia 
 
 .'{. Find tho amount of 9810 for 8 yonrn at 3^ per cent, interont, 
 |)oi' Hiiniuiu 
 
 4. A bicyrlisfc rode from Uo^inM to ('arron, a disfanno «>f 54 n\\\m, 
 at t)iu ralo of H iniluH an hour, il.ilf an hour aft or a lOW-hoy lut'r, 
 lU'^ina on lioischack and ruachud Cair<>n 15 niinutuN bufuru tho 
 ItioyoliHt. t'in<l tho cow-boy'H rato ptjr hour. 
 
 5. What will bo tho coKt of covering wi<h load, a flat roof, 40 
 foot h>tij,', *J1 fi'ot ni'lo, tho load lusin^ ,'(, of jiu inch thi<;k, wuighing 
 702 ll)H. to (ho cubic foot uiid costing 5 uontH a lb. / 
 
 0. Tho (listunco botwoon I \\ lowns Ih 14 niiloH, and <»n a crrtain 
 map tm ir pjaucs aro marked o^ uiohoH apart. On vvhat scalo in tho 
 map drawn t 
 
 I 7. Ilou^ht 8 do/(jii bundlort of gloves of a <lozon oair rach, and 
 *sold tlu'Mi all for !iHi;{82.40, gainins,' :i.\\ per cunt. What did thoy 
 ooHt m«) a pair / 
 
 8. The interest on a curtain sum for 3 years, months at 8 i)ur 
 cunt, pur annum is $7(3.00. What fiaction oi the principal is tlir 
 yearly inturustV 
 
 9. At what rate por cent, will .1^1170 produce $131.20 as interest 
 in 8 montliB t 
 
 10. .\ cart holds 1^ coxl-fout of stono. How many such cart 
 loads of sLono will it takt' t" Wuild 'i wall undt-r a barn 80 foot long, 
 by 48 feet, wide (outsido moasuruinunt.), tho wall boinjjf 18 inches 
 thick and 8 foot high, idlowanco being m.iko for 4 doors each 7' x <>' 
 and ten windows each i' x 3' ? 
 
 11. A ton of bricks measures 20.83 cubic foot, and a brick is 
 8 inches long, 4^ inches wide, and 2^ inches thick. How many 
 bricks weigh 13 t< ins ? 
 
 12. In .i ccmxposition of puio air, oxygen is to nitrogen as 1 ; 4. 
 How muci' por cent, of pure air is tho nitrogen it contains ? 
 
 13. A .sets out on foot at 4 miles an lioiir, at 7 a.m. ; B sets out 
 '2b per cunt, faster, i)er hour, than A at 10 a.m. ; and C, on hor.suback, 
 at 12^ miles per hour at 2 p.m. At what o'clock will C be midway 
 between A and B i 
 
 Exercise XLII. 
 
 1. Two bicyclists, A and B, going 18 and 12 miles an hour, 
 resijoctively, start together from the same point at the same time to 
 go in the same direction roinid a circular course 101 rods, 13i feet 
 in diameter, (a) In what time will A overtake B ? (6) How far wilJ 
 A have riddea ? 
 
 t 
 
 P:/ 
 

 fOtfKTn CLA«»i. 4t 
 
 'J. If 12 in.n i\n "* of !i pior^ of work in 20 dnvHof 8 hmirn oiich. 
 Ill wlidf titnn woald 20 iiujii do 2r» Liiue« na inuoh work, working 10 
 
 luillfH ft <lflV ? 
 
 l\, F'r<i|»M*iy in ;ihhi<«so<1 at two Hiirdn of its hmI VHln»\ft!ul n iimii 
 who owiiM ;i f;irm, Mio o 'rmtrof which in within Mu» lunitH of a town, 
 piVH \l milU on fhi' <h>n(ir for townshi|. rates, Jl rouiity rftti"«, ^* 
 \viit<'r riitiis, 'J'l rti!ho.(l riti'M, i\ y.iH r;itt'H, iin-l li railw.iy niton. 
 \Vh;it (loc'H hu pay on hi.s ])rup> riy, tiiu real valuu of which iii 
 
 I. A ran mow O.v- r(»s in 12 days, B ran mow lo iicros in 21 dayn. 
 fn iiow many days ooiihl thi^y both, worUini» to;^ether, mow 10 acroH, 
 SO rods i 
 
 5. If ir» OZ.H. of whoaf HOW 1 Sfj. rod of lund, wliat, will it cost u^ 
 Manitol»;i firmer to 8ow a Hertitm of land wh<n whi-at is 90 conta ir 
 huHhol / 
 
 r». IIf>w many fons, Ihs. and w/.^. of ion are thc.rci on a cinMdar 
 poiid, fro/-<'ii 7 iiuh<'-t thi'-k, it the (li.im''lor of the puml bo 84 rods*, 
 ind the ice wci-^di j",t as much as wator? ( tt = 3}). 
 
 7. A can win fi"m li 10 ujamos of marbhis in 30 games played, 
 and B can win fi'om C 5 i^mukss in 10 played. How many games 
 could .'\ win fron: in .'JO liames played? 
 
 8. Hou'^ht .'IcUJO llts. of apples ('uiidried) nt 20 cenhs h biishol^and 
 sold them at iivo-nir.tliH of a cent a, lb. What per cent, did I gain? 
 
 9. Sold a house for S'J 100, u;nniii',' 12j jut eeiit. of tin- proceeds. 
 Mow mneh would 1 have received [><i' it, had I lost 71 per cent, of 
 the cost ? 
 
 t 
 
 JO. What would be the cost of carpotinc: a room, 53' 4" by 42' 8", 
 ivith carpeting .'{2 inches wide, running Iciigthw'so of the room, if 
 le (iarpet co.st $ 75 a yard, and 8 inches bo allowed off each strip in 
 matching ? 
 
 11. If 6 oxen eat m much as cowi, and 150 bushels of barley 
 food 15 oxen for 48 days, how hmg can 108 cows be kept for §182.40, 
 when barley is 70 cents a busiiol '{ 
 
 12. A speculator bought a block of land, 140 chains long and 55 
 chains widi-, at .S'oO a perch, lie then sold 20 per cent, of it at 
 §-'45 an acre, and th9 remainder at ^\iO an acre. What por cent, 
 did he gain or lose ? 
 
 I ;. If $14.40 is the interest on $120 at fi^ for a certain time, at 
 what rate per cent, is $34, the interest on $340 for the same time ? 
 
 Mt 
 
 i; 
 
60 
 
 IIRIK'IHKI lit ARITHMRTtO. 
 
 E.teroiHe XLIII. 
 
 1. A mnn bnuglit w!i it l»o ,sii(>[nmo<l wnn twi'iityfnur clolUrt 
 And ui;{lity ('ctitN* wnrlli • t ioii t\t Mi ctintH u ll>., Init tiiu (.'t'ocui hud 
 UR*'il A \vri</lit of 15^ ntiiH on for u lb. in wi iu'liiiijj thu ten. (a) 
 Wliiit (lid till) nu'icliiiiit ^ain in nionuy? (/>) What pur (.•••nt. did 
 thu cuMtoiih>r loNo ? 
 
 2. Ifuw iMiiiiy ^ullonit will a tniik, 8 fo<>t Hciimro nt tho hiiHO nnd 
 fuut duop, liuld '/ 
 
 M. flow iiiHiiy Umn of ('".il, ftt f5 n, ton, must I mix with 1*2 tonii 
 ^ at $8 u toll, HO that, by Mt-ilinu thu mixturu at ^7 a ton, 1 mny givin 
 25 pur cent. ? 
 
 4 A farmtn* has n hiii, ol font loni^ 4 fout hi;jfi», mid M f<ot wide, 
 '%till<'d with outs. Wiifit. ato thuy wui'th at 34 ouiitti a Itutiiiul? (1 
 cub. foot.— 25,', 11)8.) 
 
 5. Si.xfci M IIh. of iiotlV'fl -it lOcentHrt Il». wuro mixtxlwith \ IhH. at 
 66 coiitN a 11)., find tho ini "luio Nuld ut lo.v',; ounts u Ih. Kind tlia 
 gjiin por cent, at whi<'h tiio mixture wuii Holil. 
 
 6. A corn crib, <1 fui^t wido at tho top and .T ftot wido at the 
 bottom, 10 ft'ct h)ii</ and 8 Wwl hi','li, in lilii-d with corn oii tho cob. 
 What is it wortli at 25 cunU a luiiiliul { (1 cub. foot =■ 22 lbs.) 
 
 7. Dlvido 81140 amoti;'; A, B and in such a maniior that 4| 
 tiniuB A's shaiu -— 1^ tiiiu;3 lis Hhaio Ct wharu. 
 
 8. Tfow mudi ooHc(f ;d 40 cunts a lb. must T mix with 5 lbs. 
 chicory at 25 cunts a lb. U> mako a mixtuio wortli oO cunts a lb. 1 
 
 9. A whol(ysalo and \\t.u\ merchant deducts 20 por oont. from 
 his rt't-ail price in sclliiiv, a rotuilur an iiivoico t)f gooda. If tho 
 retailer gain 40 pur cunt, in retailing hia goods, what por cent, 
 advanco on thu whulosalo niurclw.nt'H retail price doos he sell his 
 goods i 
 
 10. A reduction of 20}^ on tho cost price of epofs onalilos a buyer 
 to pui'cliasu IM) do/, more cgg.s for S18 than ho could, before the 
 vediutioii. Find tiio price of eggs per doz., both before and after 
 the reduction. 
 
 11. A Kauri-pino tree yields 0520 feet of hnubor and 200 lbs. of 
 Kauri-gum. it' liimbor i.s wortli %?24 a thousand, and gum 5 cents 
 an oz., lind tho total value of the tree. 
 
 '2iV 1 rj 35 
 12. Simplify: ■{ — of | of 240V^-^— + 
 
 ■I 
 
 ]■ 
 
fOITRTn n.AM. 
 
 •1 
 
 l.M I Hnrtif \ of my iiionoy aikI tl»r«« floMnr* tnor«», wht«n I hml 
 ■till lut't (j of my iiionny ult but » ilollitr. How mu(!li moiioy hud I 
 at tirnt ? 
 
 ExeroiMo XLIV. 
 
 1. A mnp oorrM'fl f.'l Sl< rliiiij in 5 ili\> of tfii Iionrn rnoli. At 
 thin rutu, wiiiit vvoiiM lialt u <luy n m<i,{(*h bn in dolt. ii.s and cuiiInI 
 
 2. BiiMplify : 
 
 3. In wimt timo will Bi^tO umount to Si;()7.r)0Ht5 por cent. 
 Hitnplu intuK'Ht Y 
 
 4. A, It and G lo<.!<-tliur huvo ^270. B litis g uh much nioiiuy lui 
 0, and for uvt'iy >5l.r»() tlwit A Ims, U uul C togctlior liuvn iBlll. 
 iluvv niui'li uuMuy li.is each ( 
 
 5. IIow ui.iny boys, i-ach dninj; ^ of a nmn'n wnilv, niust be 
 ompioyid with '.>',) u.> n lo do in J 'J dav < whatilli luun could do in 20 
 dttya ? 
 
 0. To ft certain nuinlxr 5 is addtMJ, nnd SO por cont. of tho result 
 is tlii'Ti sulitr.K-tcd ; to the r('ni;iiii<li<t' ir> is added and 5 pur 
 cont. of tho ro-.ult is sulttracted, leavinj^ '.♦.>. What is tho number? 
 
 7. Eij,diteou ehi'piers a^Tee to have a contract of wood cut in 
 40 dass. Wilt II ,' ot till- contract is lini 1; d, <> of tlio men lo.ivo ; 
 how Miucli moro than an avor.i^'o day's work will bo ru(piired, on 
 the part of oach of tho rouiainin;,' niou, to finish tlio contract on 
 timo 7 
 
 8. Tf ft liariol of whito-fisli costs 810, ho^v iiiiieh will 3 do/.t.n of 
 tho ii.sh, oach weigliin<{ 2 lbs., 2 o^s., cost y 
 
 9. What sum will amount to 82250 in 4 years at 5 per cont ? 
 
 10. What will it cost, at l'^ cents a h(\. .yard, to |>aiiit Iho walls, 
 ceiling and lloor of a rin»m 42 feet, (J in. ion^, .*>(> fcit, M in. wide, 
 and 15 feet high, an alhjwanco of 1075 sq. feot, UO sq. iiichos, being 
 made for doors, w indowj and baseboards ? 
 
 11. A man borr<nvod 8500 at tho IJank of Ontario, on Fob. Ist, 
 1888, at 8 por cent. ])er annum. lie rotunit'd the Bank, at tlio end 
 of a certain time, $51)5.84. Find tho time when ho returned it. 
 (3C5 days =1 year). 
 
 I 
 
 'it 
 
 
52 
 
 EXERCISES IN AUITIIMETIC. 
 
 f'i 
 
 12. A tank can be liiilf filled by two t;i|».s, A un<\ B, in I In mi', 12 
 minutes, unci it can bu lilhal by ]J alon*- in O JKuirs, or t'ni|ttiu i by a 
 tap C in 2 lionrs. I'lio liiniv is ompty ami A is optnuMl for 40 min- 
 utes. A is ilicn clost'd and H is o|). nud for 3 hours, w In-n thn taps 
 are all oponr'd. In wiiat r,imo will the tank bo rmptiud, afr-cr all 
 the taps are openeil^ 
 
 13. A debt of .^200 is paid in francs, valued at Jr' cents each, at 
 a time when (I^ francs are wortli $1.00. What does the creditor 
 gain ur lose t 
 
 Exercise XLV. 
 
 1. 0, who earns 50 cents an hour for ei^jht hours a day, can earn 
 as much in 8 days and 2 hours, as A and li together can earn in 6 
 days of 10 hours each, and A earns 20 i>er cent, more wages than B. 
 What sum would all thrcjo, together, earn in \'A weeks, working 9 
 hours a day ? 
 
 2. The Savings' Bank pays 4 per cent, per annum, and U de- 
 posits $32 at the beginning of the yo.U' ; .SiS umre at the end of 
 three months ; $25 more at tlie end of six nionilis ; and i^oO at the 
 end of 9 months. At tlio end of tlie year lie witlidraws it all and 
 invests the money in an enterj)rise. ])ayiiig 35 per eent. yearly. 
 Row much will he have at the end of (> years from the time when 
 he put the first money in the Savings' Baidc 'i 
 
 3. A man bought 80 sacks of bran of 80 lbs. each at $10 a ton, 
 and paid for it with apples at $1.60 a barrel. How many barrels 
 did it take ? 
 
 4. If 13 geese or 7 turkeys cost $9.10, what will be the value of 
 42 geese and 13 turkeys ? 
 
 5. A man walks 860 yards in 8 minutes, 
 in Qfoing 180(5 miles ? 
 
 How long will he be 
 
 6. A fisherman buys codfish at 8 cents a lb. and sells it out at 
 $12 a cwt. ; find his gain per cent, 
 
 7. A breAver has a vat 30 ft., 9 in. long, 16 ft., 8 in. wide, and 6 ft., 
 4 in. deep, filh^d with beer, which ho wishes to put into quarter- 
 barrel casks. How many casks does he require, given that a cubic 
 foot contains 25 quarts ? 
 
 8. The circumference of I lu; hind and fore wheels of a carriage 
 are, respectively, 16^ and lo| ft. How far has tlie carria^e gone 
 when the hind wheel has made 1536 revolutions lean than the fore 
 wheel ? 
 
FOURTH CLASS. 
 
 A8 
 
 9. A person travelled 1440 miles by water, rail and stafje. The 
 distill K^e by statue was ^ that by rail, and the distance by rail was 1^ 
 that by water. The cost of travelling l)y water, rail and stage was 
 as 2 : .S : 5. Find the cost of the journtjy, given that an equal 
 iiinnl)er of miles, by (-ach mode of travelling, averaged 3^ cents a 
 mile. 
 
 10. A rectangular court is 240 ft. long b}' 45 ft. wide (outside 
 measurement) and a })ath of the uniform width of 3 yds. runs round 
 it on the inside. Find tlie cost "f paving the patli witli Hag-stones 
 at 80 cents a stj. yard, and the remainder of the court with turf at 
 §1 50 a hundred sq. feet. 
 
 11. If four men can do as much in a day as 7 women, and 2 
 Women as much as four boys, and 7 boys working together for 8 
 days earn 5544, wliat will be the earnings of 8 men and 6 women 
 working togetlier for 70 days ? 
 
 12. A freight train is U) miles ahead of an express which travels 
 at the uniform rate of a mile in 1 min. and 15 seconds. It is run 
 into in 40 min. How many miles an hour was the freight running? 
 
 13. What is tlie value, at 81.60 a cord, of all the 18-inch wood 
 that can be closely piled 6ft. high on J of an acre of ground 1 
 
 Exercise XLVI. 
 
 1. If 20 of A count for 12 of B, and 45 of B count for 29 of 0, 
 and 20 of C for 9 of D, and 6 of D for 100 of E, how many of E 
 count for 150 of A ? 
 
 2. If 40 apples = 2 dozen oranges, and half a dozen oranges = 9 
 pears, and 28 pears = 2 lbs. coti'oe, how m;iny apples are 72 lbs. 
 of coffee worth 'I 
 
 3. If 50 lbs. of dates are worth 80 lbs. candy, and 6 lbs. candy 
 are worth 5 lbs. figs, what is the value of a lb. of dates when figs 
 are 30 cents a lb. i 
 
 4. If £6 = 40 thalors, and 25 thalers = 93 francs, and 27 
 francs = 5 scudi, and 31 scudi — 67-i gulden, how many gulden 
 ■= £210 lOsli. ? " • , 
 
 5. If 4 horses cost as much as 6 cows, and 9 cows cost as much 
 as 30 sheep, and 45 sheep cost §810, find the value of a car-load of 
 17 horses. 
 
 6. If 4 lbs. of tea be worth 40 lbs. suyar, and 16 lbs. sugar be 
 worth 3 lbs. coffee, and GO lbs. of colTee be worth 240 lbs. biscuit, 
 how many lbs. of biscuit would 20 lbs. tea buy ? 
 
 i 
 
54 
 
 KXER0ISE8 IN ARITHMETIC. 
 
 7. If 10 horses cm move as much an 6 mules, and 4 mules as 
 much !\H 1 ol>'i)h;int, and 4 t'lcpliants as niiiuh as 130 men, how 
 many horses Wf)uM move as much as 15(5 uion ? 
 
 8. If '>0 bushels oats = 15 bushels wheat--, and 5 biishels wheat 
 = 9 buslii-ls pisasc, and I'J bushels poa^o =^ HO bushels rye, how 
 many Ijushels of oats should bo <'xoliani,'oil for 2J0 bushels rye? 
 
 9. Fire per cent, of a certain sinii and Uiree per cent, of another 
 sum amount to s"14.()5 ; but when the pvr cents, are interchanged 
 the amount is $17.75. Find the .sums. 
 
 10. The m.ip of a ciirtain country is dr.iwn on a scale of | of an 
 inch to the mile. What area on ihe map will represent a lake 
 whose area is IGOOO acies ? 
 
 11. Find the total cost of 17 tons of o.its at 50 cents a bushel ; 
 800 cwt. of wheal at .^1.11 a bu.^hel ; 40 cliains, 3 rods of ditching at 
 ^2.40 a chain ; and (55 tons of Won at 5 cents a lb. 
 
 12. A vintiier mixed two kinds of wiii'>, wortli resi)ectively *3.H0 
 and S4.20a gallon, in such pro])ortioii that by selling the mixture 
 at $b.i)0 a gallon he niade a profit of 421.- per cent. Find the pro- 
 portion in which the wines were mixed. 
 
 13. (a) A man sold 13 fowls for .*!10. 10. There were as many 
 geese as cliickens, and twice as many turkeys as ducks. Find the 
 number of each sold, given lliat a turkey sold for 81.10, a goose for 
 80 cents, a duck for 50 cents, and a chiel.i ii for .'Jo cents. (6) From 
 £10 lOsh. 8d., take -{ (^ of i of j''o)-T-/,r \- of $&2.bi)ij. 
 
 Exercise XLVII. 
 
 1. What is the G.C.M. of f, ?, |^, and ^1 
 
 2. Is a fraction a number, and why ? 
 
 3. When must the following note be paid at the Bank of Mont- 
 real, and how much ready cash will redi em it ? 
 
 S^GOOOO. MoNTiiJiAL, Que., Juno 13tli, 1889. 
 
 Fiightcen months after date, I promise to pay Samuel Collins 
 or order, at the Bank of Montreal in Winnipeg, the sum of six hun- 
 dred dollars, with interest at the rate of six per cent, per annum, 
 for value received. Thoimas W. Tame. 
 
 4. An inn-keoper buys 10 gallons of spirits at 82.40 a gallon, 15 
 gallons at 90 cents a gallon and 18 gallons at $1.15 a gallon. At 
 what price per galhm must he sell the mixture to gain $8.45 on 
 his outkiy ? 
 
 5. Simplify : l\ of 6^ + . 
 
 lA i of ^ 
 
FOURTH CLASS. 
 
 65 
 
 6. Divide 82464 among A, B and 0, so that A's money put out 
 for a year at 7 per cont., B's at 5 ptT cont., anil C's at 3^ per cout., 
 will each accuniuliito tiie same yourly interest. 
 
 7. Make out the following l)ill : 
 
 2 barrels of fish, ('»() doz. each, at $1 a dozen. 
 14 lbs. raisins at 13 cents a lb. 
 
 10 lbs. bacon at J8 cents a lb. 
 
 3 cheeses, 70 lbs. each, at 12 cents a lb. 
 180 CLfgs at 13 cents a dozen. 
 
 600 lbs. sugar at 20 lbs. for $1. 
 
 20 lbs. 4 ozs. butter at 20 cents a lb. 
 
 5J ozs. ginger at 54 cents a lb. 
 
 8. Thirty-iive women can do as much work as 20 boys, and 16 
 boys as much as 7 men ; how many women can do the work of 33 
 men ? 
 
 9. Bought cherries at eight cents a quart and sold them at $3.37^. 
 cents a bushel, by which 1 gained $34.23 ; find the number of 
 bushels bought i 
 
 10. Find the cost of 85 tons, 1060 lbs., of pease at 45 cents a 
 bushel. 
 
 11. What will it cost to fence a lot 60 ft. front and 60 yds. depth 
 at $.87^ a foot? 
 
 12. Bought barley at 60 cents a bushel, and sold it at $1*5625 a 
 cental ; what was my gain per cent.? 
 
 13. (a) Fifty per cent, added to a number, and 40 per cent, of 
 the result added to that, gives the number 1764. What was the 
 original number ? (b) What must be the width of a box 4 ft. long 
 by 3 ft. deep in order to hold ^ of a cord of cordwood ? 
 
 Ill 
 
 Exercise XLVIII. 
 
 1. An estate is divided among A, B and C, so that A has ^q of 
 the whole estate, and has 4-i times as much as C, who has 17800 
 acres less than B. What is C's share worth in dollars at £15 
 Sterling an acre ? 
 
 2. A, B and C agreed to dig a well 80 feet deep for $112. At 
 the depth of 30 feet A left, and at the depth of 50 feet C left, and 
 B finished the digging alone. How should the money be divided 
 among them ? 
 
 3. The map of a county is drawn on a scale of 6 inches to a 
 mile. What area on it will represent a township of 36000 acres ? 
 
 
 :; 
 
56 
 
 EZKKCISIS IN AUirUMKTiO. 
 
 i. One vessel, A, contains 30 gallcMis of wine ; another vessel, B, 
 contains 20 irallons of w.itor. Five gallons are taken from each and 
 poiireil into the other Thia is repeated tlu-ee times, llow much 
 wine and how much water will the vessels then rtsijectively contain 'f 
 
 5. By selling |j| of my shoep for ^2(iOO, I gain 25 cents a head 
 more than by selling them for $2437.50. How many shoep have M 
 
 6. A had $10 less than B, and B had $4 less than C. A gave 
 i*>() to B and $8 to C. How many dollars had C more than A then '. 
 
 7. A sum of monty was divided among A, B and C, so that A 
 received f of the sum ; B $10 more tlian \ of what was then left, 
 and the remainder, which was 4 times B's share, was given to 0. 
 Find the sum and the share of each. 
 
 8. Reduce to its simplest form : 
 
 2 
 2 
 
 ( 
 
 2-1 
 
 2 + lJ 
 
 n 
 
 f 
 
 9. A bin is 40 feet long, 10 feet wide, and 4 feet high. How 
 much more or less will it cost to fill it with oats at 40 cents a bushel 
 than to till it with potatoes at 50 cents a bushel 'i 
 
 10. A dealer buys pork at $4.20 a cwt. ; at what price per stone 
 must he sell it to gain 25 per cent. ? 
 
 11. A lump of lead is b inches long, 4 in^-hes wide, and 3 inches 
 tliick ; what does it weigh assuming it to be 8 "64 times as heavy as 
 water ? 
 
 12. If 4 men and 5 boys earn $54.50 in 5 days, and 6 men and 7 
 boys earn $47.70 in 3 days, how much will 6 men and 6 boys earn 
 in 6 days ? 
 
 13. (a) Find the number of steel rails, each 22 feet long and 
 woigliing 20 lbs, 4 ozs. per foot, that can be made out of 112 tons, 
 5;i2 lbs. of steel. (6) Fvora £(| of | of 21f) Sterling take $62.40, 
 and invest the balance in cotton at 4 cents a yd. 
 
 Exercise XLIX. 
 
 1. k bin 8 feet long, 4 feet wide, and 4 feet high, is filled with 
 wheat. Find the value of it it at $1.20 a bushel. 
 
 2. A gives B 6 yards the start in a race of 206 yards. B gives 
 C 20 yards the start in a race of 100 yards. How many yards 
 could A give in a race of 515 yards t 
 
FOURTH CLASS. 
 
 «7 
 
 3. A Bpeculator boucrht a numher of horses at SfiO a head, and 
 '.> times as many sluje)) at ^~) a head. |)ayin'_' fiT the lot .SIHOO. Had 
 hi! hoiiLfht the whole nuitihcr at^l'J a lu;ad all round, lie would 
 have paid $*iO K ,s.s than li' di<l. Find the n\nnber of each bought. 
 
 4. Thor.' are four casks of ditforent si/os. The first is full of 
 water ; tlie rest are toujjty. The second is filled from the flrst 
 loaviu'^' the tirst }f full ; thc^ third is then filled from the second, 
 leaving the second ji full ; the fourth is then filled j^ fuIi from thf 
 eutii'i' eontents of rjie thii'd. The third and fourth casks, toi^ether. 
 hold 5 gallons less than the tirst. EIow many galh»ns does the 
 second ca;}k hold ? 
 
 5. A certain sum amounts to $733,20 in 6 months, and to 
 S789,60 in eighteen months, at simple intoroat. What is the ratt; 
 per cent. ? 
 
 6. What number, diminished by | of f of itself, leaves a re- 
 mainder of 580? 
 
 :h 
 
 7. The sum of two fractions is 1,^1 ; one of the fractions is ^ ; 
 find the (piotient of the greater divided by the smaller. 
 
 ^ of 2t H 
 
 8. Square the quotient of ■ -. 
 
 6| of i\ 9 
 
 9. Trees are i)lanted, 7 feet apart, around the edge of a circular 
 pond, having an area of -^^M ^^^ '^^^ acre. Find the number of Lrees 
 required, (ir = d^). 
 
 10. Sold a lot, which cost mo $800, gaining 11| per cent, of the 
 selling price ; and also a second lot, Avhich cost me S700, gaining 
 12^ per cent, of the selling price. Find my gain or h)ss per cent" 
 on the total investment. 
 
 11. If a lump of gold 18 carats fine, contains 81 ounces of alloy. 
 how many ounces of alloy are there in a lump of gold of equal 
 weight, only 14 carats fine ? 
 
 12. How many times does a wheel, whose circumference is 18 ft. 
 4 in., turn in going the distance of 27^;^ miles ? 
 
 13. How much tea, worth respectively 60 and 70 cents a lb., mtist 
 be mixed with 50 lbs. , worth 84 cents a lb., in order to make a 
 mixture worth 75 cents a lb. ? 
 
 1 
 
68 
 
 EXERCISES IN ARITIIMBTIO. 
 
 Exercise L. 
 
 1. A person asked, for a lot of limd, 40 per cont.. more than it 
 cost him ; l)iif finally roducod his prico 15 por cx-nt., gaining '>u the 
 wholo lot $1!)U0. For how much did hu sull tlio land t 
 
 2. Simplify :\ ^ x 41^ U -^ x 202»o \. 
 
 ( 3iJ 8} J l(;;iof8-|-4Hof5 + 5^.of4 J 
 
 3. The quotient of two numbers i.s H7'.), and 6 timoH tho smaller 
 number is 40476 ; find tho greater number. 
 
 4. Find the cost of 3G60 lbs. cranberries at $2 a bushel. 
 
 5. Find tho cost of 30 bushels dried apploa at 16 cents a lb., 
 and 5628 ll)s. of dried peaches at ^8 a bushel, 
 
 6. Make out tho following bill : 
 
 13 dozen hinges, 4 lbs. each, at 8 cents a lb. 
 
 45 gals, seal oil at DO cents a gallon. 
 
 25 gals, coal oil at 11 cents a quart. 
 
 90 dozen lamp wicks at 2 cents each. 
 
 45 yards wire screening at 25 cents a yard. 
 
 20 scoro bolts at 30 cents a dozen. 
 
 7. If 20 per cent, be gained by selling a horse for $210, what 
 per cent, would be lost by selling it for Ji;?! GO ? 
 
 8. A man sold 3(> bushels of flax-seed at 8 cents a lb. How 
 many boxes of figs can he purchase, with tho money received, at 
 $4.50 a doze 1 boxes? 
 
 9. A retiil tradesman professes to charge 20 jier cent, above the 
 wholesale price;, but he has adulterated his goods with 25 per cent, 
 of au inferior kind, costing (mly half as much. Wliat is his real 
 rate per cent, of profit ? 
 
 10. Find all the prime factors of 0349, 4500 and 6400. 
 
 11. What is the sum of all the prime factors of 172800? 
 
 12. Two men start t<> go round a circular racecourse, 1197 rods 
 in circumference, one at tlu rate of a}, and the other at the rate of 
 7 miles an hour. IIuw long .vill it take each one to make the 
 circuit ? 
 
 13. Find the total cost of GOO lbs, rape seed at 55 cents a bushel ; 
 380 lbs. red-top grass-seed at $5 a bushel ; 1700 lbs. lime at $3 a 
 barrel ; 960 lbs. millet at $4 a bushel. 
 
FOUKTII CLASS. 
 
 Exercifle LI. 
 
 59 
 
 1. Thn't) p;ra/,iers, A, H Jind 0, hire a p;isturo for tlioir common 
 us(! for vvliii;li tlioy pay >lL*t. A puts in !) lioi-sis for 4 montlis, B 
 12 colt.s foi" months, ;iu(l C >< htr.itjs for 5 iiitiiths. How much 
 oi the rout shoiiM eacli pay, 2 horses Loiir^ < <[iial to 3 c.!>lts '< 
 
 2. What is tlio cost at 5 conts a s(piaru yard of |iainting the 
 roof of 1. l)arii, each side of which is 00 feet long ami 24 feet wide 
 from the eave to the riiij^e i 
 
 ^■■j:;;;^ 3. Simplify •' of J -j- 9 of U x t ^ f of W- 
 
 4. A shaft, ".)() feci deep, is sunk through the olny, san<l and 
 rock. Two fiiut moi't' ihaii \ ot the distamio through the rock is \ 
 of tiie distance throU';h the clay which is ;'; of the disLaiico through 
 the said. Find iho distance tlirough each stratum, the distance 
 through the clay and sand together hcing 72 feet. 
 
 6. If 4 smiths e.irn as mucli as 5 fitters, and 5 smiths earn 
 $135 in 15 days, how long will it take 13 titters to earn $243.30? 
 
 6. A person begins to distriluite -14.50 among a number of 
 children, giving each one 50 c<nts ; but, aftei- having given this 
 Kum to the half of them, he timls that he has enough money left to 
 give the others each 54 cunts, blow many were there in all \ 
 
 7. Divide the L. C. M. of 24, 48, !>(>, 120, 42 and 72 by the 
 G. 0. M. of all the eucH numbers between 241 aiul 247. 
 
 8. If 2 men cut 10 cords of wood in 2 weeks, how long will it 
 take 1 2 men to cut 40 cords ? 
 
 9. (ct) Name the two kinds of fractions, and stivte the diflerence 
 between them: — (/>) Coui])are rhe dillcrt.'iice between the two kinds 
 of fractions, with the diiieienco between the {Sim[)le and the C'om- 
 p(mnd rules of Arithmetic ; (c) Simplify : — (i.) i + | ~ if + i^ff-H 
 
 •2- -m 
 
 of 3-27 
 
 •0043(i 1 
 
 .5; {d) (i.) Divide the diflerence 
 
 ^"•^1-3+ 02 
 
 between twenty hundred hundred, and nine hundred and ninety- 
 nine hundred and ninety-nine l)y eleven; (ii.) Multiply 20 ac, 
 85 rods, l9 yds., by 15, and divide the product by 5. 
 
 10. If % of a ship be worth \ of her cargo, and half the difference 
 between them be Ji$ll500, find the value of the ship and her cargo. 
 
 11. It costs 838 "40 to carpet a room 24' x 16', with carpet of a 
 certain quality. What will it cost to carpet a room feet longer 
 and 4 feet wider with a carpet of the same width, 20 per cent, better 
 in quality ? 
 
 iM 
 
 1 1 
 
 t i 
 
 i^ii 
 
 J: 
 
60 
 
 UXKKCmF^ IN AKlTilMKTIi;. 
 
 12. Divide 91640 betwoen A und B, ho tlmt A'a ttliure in to Its 
 UH 3 : 5. 
 
 13. A qujinfity of cofToo lias chicory iiddnfl to it, so tlmt tlio 
 cliicory is Jj of Mie wliolit iiiixtiim. It the mixture is \v(»rfh 'M cents 
 u Ih., and thu c^hicury 8 cuuIh a lb., what is tho prioo pur lb. of the 
 
 l»iiru CO 
 
 fr(;o1 
 
 Exercise LII- 
 
 1. A mMi, having a farm, sold part, of it;. He then hou^'ht 
 7 times as much liuid a.s ho sold, whdu hn t'niiiid Im li;r<l I IJO .■k tch. or 
 76 nor cent, more land tlum he had at first. How much lai.d did 
 he buy ? 
 
 2. If I buy Hi.\ busliels of raHpherrioM at .f 2 a bushel, and sell 
 them a^ain at 8 c^jnts a lb., what do I. gain po5; oeut., asHunmig that 
 a quart of berries weighs l\ lbs. 
 
 3. Simplify : 
 
 n-i'H+^-n)><'^ 
 
 109 
 
 7i-(3Hil)-Ux^ 416 
 
 4. How many lbs. of tobaoco at (!0 cents a lb. must a, tobacc<mi.st 
 mix with 3 lbs, at 80 cents a lb., in order to luake a iirotit li' lij pur 
 fjent. by selling the mixture at 75 cents a lb, i 
 
 5. What is tho financial standing of a man who owns -i ^ - \ + 
 ^-^y of ^270? 
 
 <). (a) Find the H.C.F. of 5080. 4015 and oWJ. (/>) Find the 
 i J.M. of 20, 01, 180, 240, 95, 133, 380. 
 
 7. A and B build a wall in 45 days, and B does one-third of 
 tho work that A docs ; how long will ii take each to build it? 
 
 8. Find the value of : 1596 x -472 -v- 2'7. 
 
 9. If 10 per cent, be lost on a horse sold for $90, what was the 
 cost of the horse ? 
 
 10. How often does a hoop, 2 yards, 10 inches in circumference, 
 turn in going 4 miles ? 
 
 11. A bookseller sells 7000 copies of a 1}ook at $2.14, and takes 
 in exchange a note for one vear for the amount. What would he 
 gain or lose by selling them instead for cash at. Ji;<l.80, interest 
 being at 7 per cent, per annum 1 
 
 12. A room, 11 feel high, is half as long again as it is wide, and 
 its cubical contents 4708*5 feet. Find its length and breadth. 
 
POIIRTII CLAM. 
 
 61 
 
 I.J. (/») NVImt will it rosf,, i\t (H* .•••nN .1, |.. ivli, fo put a w.ill 
 t> feot U\<j,\\ under a hirn, 56 fett l"ii'.; l»y •"••i n;(r, wi.lf, the wtxii 
 \u''\uf IS iiirh.s Hiick, .iiid the ooiii. TH liomu oounti'.l liorh on tlio 
 HiiUiTm'! »!iil ,v;ill't, hut iiu (ill-'W'.itict) of Inilf l.tMH'4 minle »'< u- 5 doors 
 yiK'li H it. by I 0. <» in., and 1'2 wimlow.s. each .'J ft. hy 2 ft. «» in., ft 
 pfich heiii'4 lii.'i .Milii.- fcMjt ^ '[h) l(ift<'.I a notr \vh<»Mi' fac' v;ihie 
 w.is ?:«."{:iO, au'l \vhit:li liad heon n^ iiitorest fur 7;; .liiy- a.l 8 (ht r.-nt. 
 pur Hunuin, in order t(^ pay a grocery bill of ii'SA^). What had I loft 
 out of blio procoods of my nobo after paying tho bill ? 
 
 Exercise LIII. 
 
 1. How mtich per cwt. is 76 contn a, bushel for wheat ? 
 
 2. What is tho value of ^\ of a pit of apples, if ^^ of it be worth 
 
 3. Find the total value of 4 piles of cord-wood of tho following 
 dimensions ;it, .^4.12.\ a cord : (n) 20 ft. lon^, 12 ft. wide and 7 feet 
 iiigh ; (h) 3:1 fr. \>—l 8 ft. wide and 6 feet hi-h ; (0) 45 ft. long, 21 
 ft. wide and !> feec hiyh ; (</) 140 ft. h>iig, 12 ft. wide and 5 ft high. 
 
 4. Find the cost of a strip of carpeting 8 inilo!*, 40 rods long and 
 2 ft. G in. wide, at 04 cont.s for 10 .s<j. feet, 
 
 6. It jl of a loaf of bread wuii^diing 16 ounces is worth 2 cents, 
 
 what is bread \v<>rth a lb.? 
 
 6. A tisliernian had 32 totis, U20 lbs. of trout to barrel. Re 
 used 2^ Ib.s. of salt to each barrel of fish, wliich he sold at $6 a 
 l)arrel, net. Find his gain, if tlie tish cost him 2 cents a lb. 
 
 7. Find the cost of 440 lbs. of charcoal at 15 cents a bushel, and 
 7210 lbs. of bituminous coal at 26 cents a bushel. 
 
 8. A man exchanges 7200 lbs. of potatoes, worth 45 cents a 
 bushel, with another man for 9(50 lbs. of apples at 75 cents a bag, 
 and the balance in money. How nmch money did the latter 
 receive ? 
 
 9. What is the value of 3l'06 lbs. of orcliard grass seed at $2 a 
 bushel, and 1428 Ih.s. of blue grass seed at 75 cents a peck? 
 
 10. A man bought Ui ton.s of lime at $7 a ton, and sold it again at 
 99 cents a Ijarrel ; tind his gain. 
 
 11. A corn-crib, ft. wide at the top and 5 ft. wide at the bot- 
 tom, 24 ft. long, and ft. high, is filled with corn on the cob. How 
 many bushels does the crib contain ? 
 
 ,1. 
 
 ■\ 
 
6t 
 
 rXFRnSKfl IN ARITII JETro. 
 
 12. A bin is 45 ft., .". inches lonj,', ft. wido un<l 1 \ foot <loop, nnil 
 iH <livi(l<'(I info tiiruu ()(|iiiil coiMpnrtrntints (hy puiH.i.xis) Uio (iirtb of 
 which is lill«!(l with whciil. Hu socoiul with outn uii<l t\w tliinl with 
 potfitofs. Kinil tho viijiii! of I ho ontii.> hiii. wlu-n \ hunt is 80 i-ontM. 
 outM ^1 cunts (iiul I il.HtuoH ri'Ji'fiit.s H hiislirl, 3 iuciiott buiug ailowud 
 oll'thu length of tlu) hin for tliu purtlHons. 
 
 l.'i. A drover boiiii^ht un niiiil nii .ibti- of shcnp and h"{,f8 for 
 $1482 ; hi) \fi\v ) $7 fur a 8h< cp and leSO fur a hog. ilow many of 
 tiuch did Ito buy 1 
 
 Exorcise LIV. 
 
 1. A mui lost Oil p.ir c<nt. of his proporty in an unfortunate 
 Hp'ciiliitinn. lit! Lh(^ii iiiVL'stcjii ."iJ-Tmio;) in .1 fill .11 wh'i-h routed for 
 $'2f*{) por an»iiiiu, .ind put, tho rtiii iiniM'4 ^tlOOO ..f lijs property ont 
 at intonat, at (> por *«'iit. per uiiniini. Jiy Ii<>w iniirh in liis inoonio 
 Ijsh pur .'uniuni tiian it would li,iv;i lie ii, had ho put it ail out at 
 interest bci'or j lie wont into Hi>eculation ? 
 
 2. I gained $705 in a wotk n the hiIo of gooda, marked por 
 cent, above cost. Wiiat vaUio in goods '1 >l I Ht 11 tliil. week? 
 
 3. Sini^.lify : (a) ^ of § -4- 1? + i*(j x § - ^ ^ 1? of 3 ; (f>) } -r 
 §of 1? + /oof §-^^l#-r3. 
 
 4. Ten Mien can do | of a ])ii3C0 of wok k in 2 days. Eij^lit of tho 
 men woik .■•tit for 5 days, wln.n lh<n' aro then joined by tho other 
 two niun. How long did the work last 1 
 
 6. Two hoys and a man coiitraot to do a certain work In 8|| days; 
 but the man vvol•l<,^ ahmu :.,t it i'oi 4 days heforo tlio bi'ys 'oiu liim, 
 and the contract occupies 10^ days. In what time would a buy have 
 done it working alnio i 
 
 6. I* § of a barrel of apples is worth 00 cents, wlu'.t is the price 
 of 200barrils? 
 
 7. Divide $840 betveon A and B, so that as often as A gets $4, 
 B will got $3. 
 
 8. If T*r of a choesa is wcth $4, what is the vahio of it? 
 
 9. Divide the least of the following fractions by tho greatest : 
 
 10. Find the compound interest on $650 for 3^ years at 8 per 
 cent. 
 
rot'ltTII CLASH. 
 
 63 
 
 11. TTow m.iMy ItMrroln of iloiir ut c<5 ii barrol ilmuM bo rroi>lv«Ml 
 fur ;{74() ll).s. (tf o.itH (It ;i5 I'. riiH u liinlifl, .f-'lHJ ll.s. wln-.if iit 81. 1" 
 u l>tis|ii>l, 5(0 11)8. cluvui'-Ni!c«i lit 3<( 00 u buhliul, niid 510 lbs. uf liout' 
 ut iii$lU a cwi.? 
 
 H X i + i -5- '4 ( ) 
 
 12. Simi.lify : - (,», - I) x /, of |>t H- g . 
 
 13 (a) NVli.it will it cn«t to t'-'ml 10 lioist » on oiitn for wiokM, 
 ^ivin;,' tMoli Imrso •'{ pfiks il;ii!y. wlirri i cits mi) wmMIi .'17^. ii'iits ii 
 hiislifW {!>) IJoiight, 10 jjjrtiMs ptiiiils ut .'{emits n «ln/.i'ii ; miM [ of 
 tlitiin ut 4 fur 5 cunts, uiul tliu rust ut for lU contM ; linil my ^ lin. 
 
 Exorcise LV. 
 
 1. A und n woro p:irti'<'rM in u l»ii.siiitss in which thoy i,'!iiiM«<l 
 !?:>•'.'{. 15. A put, ill .>::^.su(M'.ir '.t months, ;mhI I'. <10 p.r cent-,. «.l' iho 
 oniiru (.Mpit.il tor it months, llow should t!i(jL;:iin he t.iirly •lividr^U 
 
 2. Whiit multiph- of 150 <livith<l l.y 18 will </wv 225 us «iuoticnt/ 
 
 3. At whut rate, Kimj>lo inturist, will u sum hccoinu 4 tinu's it.sclf 
 in 40 yi !irs 'I 
 
 4. llovv numy sohliors will consiitno 2tiO tons, 1000 Ihs. breud in 
 4 Weeks, giving; Cii(;h man 11 unncus of bruail ilady { 
 
 5. Sold 72«;0 Ihs. poaso mi 78 .'oiits u huslu-l, 2100 ll^s. npplos at 
 75 Cents a bushel, and h(iii;.;ht citttoit with the prtH-ceds hit, after 
 losing 88 (tents. Find the number of yards bunyht, cotton being 
 12^ cents u yurd, 
 
 G. If (54 livndia cost 8448, what will u flock of 4 score bo worth 
 at the 8;imo rate '/ 
 
 7. Sold two houscj, ge':tin,r,' \:i '^^ much for tho second as for the 
 first. On tho first I gained I.") per cent, and on the second 1 lost 
 20 i)er cent., hising on tho whole .^10. I'ind the cost of each 
 house. 
 
 8. A box, 8 feet long, 7 foi't wide anil 5 feet hii^h, iis filled with 
 shelled corn. How many bushehi does the box contain ? 
 
 0. A wagon-box, 14 feet long, 3 feet 2 innhes wide, and 11 
 inches deep, is lilled with dry saml ; what is the weight of the load 
 in tons and lbs. ? 
 
 10. Find the L.C.M. of 8, CI. 128, 70, 4, 3, 18. G4 ; and the 
 Il.C.F. of 4123, and 351386. 
 
 11. Find the cost of 6 bales of hay, 430 Iba. each, at i§12 a ton. 
 
 ! 
 
 y 
 
04 
 
 ixriirrMKii m ARiTiiMKrir. 
 
 12. If j of nn (voro <>f lund will priKltiou 171 I'U^hoUof poUtovii, 
 wh'it will 2 lu-vm prtitliicu 7 
 
 IM. (,i) If <itti-2425 in tliu o<>Ht of 0910 lU. of Imy, wliut ih Imy a 
 toil ( (b) A boy inkim l.'(20 NtopM, unoli 2 fout incluM l>)ii){, iii 
 ^oiiiK roiitxl a nrtaitgiilur tiuUl 00 ro(U loii^ ; how i.niiiy iioruM ilotH 
 thu lluld ciiiituia i 
 
 Exercise LVI. 
 
 1. How oftiMi it the L.O.M. of (} uf |^) and (} of ^) oouUiiiud 
 ill X 9 / 
 
 2. A our forty fout long uiid nix fuot widu Ih loiulud to thu dfpth 
 of four foot, Hix iiicht'N, with iiiiiiuriil uoul. How iiiiiny toim aru 
 theru, HNMiiiiiiMg u cubic foot to cHituiii u bunhul of coal I 
 
 3. A cyliiidriciil tank, 8 fout in diuuiutur, is hilc) with plastering 
 hair, to Hii> dupih of ncvou leut. If a cubic foot cmitainH 10 IbH. of 
 hair, huw lumiy buHliulH of luiir arc tituru in thu tank / 
 
 4. Fill in tho followin;^ HtateiiKMit of Hovon wo«'ks' cuHh ruofipkH, 
 and piovu ihc corructncsti of your work by adding horizontally 
 and vurtiuully : 
 
 Days op Wibk. 
 
 WEEK. 
 
 MON. 
 
 TUK8. 
 
 WKD. 
 
 THUR. 
 
 FRID. 
 
 SAT. 
 
 iHt. 
 
 2nd. 
 3rd. 
 4th. 
 5th. 
 <)th. 
 7th. 
 
 805.01 
 54. 3<) 
 
 81 .27 
 
 r.1.77 
 
 81.29 
 29.04 
 40.01 
 
 888 04 
 71.29 
 29.82 
 80.41 
 44.82 
 03.84 
 28.42 
 
 «I41.82 
 30.42 
 26.71 
 
 2i.8(; 
 
 87. ".»1 
 27.<18 
 72.84 
 
 833.00 
 84.70 
 21.90 
 90.82 
 21.44 
 80.02 
 27.34 
 
 $«44.18 
 03.19 
 21M4 
 81.20 
 24.33 
 30.81 
 27.42 
 
 $29.41 
 80.24 
 24.71 
 30.82 
 20.07 
 
 %1.71 
 64. J3 
 
 TOTAL. . 
 
 
 
 
 
 
 
 TOTAL. 
 
 5. If clieesu is 9,1 } per cent, of tho milk used in its m.anufacture, 
 how many tons of ciioosi! will 42000 lbs. of milk [)roduce ? 
 
 6. Find tiio cost of sowing a field of 18 acres with wheat at 90 
 cents a bushel, if it requires jj of an oiuuie of wheat for every scjuare 
 yard of land. 
 
 7. If 4i of (A - i A) =3^ (B + i B;, what is the ratio of A to B ? 
 
FOUKTII CLAM. 
 
 «5 
 
 8. A mnn !>«<]iicf»fTn»d S'l'H'X) to liin fumily. H© iffivf* f<> hii 
 Mifoj of his |ir<i|Mit V, hiilf of ilto r"tiirilii«lor to Uin hum, uml tliu 
 runt li** <1 vidiMl iMiiMlly uiiioiig hJN tlu'uo duiiglitcrs. Find thutimru 
 
 of cHi'll of tllU iliili;{llti)rN. 
 
 0. Find Miu cortfc 
 
 (,f \ \ ll»t. of tm at 8 -70 H lb. 
 
 I 2.^ 1 
 
 .., 9^ - r» + ft*r + ii«T - A . 
 
 10. Siiholify: 1. 
 
 (* + iS) X a - «) 
 
 1 1. Kiii'l tlio oost of 18 tons, M'J.'t Hh. of huy ut $15 n ton, luid VM] 
 liii.sliuU of potntotiN at 15 ct*nts a pock. 
 
 12. A niiin lioii^rht 27 cowh ut )£|^(().7o n hoiid, nnd piiid for thi<in 
 with 't.'lM l)U.sli«!ls, ir> )))s. wheat (it >-l.rj^ a buHliul, ami tho ruat in 
 uaHh. How iiiu(!li cash di'l ho p'ly 7 
 
 13. Hoii'^ht thr*'() Ikixoh of Muap, cwh cotitalninpfan FtJ'^lish cwt. ; 
 k«*; t it all Miniinici', diinni^ wliich tiiiiM it dri< d iiwuv j in utMj^dtt. 1 
 tin II sold it at 13 cuntii a lb. Find my gain, if thu Ht)a|> ooHt uio 23 
 cuntu for 3 iba. 
 
 Exercise LVII. 
 
 1. A flock of Hljno[i, worth !?M a head and 8120 in nionoy, were 
 takon in oxchanj,'"- tor 2 horses wortli .'^ILM) a head and 8 cows worth 
 25 pur cunt, as much pur head aa a horae. How many shoup wuru 
 in thu tlo k ? 
 
 2. A person owned \ of J of a imirket-gardon, and hdM 50 per 
 cent, of his ri^'ht for $;J5. What was tho vahuj nf tho garden at 
 tiiis rate / 
 
 3. Tho proooeds of a debt of .St)8.50, given into tho hands of an 
 attorney to coUect, auioiujted to i^lM.oO fur tho creditor. VVliat per 
 cent, did tho attorney take for his services? 
 
 4. Wliat is the value of the hay in a mow, 70 feet long, 34 feet 
 wide and 18 feet deep, at J? 10 a ton ? 
 
 5. A bin 20 feet loiifj by feet wide is fdled with potatoes to 
 tho depth of 5 foot. What are they worth at 75 centa u bug i 
 
 6. Simplify: \ \ + \ . 
 
 7. A field of hay 'ik 40 rods long and 20 rods wide, and averages 
 1 ton, 14 cwt. per aero. What is the crop worth at $'J.GO a ton { 
 
 4 
 
 ' i 
 
 ¥ 
 
 -i 
 
 t 
 
66 
 
 KXUKCMSISS ly AlllTHMHTlC. 
 
 a. Sold 00 louvcs of hi'oi'l for .i?4.20, wliich wad U'J cunts luss than 
 cost. Find tlio ui.st [)i'ioo of lOO loaves, 
 
 'J. Find tlio II.C.F. of ;JI und 1472 ; and thu L.O.JVI. of all the 
 prima nnniburs from 'JO I to 22i). 
 
 10. Find tho cost of a pilo of cord-wood 3IJ foot long and 5 feet 
 lii^di at >>">.81 |)or cor<l, and also tho c(jst of a pilo of eiyhtcon-inch 
 wood, 75 foot lon^^ and 1) fut-t high, at §1.00 a cord. 
 
 11 At what fraction of tho cost prico aro goods marked which, 
 when lowered 20 por cent., still leave a profit of O5 [»er cent. ? 
 
 12. Bonglit a piece of property for>ii!)()00, andagn'ed to pay for it 
 in I) montliH with intercjst at (5 per cent, per annum. What amount 
 will bo duo at the expiration of that time ? 
 
 13. (a) A piece of ground, 88 rods long, contains 22 acres ; find 
 tlie cost of fencing it with a straight rail t'onci', the rails being 12 
 feet, inches long and costing §15 a thousand, tho fence to bo 6 
 rails liigli and 1 foot, inches, per rail-length, lo be alloved for 
 ovcrlap[)ing, (/>) IJi.iiglit 70 lbs. of tea for i?:>l.50 ; sold it, so as to 
 gain 87. Had I bought to the value of .$81, and sold it at the same 
 price per lb., what would I have gained l 
 
 Exercise LVIII. 
 
 1. A stationer gained 'r^ of the purchase money on pens, sold at 
 6 for 10 cents. What friijtlon of the purchase money would he 
 have gained by selling 8 pons for 10 cents ? 
 
 2. It required $31.20 to redeem a n(jte, given seven years ago, 
 with interest at 8 per cent per annum. What was the face of the 
 note ? 
 
 3. Simplify : (a) Hj^. (b) ^^ of ^\ of 2^. (c) Add the results 
 of (a) and (6) togcMier. 
 
 4. A stream increased 40 per cent., in volume, dtu'ing a freshet. 
 What per cent, must it then decrease to be again at its former 
 volume ? 
 
 5. A cut, I of a mile long, 00 feet wide and 20 feet deep on an 
 average, is made through a clay hill ; find the weight, in tons, of the 
 earth removed. 
 
 6. A block of marble is 9 feet long, 4 feet wide, and 8 inches 
 thick ; find its weight. 
 
 7. A man spent J of his money, then i more than f of the re- 
 mainder, when he found that he had still left $16. How much 
 money had he at first ? 
 
 <: 
 
 
FOUKTII CLASS. 
 
 6T 
 
 8. A man bou^'lifc turkeys nnd 12 i,'(!Ose for .?10.80. Tf each 
 g<)()St3 cost oO coiits, what was (ho cost pncu of tho tiirkoys? 
 
 0. A, wlio has JMst, .sold !^ of lii.s fann fo f^, iiuM-oasirn^' tlio latfrr's 
 land prnj)orty 10 ;^. has now 210 acres lesa than 13. W'liat is the 
 vahio of both farni'i at 870 an acre ? 
 
 10. A i»lot of ground, ."»(»'> foot lon-^ and 1M2 foot wi(h!, ha.s a 
 woodshed (!0 foot h»ni( and 1(5 foot wido Uiiilt on it, which can ])o 
 filhid to the hi';i,'ht of 12 fcu't with cordwood. If 20 |>er cent, of 
 tilt! plot, not occupied hy tho shod, is clo-icly [)ileil ^vilh cordwo(xl to 
 a depth of 4 foot, what fraction of the pile will till the shed i 
 
 11. 'J'ho G.C.M. of two nuniljcrs h ^^ ; their L.C.M. is 42 ; one 
 
 2 \ 
 
 ; what is tho other number? 
 
 of thenun\l)ers ia 
 
 1 + 
 
 3 + U 
 
 12. If a road is 1 chain, 50 links wide, Imw many miles of 't will 
 contain 240 acres ? 
 
 13. A stock-rais'T found that by sell ini^ his horses at 870 a head 
 ho gained half as much as ho woidd have hjst at 810 a head. Find 
 his profit on every 100 head of horses sold. 
 
 Exercise LIX. 
 
 1. If 1 can have tho use of 870:).Oi) for 5 years for 8210.00, what 
 will the usii of 80OO.OO cost me a year ? 
 
 2. One bricklayer charges 82.40 a day of 8 hours : another 
 charges 83.00 a day of 1) hours. Which had I lietter emi)loy, and 
 what woidd T save, by emjtloying the clu'a])or man, to do a job of 
 work lasting six weeks, working 5 hours a dry i 
 
 3. Find the L.C.M. of : 
 
 1-fofi 
 
 9^1^ 
 
 and 
 
 2|x^ 
 
 ir 
 
 01 
 
 1-^of^ 8i^x2,7^ .. ^ 
 
 4. If 15 men require G5 days to mow 300 acres, how long will 3 
 men require to mow 315 acres ? 
 
 5. Find the cost of ])apei-ing tho walls of a room^ 20 feet, 9 
 inches long, 11 feet inches wide and 12 feet, 3 inches liigh, with 
 paper, 22h inches wide, at 15 cents a yard. 
 
 6. A borrows 8150 for whii-lihe pays :':'2.25 a month. In what 
 time will the interest thereon be GO per cent, of tho principal? At 
 what rate per cent.? 
 
 d 
 
 i 
 
 'I 
 
68 
 
 EXBKOISICS IN ARITUMETIO. 
 
 7. A bushel of coarse salt \veii,'lis TiO lbs., and a salt, mercliaiit 
 buys 13 tons of salt for $180, wliicli he sells again at D cents a peck ; 
 find his gain per coiit. 
 
 8. A gentleman's income is 5 per cent, of his capital. He pays 
 annually 5^22.50, at 1^ per cent., as an income-tax. What is his 
 Ca[>ii:il ? 
 
 9. A merchant in New York bought 20 quintals of coffee in 
 Guatemala tor which lie was to payi%560. On weighing it, however, 
 lie found each quintal to be 5 lbs. short in weight. Wiiat should 
 he pay for it 1 
 
 10. If 7 lbs. of tea and 4 lbs. of coffee cost $7.00, and 3 lbs. of tea 
 and 7 lbs. of coffee cost };^4.85, what i.s the value of 12 lbs. of each? 
 
 11. At $70 an acre, a farm is wortii $5950. It is 170 rods long. 
 What will it cost to enclose it with a fence at 70 cents a rod ? 
 
 12. If 6 men, 10 women or 15 boys can do a work in 33 days, in 
 what time will 30 men, 30 women and 30 boys do the same work, if 
 they all work together at it ? 
 
 13. One-fifth and ^ of a number increased by 8 is equal to half 
 the number ; find the number. 
 
 Exercise LX. 
 
 1. A wagon, loaded with hay, weighs 38 cwt., and the wagon 
 alone weighs 960 lbs. ; what is the hay on it worth at $12 a ton I 
 
 2. A farmer sold 3 pits of potatoes, consisting in all of 700 
 bushels, for $306. The first pit sold at 35 cents a bushel, the 
 second at 40 cents, and the third at 50 cents. How many bushels 
 were there in each pit ? 
 
 3. Simplify : ^ of l-j- 1 X 11 + J of /^ of |2 + h 
 
 4. Bought (MO yards cloth at .$1,372 '^ y^^'^^ ; <'2| yards at $1.28 
 a yard ; and 4G| yards at {>x.92 a yard. At what price per yard 
 must I now sell it all in order to gain 14j^jj2^ per cent, on the 
 transaction ? 
 
 5. Find the L.C.M. of (^-f iHf) ^^^^ J+H^-|)- 
 
 6. In an election 15 j\ per cent, of the voters refused to vote. 
 Of the total votes in the (dectoial division A got ^\, and was 
 eUeted by a iw.tjorlty of 500 votes over B, the defeated candidate. 
 How many votes were polled for each ? 
 
FOURTH CLASS. 
 
 69 
 
 7. A pives $i.S7h for bnin ;it §15 a ton, and B givos 85.82 for 
 sciino at <iO c«3iits a cwt. What fraction of a ton does one got more 
 than tho otlior i 
 
 8. Find thu T.i.C.M. of fill tho even numbers between 41 and 101. 
 
 9. A and B a^rood to dt) a ])ii'ct! of work for $62. A worked 12 
 days of 8 hours tiach, and B worked '.> days of 10 hours each. How 
 much of the money should each receive^ 1 
 
 10. If a bushel of vviieafc makes 40 lbs. of flour, how many barrels 
 of flour can a miller put up out of 127 tons, 17 cwt., 80 lbs. of 
 wheat ? 
 
 11. A barters GO busliels, 48 lbs. of beans at $1.60 a bushel ; 26 
 bushels, 14 ll)s, rye at 80 cents a bushel ; and 7200 feet of lumber 
 at $15.80 a thousand, with B, for a village lot wortli $ri8.01 per 
 acre. Find the size of the lot. 
 
 If 
 
 12. Simplify : -6 of 3-3 + — of 1^ "4 of 5-75. 
 
 13. The interest on a certain sum of money for 3 years at 7 per 
 cent, is less by $39.20 than the interest on the same sum for 7 
 years at 5 per cent. What is the sum ? 
 
 Exercise LXI. 
 
 1. If 3 horses, 4 oxen or 5 cows can be pastured for one month 
 for $4.80, what should be paid for pasturing a horse, 2 oxen and 3 
 cows for 5 months ? 
 
 2. A person owning § of | of |f of a factory which is worth 
 $39000 sells I of his share, what fractional part of the factory has he 
 left, and what is it worth ? 
 
 3. If 40 women do a piece of work in 20 days, in how many 
 days will 15 men do the same work, the work of 6 women being 
 equal to that of 3 men ? 
 
 4. A and B rented a farm together ; they grew 850 bushels of 
 grain, which they divided in such a manner that f of the number of 
 bushels A received was equal to | of the number of bushels B re- 
 ceived. How many bushels did each receive ? 
 
 5. Tom has $400. Ho gives away § of his money and then ^ of 
 tho remainder. How much has he left ? 
 
 6. How much hay can I buy with $35 at the rate of '25 of a cent 
 
 for 3 ozs. ? 
 
 .1 
 
70 
 
 EXKRCISES IN ARITIIMKTIO. 
 
 7. If 1 bnshol, 20 Ihs. of wheat will sow 1 Jiore, 80 sq. rods of 
 1,111(1, wliftt will the who.'it cust for 'J.7 Jicros of IuikI at §1 OlL'o pur 
 hiishol ? 
 
 8. What will bo tlio cost of l)iiildiii'.( a stono dyko 80 ft. long, 10 
 fL wide and 15 ft. hij^h at IG^'j pence. Sterling,', ]Jor perch? (a perch 
 -■=l(i.\ cubic ft.) 
 
 9. A inerchant lost ^ of his capih-il and then giiincd $500 ; after 
 which ho was worth l;?2i)00. How much did he lose ? 
 
 10. The sum of 4 numbers is 2 ; tlio Hi-st nuiubor is §, the second 
 is 5 of ° of ^2^ ^"^^ the third ,^3 ; liixl the fourth. 
 
 1 1. A man buys an article and sells it so as to ^nin 50 ])er cent. 
 If hu liaci bought it at 20 p'cr cent. K'ss and sold it for $5 less, he 
 W(juld have yaiued 7 1 }, per cuiit. Fin.l the coat price of the article. 
 
 12. A boy buys oranges at the rate of 4 for W cents and soils 
 them at the rate of for 5 cents. How many must he buy and sell 
 again to make a profit of 80 ceats? 
 
 13. (a) By selling cloth at $1.90 per yard a merchant lo.ses 5 per 
 cent. What per cent, docs ho gain or lose by .selling at $2.20 jier 
 yard? (h) One bell tolls 5 times in 8 minutes, and another bell 
 tolls 4 times in 5 minutes ; how often will they toll together in 18 
 hours? 
 
 Exercise LXII. 
 
 (1^ ) 
 
 1. A man owing < — + 2} of 1^ - 4| + 2J > - ?[!- of a mine 
 
 sold out ^ of his share by which he decreased his property $00,000. 
 H<nv much was the mine worth? 
 
 2. Divide $1280 among A, B and C, so that A may have three 
 times as much as B, and that C may have as much as A and B to- 
 gether. 
 
 3. Two lbs. of tea and 5 lbs. sugar together cost $2 ; but if tea 
 were to rise 25 per cent., and sugar were to rise 12^ per cent, in 
 price, they would together cost $2.45. Find the value at this rate, 
 of a barrel of 300 lbs. of sugar. 
 
 4. What will carpeting, 30 inches wide, at $1.15 a yard, cost for 
 a hall GO feet long by 8 feet wide ? 
 
 5. How many flag stones, each 2 feet 2'4 inches square on the 
 surface, will be recjuired to pave a rectangular court-yard, 60 links 
 long, by 45 links wide ? 
 
FOUUTH CLASS, 
 
 71 
 
 \i 
 
 C. Finrl tlio fdlliwiii'^ Mil of proditco : — 5SS lbs. dried poafhes 
 at 81-20 ii l)iislicl, 8 Itiislu'l.s of craiilxrries at 3 cotits a lb., 7 c\vt. 
 of onions at .S'» a busliul, *> l.a.slu;l.s (;f timoiliy .soeil at 5 cunts a lb., 
 (•<) lbs. of p!irHni[is at 81.50 a bushel, and 7-* lbs. of new potatoes at 
 Four cents oil' the d(jllar for ca.sh. i''ind amount 
 
 i^ I. no a ba<^ 
 
 7. How many dollars will a tract of hind, 75 chains scjuare, cost 
 at t'lO (Sterling pur acre ? 
 
 8. A room. 7"^ feet lonq;, CO feet wide and 10 feet hi-^di, contains 
 2 doors each 7 i^uut Ity 4 feiit, (J windows each 5 fuct, inches, l»y 4 
 feet, and one window 2 ft. stpiare. How many yards of paper 2 ft. 
 wide will be required to cover its walls i 
 
 0. A seed merchant bought one-eighth of ,» bon of orchard grass 
 seed at .^7 a bushel, 2 cwt. of En-lish blue grass seed at $15 a 
 l)ushel. ITe mixed it and sold the whole at 60 cents alb. Find 
 his gain per cent. 
 
 10. Divide 8^2.84 among 12 boys and 15 girls, so that each girl 
 may have twice a.s much money as a boy, and lind the share of each. 
 
 11. A barrel holds somewhere between 42 and 48 gallons. It can 
 be filled by an exact number of 3 or 5 quart measures. Find its 
 capacity in gallons. 
 
 12. Wh'jn an ounce of gold is worth §18.75, what is the value of 
 •38 of a lb. ? 
 
 13. What relative quantities of sugar at 7, 8, 11 and 14 cents a 
 lb. must ])e sold, in a mixture, in order to realize an average of 10 
 cents a lb. ? 
 
 Exercise LXIII. 
 
 1. Simplify V,} of I of 8^ of 2^^ of 2^ of ^i:,. 
 
 2. Hay is V orth $8 a ton and lambs are worth ^4.50 a head. 
 How mucli hay should be given for 144 lambs '{ 
 
 3. A mail, af |-.er paying 3 cents on the dollar of his income and 
 spending §1.20 a day, is able to save $823 a year. Find his annual 
 income. 
 
 4. A tradesman adds 40 per cent, to the cost price of his goods, 
 and allov,'.s his customers a reduo'ion of 14^ per cent, off their bills. 
 What per cent, profit does he still make ? 
 
 5. A bought 20 hogs from B at $4.50 a head, and 80 from C at 
 $4.75 a head. He then sold 75% of his entire drove to E at $4.80 
 a head. At what rate per head must he then sell the remainder, so 
 as to gain $150 by the transaction ? 
 
 (Iri 
 
 \^ 
 
72 
 
 EXERCISES IN ARITFIMKTIO. 
 
 6. Two men travelled a corUin distance on bicycles. The 
 drive-wheol on one is foet in diaiiuitor, and tho (Irivtj-wluu'l on 
 the other is 7 foot inchcH in diamutijr. How fai* are tlioy on tho 
 road will n the drive-wluiol on tho Hmallor niachiiio has made IJ.'UJO 
 rovolutiona more than the drive-wheel on tho larger? 
 
 7. A rootangular field, whose lonLjth is to its breadth as 8 . 7, 
 contains .'i5 acres. What will it cost to enclose it with a hedge at 
 Jiill.20arod? 
 
 8. A can do a piece of work in 2 days and B can do it, in 3 days. 
 In how many days can they both working together do ^ of ir, ( 
 
 9. If the divisor be ^ of the quotient and 6 tinit'S the reniaind(!r, 
 and twice the half of the sum of the three be 1008, find the 
 dividend. 
 
 10. A rectanpjular plot of ground, 20 rods long and IG rods wide, 
 is .surrounded by a gravel walk 12 foet wide, and on the outside of 
 this walk a platform, 20 feet wide, is built of two-inch plank, sur- 
 rounding the grounds. Find the value of tho plank, in the plat- 
 form, at $25 a thousand feet, inch measure. 
 
 11. The less of two numbers is {^^-t-^} + \V^)i '^"^ their difleronco 
 is ^ 10J-(2^-f §) ^ ; what is tho greater number/ 
 
 12. If the time past noon is f of the time till midnight, what is 
 the time 1 
 
 13. Find the areas of the folio win.; annul i whose radii are re- 
 spectively : (a) 18 and 17 inches ; (6) 26 and 10 inches ; (c) 57 and 
 50 inches. 
 
 Exercise LXIV. 
 
 1. The diameter of a circle is 14 inches ; find its area. 
 
 2. The circumference of a circle is 66 feet ; find its radius. 
 
 3. The area of a circle is 2464 sq. yards ; find its diameter. 
 
 4. The radius of a circle is 24 yards, 1 foot, 6 inches ; find its 
 area, 
 
 5. What is the area of a circular plot of ground whose radius is 
 112 yards 1 
 
 6. Find the area of an annulus whose radii are 80 and 60 inches 
 respectively. 
 
 7. What ig the volume of a a solid cylinder 7 inches in diameter 
 and 28 inches long ? 
 
rOURTn CLAS9. 
 
 73 
 
 8. Finrl, fo twu (lecini.il places, tho area of a cirolo 28 inclins in 
 iliaiiiotor t'roiii wliicli a tiiuiigjilur piece, IG inclies to u sido, is tnit. 
 
 0. Find tlio Holid contoiits of a circular pieco (»f lead 18 iuches 
 ill diunioier, and M^ inches thick. 
 
 10. Tho drivi!-\vhf>(d8 of a locomotive on(jine .no tacli 7 feot, 4 
 inches in (•in'Miiift'r<'nco and the pistnn sliaft is faHfcmid I inches 
 fnnn the cireiiiufiTtMico of iho whuuls. Find tho length of the 
 piston sli'itlio. 
 
 11. The area of a circle is 1380 sq. rods ; what is its diamotor ? 
 
 12. Tho solid contents of a circular [ilato of inetiil is 1 cuhic foot, 
 472 cubic inches ; wiiat is its radius, the plate })ein,<4 1.^ inches thick? 
 
 13. (a) A solid piece of metal, 31 feet loriij;, 5^ inches wide and 4 
 inches tliick, is melted and cast into a Imiluw cylinder whose 
 external diameter is 17 inches, jind whoso thickness is \\ inches. 
 Find tho lehi^'tji of the cylinder, (h) Reduco ,\ of an acre to sq. 
 rods, etc., and | of a sq. rod to sq. yds., etc., and subtract the results. 
 
 Exercise LXV. 
 
 1. A farmer took to market 2 hnor.s, 100 lbs. «;ach ; 14 bags 
 pease, 150 lbs. each ; 00 dozen eggs ; and 70 lbs. butter. He got 
 ,% .a cwt. for pork, 7'^' cents a busliel for pease, 10 cents for 15 eggs, 
 and 20 cents a lb. for butter. How much money did he receive? 
 
 2. What is tho value of 72716 lbs. of flour at $3.40 a barrel ? 
 
 3. Find the co.st of 13 tons 1520 lbs. hay at $12 a ton. 
 
 4. Find tlio freight rates on two railroads, one of which charges 
 $20 for the carriage of 40 cwt. 50 miles, and the other $70 for tho 
 carriage of 100 cwt. 70 miles. 
 
 5. A gold ornament, weighing 311)8., 2 ozs., cost $800. If it 
 is made of gold worth $15 an oz. what is charged for manufacture? 
 
 6. (a) In which order should the signs "of," " X,'" and "-r," be 
 taken, in hrackcthig an expre.ssion in fractions ? 
 
 (6; Simplify : ^ of If-ff of f x ^«^-^^ of f. 
 
 7. Simplify: (a) ^ of {jx ^-5-1^5. 
 
 (6)ixKfof,V 
 (c)Htoffx,V 
 
 8. If 80 men dig 5 acres, 80 rods in 15 days, how long will 45 
 men require to dig 10 acres, 40 rods, 005 yards ? 
 
 li 
 
 ' I 
 
 li 
 
 1 i 
 
 1 
 
 ^ 1 
 
 i 
 
EXKIUU8K8 \S AUIIIIMKIIO. 
 
 9. A aii<l n iM (\i\yn tiniko 45 diiiis, A ;iii(l f' in 8 dtxys nmke 
 28 <'!i;iirs, r. ,'111(1 (J in 12iliys m.ikt! 51 cliiirs. Ilow immy do/cii 
 chiiir.s c;uiil(l A, 15 and C tn;^',jtlK;i' m.iUo in oHO diiyH ( 
 
 10. A horsc-dcali'i* sold 10 li(>r.si;s ah $1 M a iu-atl. On half of 
 thvin lio <,Min<'d l(»:[ jut otsnt. and on th(> of hur half ho lost I'J^ por 
 ctnt. hid ho ^ain or lose on tho lot <ind how i inch :* 
 
 11. Tn uiaKint^a drain, tlio miturial cost \\ times as nnich U8 the 
 lalior for diL^Liiin'^ it. I»iit had tlio foi'mt.-r conh I..", |u;i' cent, morn, 
 and tlif) lattt'i- HV:^ prr ct-nt, nioro, tin tota' st would have; hoon 
 ^1:57. Kind th . actuul cost. 
 
 12. Ohan*:jo to 0(|nivaltMit fractions h- .iiit^ tl" least conunon de- 
 nominator fijl, f^'fj and Hf?^, and add. 
 
 l.'J. How lon'^' nnist 8510.20 bu on interest to amount to $810.30 
 at 5 per cent, per unninn / 
 
 Exercise LXVI. 
 
 1. Simplify : (a) 
 
 (h) 
 
 iVx5\ 1,\ 
 3i of 4^ 
 
 x4|. 
 
 (2h-l)oiC.',\-l) 
 
 2. Tlie net j)rooeod.s of a salo of 1)5)0 Larrel.s of flonr, after do- 
 duct iii<? a connnission of 5 per cH'nt. for .sellin'^ and !?-00.«'iO for other 
 expenses, are !:i>54'J4. What is the price per barrel ? 
 
 3. In wliicli direction from Woodstock might you travel and 
 your watch keep correct time ? 
 
 4. Find tlio total cost of 75 busluds apples at 3 cents a quart, 45 
 lbs. barley at 00 cents a bushel, 12 pecks of chjver seed at 12 cents 
 a lb., 18 gallons vinegar at 5 cmts a pint, and 2 barrels sugar of 140 
 lbs. each, at .'IJ,- ll).s. for 25 cents. 
 
 5. How many miles can a man travel in 312 days of 10 hours 
 each, going at the rate of 801) rods in an hour ? 
 
 0. Multiply 15 acres, 88 rods, yards, 2 feet 30 inches by 9 and 
 divide the product by 15. 
 
 7 How much more will 120 barrels of flour weigh than '5 of 14 
 barrels of water I 
 
 8. If if of iV of ^ cheese cost 24 cents, what would a car-load of 
 470 cheeses cost 1 
 
 y. If 20 cords of wood cost §36, what will 74 cords coat ? 
 
fOt'KTII (LASH. 
 
 T5 
 
 10. Diviilr ITilo timrbU'H iiriiniig 11 hoy.s nH f()ll(»\vs : Givo tf) tlie 
 fii-Ht i of tlitiii . to ttu' K(M)iul }f i)i thuiu ; hiuI UiviUu tli<- mst 
 t)(|Uiilly uiiioii<4 til*.' utiier boys. 
 
 11. Fin<l tliu coHt of Oti'3 ll)H. uf Uuii^iiriiin giam Hui'd at $1.20 a 
 busln^l. 
 
 I'J. A (Inivcr Ixiiiijht 50 hiad of cattlo nt $:U oacli, and sold 
 tht'iii, Kaiiiiujj; nii all ^lTiO. W li.it did In- -^ot for JU of tlioiii / 
 
 i:{. 00 Simplify i (4 L'Dof ((;j.-'j:;f(L'A + ,^)-h(:n-i) !> +„Y«. 
 
 (1)) hniijLjht H llts. of ti'H and i;{ 11m. iniiri.-f for 8''.0J, imyin^j; Hu. a lb. 
 mure for tUu tun tlmn t<>r tin; coH'uu ; tind tUo priuo of uach. 
 
 If - I i - A 
 
 1. Simplify : of 
 
 4 ~ (t I 2 ~ f 
 
 Exercise LXVII. 
 
 r-7" 
 
 2. Wjiiit is tlu! sulling priou, per hiislitd, of wlioat, whiiu i 
 advanuo of per cent., on tho cost, mised tlio prico $0 on a lUO 
 bu.sliols 'i 
 
 3. A t^'rocor <^ivos 8 lbs. of prunes for a dollar, and thorel»y gains 
 25 per cent, lie afterwanls rediiees his gain on prunes to .10 j)or 
 cent. How many Ib.s. by the latter unangement does he give for a 
 dollar 'i 
 
 4. Five more than I of A's sheep were stohui ; live les> than ^ 
 of the reiiiaiuiler (sti'.iyed ; 10 more than I of what then irmained 
 died ; and he then sold 'J more than y^y of what was still left, when 
 his (look still numbered 5 shee[». How m.iny were in tho flock at 
 first ? 
 
 5. A and B start in n])pf)sit(> directions, away from each other, 
 from two points C and 1), on a ciicular course OiiO i.xls in ciicum- 
 forence, and they ])as.seach otliev wlun A lias gone 4i)0 yards farther 
 than 1$. How many yards will 15 be from C (A's starting point) 
 when A has reaoluMl D (I* s startiuLj [loint}, the shorter distance be- 
 tween these pi ints bi'ing 100 rods i 
 
 6. A can dig a trench in 8 ii^urs, B in 12 hours, and C in 20 
 hours. How long will it take A and B to tinish tho trench after C 
 has worked in it for 2k hours ? 
 
 7. A dairyman buys millv at 5 cents a quart and dilutes it with 
 water, so that, by selling it at (i cents a cpuirt, he makes a pnjfit of 
 80 per cent, on his outlay. How much water does he mix with 
 each quart of milk 1 
 
 'v 
 
76 
 
 ETRRCTRP« i?f AiMTrnnrna 
 
 8. A ikkI W ufart %t oppnslt© rornorH of n rei lunRlo, who^o porl- 
 liic' iM' IN 'J(I(MI \.ii-<U, iii\il HiiliH ai'u to Udcli otiirt' iih H : 5, himI wiilk 
 round it in tlm wiinu diii'ct inn. A wiilks 'JO yiirilN, wliilu U wnlkH \tt 
 Nai'ils. At \\li;it point will tlicy Ix- to;{t*l}itr, and lioiv niuny tintDN 
 will uHoli Imvu passfd litH cornur / 
 
 9. A man Ixuii^'lit a Hofho and rnrrinL'o fm- MHO ; tlio horsu cont 
 1 118 much HM llio ».iuiiiij(«» ; what \\n^ llu' "oHt of ciich / 
 
 10. A iiwin, iiftor spi'TidiiiLr !?*20 li'f,.t tliaii i of his mom<y, had ^<»0 
 nioi'O th;iii ,', o| it lult. 1Im\v mui-h nii'iioy h.id hu at tii>ii '/ 
 
 11. Oiii; lildi of the ditlcmrK n iM'lwtten two iiuinl)i!tH in oqnal to 
 tho ihirticlh part of thu largur nuiidjur. Thu auiullur nunilicr is 
 O'JD ; tind thr liugur. 
 
 12. By Hclliii;^ wino at 83 a u-dlon, T f:ivn (5 per cent. Wli.it 
 BhuuUl 1 gain, per cunt., if 1 huU at i!;f:(..'t*.^|} n gallon 9 
 
 l.'l. A hlock of Htone, ir'x7''xr)" is placed in a cylindiiral tiil», 
 14 iiK'lx'H in diaiii'tcr, and \'2 iiichcH diH>p. 'I'lit; tiil> is tlicn tillfd 
 witli wiittT, and Lho lilock is removed. IJow duel) ^^^^ '''"J vvatcr 
 then bu in the tub 1 
 
 Exercise LXVIII. 
 
 1. (a) Distinguish luitwoen multijih'. and fnrfor; find tho L.C.M. 
 of l"»fi, 170, 27'A -'73, 378, and 45"). (/;,) Of what Muini)er are 111 
 148, 185, 222, 259, 290 and '3li'6 mnUiidHsi Which muUipUs uro 
 thoy 1 
 
 2. (a) Define : policy, i')isu,r(inre, prcmitim, and rate per cent. 
 
 (b) A's barn is insured for Jii'JIiOO at jj j)er cent. Kind the premium. 
 
 (c) If a merchant gain ^1.44 on an article sold for ^7.20, what is 
 his gain i)or cent, 'i 
 
 3. (a) DefiiU! : barter, ratio, praportion, corn/dec fnu-fiov, 
 principal and interest, (h) A barters (lour at 85.50 a barrel with 
 B for 30 cwt. 30 ll)s. of dried apples at ^5 a bushel, llow nuuiy 
 barrels of dour should B get] 
 
 4. A grocer mixes tea at 45 cents a lb. with tea at 50 cents a lb. 
 in the ratio of 5 lbs. of tlie former to 3 lbs. of tiii; latter. At what 
 price per lb. must he sell the n>ixture to j^ain GO pur cent. ? 
 
 5. On May 1st, 1890, 1 lout .i?14(>0 at 5 per cent. i)er annum. 
 On what date will tho amount due me be $1474.60/ (305 days == 
 ft year). 
 
 6. A and B can do a certain work in half a day, B and C in one- 
 fourth of a day, and A and C in one-lifth of a day. In what tiine 
 could B do tliB wliole work alone I 
 
roUHTII CLAflt. 
 
 TT 
 
 A - \ -eft - 2 
 
 7. IMvldo the trim of mi I hy th»ir di^ertnr§. 
 
 fl. Stufe thn nilo for /nlditij? rof»otonrlM. Add 1*78 1-310 + 
 
 • • • • 
 
 l«» 4021 + 17'4.>.'J, Hi) as to exiiiUit lliu wliolu vvtuk. 
 
 !). A <-<ii> <lo iiH iniicli work it)*5 tliiyriu.s M uuti do in ni'^'ht d/iyn, 
 iiiid toj^titlii-r tln>v iiro oiiMipiuil 1«) iluvs in div^ini? .vditiih for wliitili 
 !*r)'J is piiid. ('0 VVIiJit sli irn of tin' inoncy slioiild A roouive ? (6) 
 iluw lung wuuld tho work litivo occiipiud li uloiiu '\ 
 
 10. Tf my nvilwiiy t'lini from Torniito to Port Arflmr bo I?'-*"). 05 at 
 lluj riitt) of .'{ conts (i milo, iiixl my Htcjiinlio it taio, rot iiriiin<^ to 
 Toronto l»y w-itur, ht- 'X\\ pir coiit. \wv mil.. (;li»'.i|M!r, find my tnkub 
 for tiiu roiiinl trip, \\w distunuo by botvt biin^ 20 por cunt fnrtliur 
 than blio ilistum^u by mil. 
 
 11. In a b.iskt't of onvngos .niil lfm<mH, tlm orcnvjoa numbered 
 ^of tlio lomon.s ; but whuii iiimtlii r An/.vw of b>moiiH Wt-ri' piiL into 
 tho })uskot, flio orjiiij^os niimborcil [ of tlio wholo bu.sUct ; how 
 many dozen, in uil, worts thoro in tlio baskot at first ? 
 
 12. How many milos will a man, who drivoH 11 chains 11 feet i'i 
 a minuto, drive in 8 hoia\s ? 
 
 l:{. Divide $liG among A, B and 0, so that i A'a = } B's = 
 
 Exercise LXIX. 
 
 1. Twelve men can do a cirtain work in 15 days ; but owing to 
 3 of the men leavinj^ a certain number of days after the work was 
 bej,nin, it was prolonged '6\ days. How many days diet nhe .',hree 
 men work \ 
 
 2. A train from Winnipo'^ to INToosojaw, IJOO milos, is due in 21 
 hours ; for one-thiid of the distance it makes 40 miles an liour, and 
 for the remainder of the way 20 miles an liour ; how many Imurs, 
 minutes and seconds is it (Omul of time at Moosejuw ? 
 
 3. A, H and togetlior have 87. oO. A has 84' ; W lias 'S much 
 money as A and J as much as C, and C ha^ lA times as much as A 
 and IJ together. How much money has C ? 
 
 4. The hind wheel of a carria'^e is V.\ feet, and tho fore wheel 10 
 feet in cncuuiference. How far has the carriaLje ■cmu', in miles, 
 when the fore wheel has made 1584 revolutions more than iho hind 
 wheel? 
 
 
 II 
 
 V < 
 
 4 
 
7fl 
 
 txr.na\nitM iv AR:riiMRrta 
 
 n. IImw iiiiich tuik tit 45 «'Miir>4 II I)). nuHt Im< iiiixcd with 10 1I>h. 
 lit n2 OfiiiH II III., ill unit!!' to in.iki) u mixturu whicli, Mold ut (U) cuittM 
 a 1 1)., ({ivc'M (I |>i''>lii of *J0 por ci*iit. / 
 
 H. A frititor lioii^^ht Mmti)<0'« ut tliu rutu of 85 pur litiitilitil, tint 
 fiitiiid titut. I>v iniHttlvi' Uv liuil ^Mt 1 10 oritiiKi.'H iuntcml of onu liiin- 
 ili'ixl fort||i>!^5. Ilf ii'Vv ruist'il tlin rosf pricn of oriiii<{uN 15 prr 
 U(>nt. (illil snlil out till* wtmlo jut ; liiid Iiih i^mti por rent. 
 
 7. H'>ll'_'ht It poitioii of lalitl. ill tin; funn of j( rrcl.iiijlo, IM) l»y HO 
 ni'N at h75 iiii m ri«. f ^iiim-il .Sl."<>5 l.y Mrjliiivf it oil' in lntH ut ^\li 
 
 uiKtIi. WImt ti'mtioiiil piii't of im utru did uacli lot loiitain V 
 
 8. Iludiuui lU 1I>M., 4 oz«., 17 dwt., 12 gt'H., tioijf to IUh. and o/ji., 
 
 illvinllllKtiH, 
 
 \). A ructiinuiilar fiirm i.H .'KJO rods I<>ti'^, and itH porimutor i» 4 
 iiiilus, 80 I'odM. Kind itH valno at 2i:<l»0 an iu:t'o. 
 
 10. (ti) Iftiw many '♦t'condH worn tlioroin Kidirnaty, 18(10/ (/>) Om; 
 lioll tolls OtiinuH in 8 iiiiiiiitt.'H, ainl unotluT lull lolls 5 tiiiiuH in 7 
 iiiiniitcs ; liuw oflm will lliuy toll loyntlur in :S lionrs, 10 inlnutos < 
 
 11. Ah inonoy is I of B'h ; Imt 11 j,'ivoH A ^.'J5, afti-r which A has 
 1\ tinius as much uh iiu had at first ; hovsr much money had uach ut 
 tirst i 
 
 12. flow much heavier will Idils. of flour mid TJ bbla. of pork 
 weigh than 2 oul»ic yds., 2 culiic It. of water? 
 
 l',\ A owns finiy roctun^uliir plots of land ; thu Jirst 101 l»y HO 
 rods, the firroiiil 14 Ity 5 chains, the tliiid oO l»y It cjiains, and the 
 fuurtli. UO chains hy \',i chains, 40 links. What in tho vuluo of A'b 
 fuur pluttt of land ut i^5(i an aero ? 
 
 Exorcise LXX. 
 
 1. At 13 contsH s(piare y ' -'., it cost .^20.80 to pnvo tho surface 
 of a roctanu'ular court, whose width was feet ; find its loni,'th. 
 
 2. Tho dimensions of a rectan,L(ular farm areas 9 : 8, and it costs 
 ^74.80 to fence it at 4 cents a yard. Find its sizo in acres. 
 
 3. Efpial weights of ryo at 70 cents, peas at 75 cents, and millet 
 at 00 cents, are clioppiid together ; what is tho value of the mixture 
 per bushel, givoti that tho mixture increases 7^3 per cent., in bulk, 
 m tho grinding pnjcosa ? 
 
 4. A man spent ^ of his money, after which he gained 5 times 
 what he spent ; he then hud $5000 ; what was his money at first i 
 
roi'itrii CLADi. 
 
 IV 
 
 ft. A hr\s $'\y7, nnd M, hli britlior in Mi'llinnrno, lnf» CIT.'ft 
 Stfiliiiv; II tw iiKtiiy tlolUiM hIiouM A recti vu t'l'oiii Li tliut Ihuir 
 xmuN limy ho i>i|iiul / 
 
 0. Tliror IIh. I» iiin.l l 1I>m. cotr.o, o.»*f »..„^.tb..p !?.'], flO, iin<l M» 
 |I>H. tea mill •( II)h. C'lluu, intt tnj^rthur ii7>'*i't ', liml tiiu vuliiu of 1 
 cwt. of tua. 
 
 7. Divltlo if" Of);uMMii.i A. H im.l (\ H.) timt It hIi.iII n-rolvo *»."►() 
 iiiort* tliiU) A, uikI that (' hIiuII ivoiivo MHiiiiich iih A aiitl It togolhiT. 
 
 H. A iiiiui mniH liruL*.** ivrrv JU inuiithM, atul hikmiIh in iiioiitliit 
 whiit III) I'urim in 4 iiionths. What will ho huvd hi 13 ycurs and h\\ 
 iuoiiIIimY 
 
 0. F'lttr pi'iHonM ftirni n |)iu'tnfi>liip ; tliii Hci'iinil pnts in twico uh 
 liiU(;li us tilt! lilst, tht> thii'l half uh iiiiirli as the Ht.«l and srcoiid to- 
 yuthor, and iho fourth a^ iii'i'h as flu-othiT tliiut.'. Thiy j^iin in 
 riUhiiiDHH ii'uiUO. How Hhoulil this hu divided / 
 
 10. Simplify : — of ij «>f ,1 of j + J x J rf ^liO dollars. 
 7 
 
 II. A has 1(> an., 18 hi], in. of land ; IS has 117 ho, i-ndH, 2 h({. 
 ft., 18 .s(|. in. ; (- his 17 ac, lo si|. rods, ,M}, hi|. fi-ot ; I) han 175 scj. 
 riids, 2 s(|. ft'fl, lOS sii. ill , ;ind M has i iiuih^ni \<> llni.sh out a tifty- 
 acri) lot. liow niiicli land has K h.'.ss than .V i 
 
 12. How often doos the L. C. M. of 
 contain tlieir If. C. F. ? 
 
 «i X ^ 
 
 and i -^ 8 of /j2 x 
 
 I'j 
 
 i'o 
 
 V,\. Find tho total cost of 2 • wt., 1.T ll.s., 12 ozs. hnttor at 18 
 cents a Ih., U5 ^als. 2 ({in. syrup at 10 cents a '.,Mlli>n, l.S'l v^'J^a at IH 
 ci-'iits a dn/Dii, 15 husht'ls. 1 pt'ck of .■ipplus ut <»0 oi'i-.ts a hii-.hcl, 45 
 Ihs., 4 o/s. tea at 10 ci>n(s .i Ih., 70 huncln;s hiaid at i:;il2.1)ii a gfoss, 
 and 45 yds. cotton at iL'A i :t;nts a yard. 
 
 Exercise LXXI. 
 
 1. A wholesale dealer ^idls j^oods to n i-t'tail dealer at 00 pur 
 cent, profit ; l>ut tiie retail Us'iler fails, |>ayiii^' his critditors with 80 
 cents on tho dollar. What per cent, docs the whoh'.saU; dealer j,'ain 
 or lose { 
 
 2, The dift'erenoe in u'ei.,'ht oi two chests of tea is 12^ Ihs. ; the 
 value of hdtii, at 54 ouutb u lb., iu •i<47.25. lIow many \hs. arv 
 there iu each uheut 1 
 
 m 
 
 
80 
 
 EXEUCISKS IN AinTMME'l'IO. 
 
 3. Find the interest on JPODO for 4 years, 3 months, at 8 per cent, 
 per annul 1. 
 
 4. Find the amount of $720 for 3 years, 2 montlis, at 8 per cent, 
 per annum. 
 
 5. A farmer lost 02 o*' his sheep by disea.su ; '68 by theft, and 
 sold § of the reiiijvindor, aitur which he had 30 sheep left. What 
 was the number of hi.s Uoci: of shtep i 
 
 6. Bouglit pencils at 80 tonts a gross, and sold them at a cent 
 eacli ; find my gain [)er cent. 
 
 7. Bought 16 crate.sof egg.s of 40 dozcsn each, at 15 cents a dozen; 
 lost two out of every score, and sold the n;iiiainder at 25 cents a 
 dozen, paying a commission agent $7.70 for selling them ; find my 
 gain on eggs. 
 
 8. A man owned w of | of a square mile of land in Shoal Lake 
 County ; j^ of I of ";j of 121C scjuare rods in M;ir(i;iotte County, and 
 •^ of § of /g of a thousand 8(juare yards iji WiunipoL;. ITow many 
 acres, square rods, S((uare yards, etc., of land did he own altogetlier? 
 
 9. Divide $840 among A, B and C, so that A shall receive ^ of 
 the whole sum, ami that li shall receive <\ as mucli a.s C. 
 
 "3h of 3f 
 
 4 
 
 1> 
 
 u 
 
 Vx of 
 
 J 175 J 
 
 $12 ; (6) 
 
 10. Simplify (a) \ -^-— of 8§ 
 
 Add£2|, 6^8., 5§d. 
 
 11. Joseph lost f of ]^ of his money and had $15 more than f of 
 it left. How nuich money had he at hrst ? 
 
 12. Find the difference between iH^ is + \\-^^- ia }- x 52 
 and i Hy{^ + H^H)~is y x78. 
 
 13. (a) Divide the L.C.M. of 4, 6, 18, 27, 54, 72 and 99 by the 
 
 H.C.F. of 
 
 \ 27 
 
 25^ 
 
 480 
 
 75 
 of- - and I of 1.^. 
 12 
 
 (6) (i) In the Arabic system of Notation, what is meant by the 
 ' local value ' of a digit / (ii) In the number 570, what two values 
 has the figure 7 ? (m) To the sum of all tlie ecen nuud)er.s between 
 915 and 925, add 7282 ; square the sum ; and write the product in 
 Roman numerals. 
 
 L 
 
FOURTH CLASS. 
 
 Exercise LXXII. 
 
 ai 
 
 1. (a) Name and dofino the two kimls of fractions, giving an 
 
 (4 5 1 ^ 
 
 example of each; (6) simplify <- -r-— of Ij-r + \ 
 
 (5 18 m 
 
 'G of -83 
 
 3-5 
 
 2. (ft) Name the difTerotit kinds of decimals ; and, without unin^ 
 tlio (lonniiiiiiahor.s ot' rlnj fidlowiiig h'a(;ri()ns as divisur.s, stafo vvhicli 
 kiml of ducniial vm-Yi will pimliuH! : ,",7,y, /', and 'f;',?',^ ; (6) Simplify 
 each of the following by chaugiag it to a vulgar fraction : (i) '48125; 
 
 (II) •0541)45 ; (iiij •45(iur)(;. 
 
 3. Sold a ]r.\]v of fur mitts for 83. ."iO, gaining thereby 14^ per 
 cent, of my selling price ; what fractional part of the cost would 1 
 have lost, had I sold the mitts for 82.40 1 
 
 4. A fuel-dealer's sales, for the year 1800, anK^inited to ^3500 ; 
 tm coal, which fonued » of his sales, ho I'c.ali/cd Ki'-' iterceut. profit; 
 on wood, whicli fuiincil i of liis sales, he realized 'Jo per cent, profit, 
 and on coke, which formed the balance of his sales, he realized 11,J 
 l)er cent. pr<jfit. Find his total yearly profit. 
 
 5. A merchant's casli ]>rice, which is 20 per cent, in advance 
 of his cost price, is 20 per cent, below his marked price. Find 
 his cost price for an article marked $15. 
 
 6. A man's farm is 160 rods long and 12 cliains 50 links 
 wide ; what decimal part of a square mile of land does be own ? 
 
 7. One-fifteenth of a man's money is in the Bank of Com- 
 merce at 5 per cent, per anninu ; i in Canada Pacific Railway de- 
 bentures at 10 pel cent, per annum ; the rest in farm property, pay- 
 ing 8 per cent, per annum. Find his total yearly income, if farm 
 property, alone, yields him ^100 half-yearly income. 
 
 8. Find the H.C.F. and the L.C.M. of 4305, 1722. and 1640. 
 
 9. Express, in Roman numerals, four times the difference be- 
 tween the sum,^nd difference of XIIIXIII and VIlCDIil. 
 
 10. If eight bushels of wheat will sow 4 acres, 80 sq. rods of land, 
 what will the wheat, necessary for sowing a "quarter-section" of 
 land, cost at $1.35 a bushel i 
 
 11. B lost I of § of }| of his money on Monday, and 75 cents 
 more than ^ of the remainder on Tuesday, after which be had $13 
 left J how much money had he it first 1 
 
 II 
 
 f 
 
 r 
 
 !^ i r 
 
 
 n li' 
 
 1^ 'i 
 
 ; 
 
82 
 
 EXKKCISIiS IV AUITHMETIC. 
 
 12. If 4 11)3. of whofih niako 3 llj.s. of flour, how many bbls. of 
 flour can bu iiuulo from '.".'.> lmsli(.'ls, 54 lUs., 1(>!-| ri/s. of whuat ? 
 
 !.*>, A <,'(MiM('iii;in'H osl.il^o consists of 51) Mfjuiro liclds, each 14 
 chains, 4U links t^o a side ; how i.-iany acres, nxls, etc., of land does 
 ho own ? 
 
 Exorcise LXXIII. 
 
 1. Ai 20 por cont. a la ^vchaut pays $151*2 <lnty on 700 [luncheons 
 of molasses. If tho cost, price per ijaUon of ni>lasse.s is 15 cents, 
 what is tlio size of a puncheon in <4alloii3 i 
 
 2. A i^'rocei', by selliir4 15 lbs. of su;j;ar for a dollar, gains 10 per 
 cent.; what [tav cent, do s ho gain by selling 12 lbs. for a dollar? 
 
 3. Which is the gre;iti r r",te of interest, and by how much. [)0r 
 -814.40 on 800 ;or '.'> years, or 81^ on 840 for 5 years? 
 
 4. Sold two tubs of Imtter weighing together 80 Ib.-i., 2 ozs. ; the 
 larger tub l)rouglit 24 criis. and the s iiall.r one 20 cents a lb. If 
 tho larL'or tub weighed !> lb>. 2 o/.s. more than the smaller, find the 
 total receipts for both tubs of butter. 
 
 5. The hands of a clock indicate 10 a.m. What o'clock is it 
 when the iiands are 130 d. gi c^es apart i 
 
 6. At 1!) cents a squMve yard, it costs 87.02 to i)aint the floor of 
 a room ; and it cos s 81*' 5'), at 15 cents a :<(]'iare yard, to paint its 
 four walls. Find tlu) diiiieiisions of the room, if its breadth is 5 of 
 its length. 
 
 7. When wheat is 81 bO a bushel, a l»arrol of flour costs 85 ; 
 what should be ilie cost of a barrid of flour when wheat is .■*1.28 a 
 bushel, the cost of marking a barrel of flour being 35 cents ? 
 
 8. Find tho v;due of a pile of wood. G rods long, 9 ft. wide and 
 12 ft. hiih, at 82.88 a coi'd. 
 
 0. An elevators cai)aci"y is 1800D busliols. and three elevating 
 spouts, A. B and 0, lill it in hours, Avhtn W(jrking together. If 
 A tills 500 bu-shels per hour more than B, and (J lills 100 bushels 
 per hour less tlian A, what fractional part of the elevator does A 
 hll in t\w (J iren t line? 
 
 10. W'licu 30 eggs are north 82.19, what is the price of eggs per 
 doicen in shillings Sterliur !* 
 
 11. Two boys together walk 7 miles. IfiO rods, in 1 hour, 30 min., 
 one walks 120 chains in 30 min. ; how many miles per hour does the 
 other walk ? 
 
FUUIITII CLASS. 
 
 83 
 
 Lf 
 
 jr 
 
 12. A oistorn holds 33 bhls. 10)t r;alH. of water ; its upper surface 
 Pleasures (5 ft. by 4 ft. ; how (h;ep is it ? 
 
 13. At 5 eunts t'Jich l>oai'(l, it costs !?7'- to huiM a hoarrl-fenco, 
 four boards hii^h, .tiomul a ructan!:;iilav ru-M -lOrotls wide, tho lidards 
 being 11 ft. long ; what will it co.^t to plough and bow the tiuld at 
 $5 an acre ? 
 
 Exercise LXXIV. 
 
 1. The sellinfj prict; of a horse was !?8J, and tho gain at which it 
 was sold was V2h per cent, of the cost. Find the cost price 
 of tho horse. 
 
 2. Find the total of the following ))y adiling, Ji<irizontally and 
 vertuallii : 
 
 1 1 
 
 706 
 
 30 
 041 
 
 44 
 
 804 
 
 
 
 10 
 
 341 
 
 
 41 
 3 
 
 2 
 
 71 
 
 14 
 
 41 
 
 140 
 
 142 
 
 19 
 
 1 
 
 2i(; 
 
 084 
 
 
 28 
 
 073 
 
 410 
 
 13 
 
 31 
 
 087 
 700 
 
 007 
 
 127 
 
 C04 
 
 457 
 
 014 
 
 41 
 
 4 
 
 741 1 
 
 71 
 
 G81 
 
 l(i8 
 
 .082 
 2c^l 
 
 2ii4 
 
 72 
 
 382 1 
 
 
 200 
 
 7 
 
 28 
 
 S71 
 
 281 ' 
 
 
 
 i 
 
 
 
 
 Totnl. 
 
 3. Reduce j^,j lb. tny-hjV lb. avi irdni.ois to ozs., dwt.,grs., 
 troy. 
 
 4. The interest on a certain sum for r, years at 7 l)or cent, is 
 greater tha ■ the interest on the same sinii ; ^r 8 years at per cent. 
 by $20.20 ; find the sum. 
 
 5. Bought 50 t(jns of coal at $4.50 j)er long ton, and sold it at 
 $45 for every seven sJioif fo)is ; liiid my gain per cent. 
 
 G. Simplify : ('0 1004 x 5 + o8iiyi-r-9 x r, - 5342 x 4 + 1 + 000 x 6. 
 (6)-{2ix|-Jbof^^-5x5of v;,-HC^^>f lO^x^if}^ +78^^^. 
 
 7. A, B and C. together, bought 150 slu'op. A invested $270, 
 B, i^l80, and 0, .^300. How .sJiould the sheep be divided, and whaC 
 is the average co.st price per head i 
 
 I ! 
 
 M: 
 
84 
 
 EXKRCISDS IN AllITHMITIO. 
 
 8. A rlid I of a ccrtfiiii piocu of work, B J of it, and C tinishod 
 it in 1] (liy.s. Of -SjO, p.-.iil foi- tliu work, how much should ouch 
 one gut !< Wliul wovo (j'h Udily wsv^oa'i 
 
 9. Divide sixly-.six and two tontijs l»y four and four tenths, and 
 reduce) the quotient to a d«!cinial. 
 
 10. A has It) acres, ITtO s(£. rods, 3.^ s(i. yds. of land ; B has 70 
 sq. rods, 3 sq. ft., 18 sq. in., and ( ' has 11 a<jres, 27 "5 sq. yds. How 
 niucli less than '15020 of a squaii' mile of l.'iml have they toget ev'{ 
 
 11. What fraction of a mile and a half is four-elevenths of ninety- 
 nine rods ? 
 
 12. Sold ()2 cwt., 40 11>H. wluN-it at 87 cents a bushel ; 28 tons 720 
 lbs. hay, at 815 a ton ; 120 lbs. l)\itter, at .'37A cents a lb., to pay a 
 n;>te of $520 which had run from May .'list, i88"J, until Jan. 5th, 
 1890, at per cent, per annum ; what had 1 left after paying the 
 1 ote ? 
 
 13. A boy gave away 40 cents more than ^ of his n)oney to hia 
 sister, who then had ^ more money th;i.n she ha<l at litst. If, iter 
 the donation, the boy had still GO cents, how much had both to- 
 gether at first ? 
 
 Exercise LXXV. 
 
 1. Find the value of a pile of cordvvood, measuring 864 cord-feet, 
 at $6.60 a cord. 
 
 2. A and H together weigh 287 lbs., 14 ozs, and A's weight is | 
 of B's ; find the weight of each. 
 
 3. A farmer sold 15 bushels, 15 \hs. of wlioat at !i^U.25 per cental, 
 
 41*493 lbs fine wool at 37 '5 cents a ib., and 129 lbs., 3 ozs. coarse 
 wool at $•0075 an ounce. With the proceeds of his sales he bought 
 carpeting, 21 inches wide, at 75 cents a yard, to cover the Hoor of a 
 room 18 feet long, 15 feet, 9 inches wide. If the stri])s ran length- 
 wise of the room, how many yards did it take, and how uuich money 
 had he left out of his sales ? 
 
 4. Bought a puncheon of beer at 8 cents a gallon, and sold it off 
 in half pint bottles at 30 cents a dozen ; find my gain on the 
 puncheon. 
 
 5. A has 40 'vres, 40 sq. rods of land, and B has a rectangular 
 field 14 chains j>>i'<^ by 5 chains wide. What is the value of both 
 pieces of ground ui ;*'5o ;.n an 9 ? 
 
 6. Bought 15 barrels flour at $5 a barrel, and put it dp in bags, 
 holding 25 lbs encl:, wliich I sold at 80 cer«3 each. Find my gain 
 or loss on the ?,'i'aie oua^.^ir/ 'I 
 
'P 
 
 FOURTH CLASS. 
 
 SIS 
 
 7. A and B working together can dig a drain in 50 hours, B and 
 C in 35 hours, and A and C in 40 hours. In what tim« would they 
 all working together dig the drain ? 
 
 8. Find the value, in acres, sq. rods and sq. yards, of 34'5 acres 
 + 475-4 s(i. roda-500«0-85 sq yards. 
 
 9. A can walk 4 and B 5 miles an hour ; how many minutes' 
 start must B give A in an eii^ditoen-milerace, so that they may come 
 out evenly ? 
 
 10. James walks 120 chains in 30 minutes, and Oeorgo walks 160 
 rods in l.'t minutes. ITow many miles apart will they be, in 3 hours, 
 walkinj^ from the same point, and in oppoaiie directions? 
 
 11. A farm of 105 acres, 125 sq. rods, 15 sq. yaids, is divided 
 into 5 fields ; the first cimtains 10 acres, 15 sq. rods, 17 .s(j. yards, 
 the second 3 times as mucli as the first, the third half as nmch as 
 the secimd, and the fonnh half as much as the third ; what does 
 the fifth contain \ 
 
 12. To 41 add h and ^ of f^, and divide the result by 83 J. (N.B. 
 — Write out the quest i(m in fraction form, so as to show that you 
 understand it ; then solve it). 
 
 13. Find the fyroduct of the L.C.M and H.C.F. of 450 and 525. 
 
 ii; 1 
 
 
 Exercise LXXVI. 
 
 1. A farmer sold 1248 lbs. of Hungarian seed at S3.12| a 
 bushel, and with the mon-y boiiylit carpeting at 37^ cents a yard. 
 How many yards and feet did ho receive ? 
 
 2. A and B can do a work in 4 -hiys, A and in 3 days, and B 
 and C in 6 days. In what time can B finivh the work alone, after 
 he works at it with A for half a dry ? 
 
 3. A merchant throws (;(F 20 per cent of the cost price < n 
 article, and tlion is paid with 50 per cent, of the remainder; wnat 
 per cent, of the cost has he actually lost ? 
 
 4. When apples are selling at |)| a peck, how many lbs jan I 
 
 3^ "i 
 buy with - | -r ^ of - x |^ I times $2.88 ? 
 
 5. 1 ordered 5 lbs. of cheese, but the grocer weighed out 4 lbs., 
 12 ozs. , to fill the order. What per rent, was I cheated ? 
 
 6. In question 5, what would the grocer gain on the sale of 19 
 lbs. cheese (by ^'JiUing orders^' as stated therein) at 13 cents a il ? 
 
 I! 
 
 
86 
 
 EXKRCISKS IN AniTHMETIC. 
 
 I 
 
 7. Tho arcii of h vinoynnl in 4800 .s(|M;iro rods, nnd its length is 
 to its l)i't!;iiUli iiH 5 : .') ; tiiid thu oust ni oiiclosiug it with u fcnco at 
 15 ciiiit.s H rod. 
 
 8. If 4 men or })oy.s can <lo h work in 12 days, how long will 
 4 tinii'S thu work occupy 4 m^n <(ii(l )io\s ? 
 
 0. TJou'^lit a qnantily of coil oil at liO ccjiits a (gallon ; ono-third 
 of it was lost hy IcakaL^o ; at what i)rico pir (jUiirt nnist I now sell 
 tho r(!niaiud(!r to '^ain 'JO pur cent, on tli" svliolo (|uantity ? 
 
 10. f^»iii^lit ir»,s7<) pounds of Hour at 81.20 a barnd, and gained 
 Sl.'U).()8 on the wliolo (plant il-y, l»y sijllin'^ It 4]' in paper hags at 00 
 cents oacli. How many [i;»unds did each iiag contain 'i 
 
 11. A. lias as many sh(!0[) as H ; but" 1' s;'oaIs 10 p^r cent, of A'h, 
 and linds tint lie lias tlum 01) shiop. What is the value of both 
 flocks at ^."),;>7^ per head ? 
 
 12. A has !?120, and B has J|:lOr> ; what per cent, is B's money of 
 
 the whole / 
 
 13. Bought pencils at 80 cents a gropi, and cleared 440 per cent, 
 on soiling them ; what was my selling ])rie!o per pencil? 
 
 Exercise LXXVII. 
 
 1. I sell 45 tons of coal for •'3281.25, thereby gaining 25 tor oont. ; 
 find the cost price of coal per c\v^t. 
 
 2. A miller sold ^ of his stock of Hoiu" at 85.50 a biirrel, renliji- 
 ing there' y !;i<o()8i.) ; wliat would ho liave rcali'-'ed on tlio sale or his 
 entire stock, had ho sold it a week soouej-, when flour was 10 per 
 cent, dearer? 
 
 3. A merchant sold 145 Itarrels of npj)les, part at §4.50, and the 
 remainder at ijiio.OO a l)artol. rciali/.ing alt(^gother $700. How many 
 barrels did he sell at eacli rate ? 
 
 4. A. 1* and C have together 8800. If A gives his money to B, 
 B will ha\c J as nuich as C, but if A gives his money tf) 0, C will 
 have 10^ times as much money as B. liow much money lias each ? 
 
 5. Simplify 37 ] ( G+ \ of I [+i>L 
 
 6. A and B throw dirks at marks, both beginning at the same 
 time, and each tilro^7ing 21 dirks. A can throw 4 dirks in 5 
 minuter and B can throw 14 dirks in 15 minutes, IIovv many dirks 
 will A have to throw after B has thrown his last one? 
 
FOl/KTH CLASS, 
 
 87 
 
 7. A cistern has throo pi|v'«i, A, R .iiul 0. It can bo fillod by A 
 in 10 huurs, iinil it can l)o fnipti«il by II and C in L'O and 'M bo\irs 
 rospoctM uly. If tbo iiisli-rn is ,1 full ami all tlio pipes art- opcnud, 
 in vviiat time will it Ito ,[ full, it luMiig found that tho cistorn hug 
 sprung A leak }; tho aizo of pipo A ? 
 
 8. A man. who can row miles an hour in still water, is occu- 
 l)ii'd Ihuur, lU) uiinur.t's in rowiH'ithat distance up a stream; howlougj 
 will he be <tcoa)>iod in riiwin<4 <b)wn a^ain i 
 
 1). Divitle ^~)\'>0 aiiionijj A, I?, and 0, giving' B ^10 more tiian half 
 as much us A, and C a;-i niueh aa A and I* t<»<4»ither. 
 
 10. A grocer hayn a b;ui\'l of HUgiir wois^liing 315 lbs. for |18. 
 What per cent, does !u;.i gain or lose l)y sollin-j; ;i of it at tho rate of 
 18 lbs. for a dollar, and the romaindi-r at J.2 1!.ih. iov u dcdlar ? 
 
 11. Tom has \ - : — of l^-i 1-1 - cents more than Bob in 
 
 It IB 8t)? J 
 
 a purse of $9.35 ; lind the sliare of oa,ch, 
 
 12. A miller bou',dit 150 cwc. of wheal at 87 cents a bushel ; he 
 ground it into Hour, gottiriL; 38 Uti. of Hour and 22 lbs. of bran and 
 shorts frt)m a bushel of wlicat ; ho anid the Hour at $4 i'/ i barrel, 
 and the bran and shorts at GO cents a «nvt. ; find his gain. 
 
 13. Divide 250 acres, 83 rods, 23 yiU., 2 fc., 30 in. by 6. 
 
 Exercise LXXVIII. 
 
 1. What will it c(\st to carpet a lioi»r 21 feet lonfi;. by 18 feet 
 wide, with cari)eting 30 incliea wide at 75 cents a yard i 
 
 2. At what time after o'clock p.m, are the hands of a watch 
 equidistant fi-om thu liguro IX? 
 
 3. Divide tlio sum of 8305 among 12 men, 10 women imd 45 
 children, so tliat ea'di man shall receive as much as 3 womeuj arnd 
 each woman as much aa 6 children. 
 
 4. Find the simple interest on $3285 for 150 days at per cent> 
 per annum. 
 
 6. A boy spent $1 more than ^ of his money on Monday ; $5 
 more than } of tho remainder on Tuesday ; then S15 more than ^ 
 of the remainder on Wednesday ; after which he had $30 left. 
 How much money had he at lirst ? 
 
 C. Bought 4 boxes of biscuits at 15 cents a lb., paying therefor 
 $13.80 ; how many lbs. were there in a box? 
 
 7. Simplify : ^ 3^ + 2^ x 3^ 1^ l^^xi. 
 
 1 
 
 h 11 
 
 r 
 
88 
 
 BXKROISBS IN ARITIIMBTia 
 
 6. Find the total c(mb of : i 
 
 08.34 1I)H. of oatH at 32 cents a buHhol. 
 8 tons, 1 10 IbH. hay at $U) a ton. 
 682 ll)n. chooNo at .ii^O.Ol an (jiitice. 
 480 ounooR fea at 02^ ct-nis a lb. 
 101)7 yards. L'Hj'^j inclum cotton a(" 6 cents a yard. 
 
 9. A apt (Milator b(tu«,'ht a certain niinibor of niiilt^s for $<'i.'<00 ; be 
 sold }^ of tliciii for J^lJiHO, j,'aiiiiii^ Mioroby iM'J |icr htad on liis HahsH. 
 What did ho i>ay per lu;ad for bis iiiuIuh i 
 
 10. A and B aj^rood todivido thoir travelling expcnsfs intbo ratio 
 of IJ : 2 ; but A pa '' $4 and li paid "^13.60 ; how much must ono pay 
 and till) othor recui. j to sottlo accounts? 
 
 11. Kind the valtio, in lbs. and ozs., of 24.'J of a ton. 
 3^ 2 
 
 (Si 2 , 
 
 12. Simplify: \— + ,\ of fVxl|x72. 
 
 I 7 lOi ) 
 
 13. .John can dig 14 bushels of potatoes in 3 hours, and Tom can 
 dig 3 I ;ks in 5 minutes. Ilow many bushels woiild th*\y both 
 together dig in a week, working hours a day ( What fracticmal 
 part of the whole does John dig in a week i 
 
 Exercise LXXIX. 
 
 1. What sum will amount to $.'58.78 in 3 years, 2 months, 15 
 days at 12 per cent, per ami rn ? 
 
 2. The oloth from a certain loom is 20 per cent, cotton, 80 per 
 cent of the remainder is worsteil, and t iie rest .silk ; what is the »dk, 
 in a web of 80 yards, worth at 83.80 per yard ^ 
 
 3. In a certai) ..ohool the l)oys were to the girls as 3; 2; but when 
 5 more girls were admitted, the girls numlna'cd j\ of the wliole 
 school ; tind the uumlwr of girls in the school at first, 
 
 4. How many yards of carpet, worth 87^ cents a yard, must be 
 given in exchange for 253 yards, 2 ft. of carpet worth !J5.25 a yard? 
 
 5. A man lost i^ of his money in an adventure. He then gained 
 $800 ; after which he had ii^tiSOO ; h^w much money did he lose? 
 
 0. The fore and hind wheels of a carriage are 12 and 15 feet, 
 respectively, in circumference ; how far nmst the carriage travel in 
 order that tlie fore wheels may each make 572 revolutions more 
 than the hiud wheels together? 
 
FOURIU CLAM. 
 
 7. If 40 oriincfon iiold for SI. 20, and the ^'uin tlmrcby ba 20 por 
 cent., finri Mie cost prico of omu'^^uH \n>v dozon. 
 
 8. A tiun^haiit hoIIh 'JO y!ir<ls of olotli at 28 cont« a yard, yainlng 
 tlierol)y 1') p.r cent., and takus ej?i^s, at 11 emits a dozen, in pay- 
 ment. What per cuul. prulit Uooh he make if 3 egjjH in a dozuii 
 ;iro ha<l ? 
 
 0. F'ind the cost of paporinjf a room MO ft., 4 in. long, by 20 ft., 
 8 in. wide, with papor L'l inches wide, woilh 40 conts a single roll, 
 iillo\van(;« \hi\U'^ m.ilu for 3 doors, each J) ft. wijo, and 5 window.s, 
 o.ich 2 It., 10 in. widi-. 
 
 10. A nmit borrowfl i?ISO for 2 years. 8 month.i and ID days at 8 
 per emit, pur annum, Hiiii|ilo intdrost. Dr.iw a noto to socuro '^he 
 paynnMit of I'viticipal ',\\v\ inUvcst at tho timo tho note in dup. 
 
 11. A floor is 3fi X 24 ftMit ; what sum of money will c.irpet it with 
 27-in«'h carpet iriL^ worth 87 i> oonts a yiinl ? 
 
 12. Honpfht H; whnep at ^Ty.'.Vih each ; sold | of them at ^.75 
 each, and the rent at ^12 ench ; wliat did I gain? 
 
 13. (a) Find tho valtie, ut .1^.'{8.37i) an acre, of a piece of land of 
 roctun<;nlHr shap"', IHO eliains loti<4 by (50 ro<l,s widu. {h) Simplify, 
 7.1 X ?if '^ i^H' (1) vvitlioiit cancel I.'ition, by puiltiplyin;^ thtinnrnm-ators 
 tojLjother for a now niimtMator, and tho dmioiniuafors together for a 
 new denominator, and th<'n dividing I ho Icrnis by their H.C.F. 
 ^2) T^y dividing Mie tenn.s of tlie new fractioii by 7, then by 8, thou 
 by 1(). {?,) By cancellation ; and .so that your cancellation shall 
 correapund with the second method. 
 
 Exercise LXXX. 
 
 1. A cistern loses, by leakage, 4 galhms, 3 quarts, 1 pint in 7 
 hours 48 mimito.s ; what is its liourly loss ? 
 
 2. Find a multiplier which will give the amount of any siim at 
 simple interest for 5 years at 4 pi.T cent., and uae it to find the 
 imiouiit of .^oOO for tho said time and rate. 
 
 3. Express as tho fraction of a pound troy, 3!^ of a pound troy + 
 -^^ of a poimd avoirdupois. 
 
 4. An agent charged $15 for sOling a sowing machine for $75 ; 
 what per cent. cf)mmissi(m did he collect ? 
 
 ll 
 
 ^3^ ^ 
 
 of 
 
 01 X 49 
 
 U X 31 
 
 7* 
 
 15 
 
 I of I -i- ii X f 
 
 1*4} 
 
 1 
 
 i 
 
 i 
 
ao 
 
 BXF.ItCISFS IN ArUTIlMKTiO. 
 
 \ I 
 
 0. If \ of J^ of <7 of 4 stacks of li.iy \n worth 1^12, wlion )my U 
 
 M««llin<j lit S7 a t»)n, liow m.iny tuns tlons tin) nUn'M contain i 
 
 7. A iiiim lia.Hu roi'taiii sum ot laouty in tlie SjivIii^h' Hank, 
 (Imwiii^ r> por oont. |>ui' aiiiiiiiii, siiiiplt! iiitiui^st. Ilo witlidrawH 
 !9lir)5)it tluM!ii(l of 13 yoaiH i tinl thu ori^^inal huiu lUtposituil in 
 tliu Malik. 
 
 S. LoiiioMs l)ou\'lit at, l|1.20 pt^r 'J\ i|i>/<n. ar<^ ho1«1 so an to yivo 
 a piolit of l«)i per (H!Mt. lIow iiiaiiy Ifiimtis aro nuM For yi^.^.TiO 'i 
 
 1). ((») Of what «1o(;h tho L. 0. M. uikI If. ('. V. of aini tir,< iiiiiii- 
 hors coMsiHt I (/>) Fiii.l tho II. 0. K. ami L. O. M. of L'.'tK) an.l '2520, 
 by rosolviiiiL,' tNuh into itH pvinw fantors, atnl wliu'tinq fmnt thine 
 fudor.H th.-'ir. 0. F. .11). I L. C. M. (.•) Tho II. (\ F. of hen nmii- 
 l)cr.s is .')! ; thoir h. C M. i.s ii'^oL'O ; oiio of tlio nninlM'is i.s 71-^ ; 
 timl tho othiir. (d) l)ivi(h) thu L. 0. U. ..f :«;(), l>Ot, I'M), i.nd 510, 
 by tho II. C. F. of V.YAH and 'JJiil. 
 
 10. Find tho product of the L. 0. M. of HIKSO, 27:50, 2484, 3105, 
 
 /.\ - ^\ 
 ir.80, lOC.O, 2S00 and tho 11, C. F. of 7 I ) of ^5 + A and 
 
 i-^ . . . " 
 
 9 -i- l.Tj of -ii. 
 
 11. A laborer at^rotiJ to di'jj ft certain ditch at 12conta a rod. Tlie 
 
 tir.st W(H'K hi'diii^ 2r> rods more tlian th • h.iif of it, and tho follo\vim( 
 wook hi! linishisd th(! rciiMiiiinn 'Jl.j rods <>f thu ditoli. I) What 
 wore his (/(<//»/ wages \\\iijii:it wuuk ? (ii) ^N'hat woro hi.s d<(ilij \vagc's 
 fhroiKjJiont tho work / 
 
 12. Divide .$200 amon«^ A, B and C, so tliat ^ A's ~ h of B's = 
 
 iJofC's. 
 
 IM. (a) Divide ^VM) nuunv^ A, li and 0, so that li .sliall rtcoive i of 
 A'a sharo + );:>L*2, and tiiat (J shall ri'coivo .S25 tnoro than half a.^ 
 much as A ,ind B to„'othor. ;/() Divide !ii<lii) ainon.ij A, B and C, 
 HO that A sliall receive IJ, times as much as B, and that C shall ro- 
 ceivo $13 ni ru than -^^(f of tho remainder. 
 
 Exercise LXXXI. 
 
 1. A man leaves J of his pr ])erty to his wife, and \ of it to his 
 son, who gets !?S00more than each of his three sist ri, among whom 
 tlie rest is equally divi<led. Find the value of tho property. 
 
 2. A cci"tain contract is to bo co)ii[ileted by 10 m mi in 12 days, 
 but every 4 days 4 of the men leave and the remainder work on ; 
 this is continued until the work i.s al);indoned ; how many ilays is 
 tho contract under way, and how much work remains unlinisheJ at 
 the end of that time ? 
 
rOUKTII rlAHB. 
 
 •1 
 
 3. A moHiint hcIIs, to i\ i»(Mll:ir, %>y\(h at ftO |»i»r coT.t. ftdvnnro 
 oncost ; ill'- |i»'tll,ii' Ih'i'oiin's haiiknipt, )iii<l pivH fiO <'«'ntii »»n th« 
 <li»IUr. \N liiit per luiit. tl.»is tin- jiu'irliaui nilly Iomu / 
 
 4. A mail inix(n4r» -.'.iIIuhn oF .ilu ui iT) »•• nts ;i },mI1..ti, uilhnft 
 ^'allitiis i>t' lu<(>r lit, \H ctiitH II ^mIIdii ; at wliiit |tiii'<> |M>i' pint imi^l liu 
 ni»\v sull tlif iiiixiuri) to ^^niii \'>i{\\ i'»'r ci'iit. on tin- \vlii»U> I 
 
 f). 'i'li(! prico «>f »oh1 ris»«s II,', p t ctMit. ; \}y how tniicli por cent, 
 must tho consiMMur luduco his consumption of coiil, ho uh not to 
 ineroiiHu hi.H I'XpiMiditui'u '( 
 
 (»- A rt'ct.vnL'uliir ph»t of ground contains lo.'JdT'HiMO ,s<piaro 
 inOics ; its icn;.;th is to its hrciulth um 5 ; 4. I'ind its U:ngt h and 
 bi'cudth in rods. 
 
 7. liracket tho foHowui'^ ; thun ro-writo in h inor« ronciae fonn 
 
 and Hiuiplify : 4^4-^ ot [;] + ,1 of H - i'!r - i x A ^- 1 2^a 
 
 7 
 M. Thu HUMi of 8(>0.ri() was di\ idi-il anioii'^ .'UJ prrsotis ; ii curtiiin 
 miuil)ci' of iln'iu ri'i'fi'. cd ji^-^ carh, ivnd ih»' lost 5l> cciili t-ach ; huvv 
 luiiny Well' tlii^ro ut, njich ratu '< 
 
 U. It sojv-wiitur contains 2^ per cent, of salt, how numy tons of 
 sou-water must ho uvH|M»rfitod ni order to obtain 1 tun, loOO Mm. 
 sidt ? 
 
 10. A pilo of cordwood contains 12S cords ; it is 1 .\ tiincsus long, 
 and }[ times as hinh as it is wi(h) ; find its dimensions in tout. 
 
 11. ]']i.,'lit men contracted to do a piece of woi'k in 20 days ; hut, 
 owing to thri'r of thti men h'aviu'^ a certain nuiaher of days after 
 tin; work was liegini, it was under contract 24i days, lluw long did 
 the three men work ? 
 
 J2. A tank contains .'}<)() j,'anons of water after a certain (piantity 
 of water lias hcen achh'd which increased its volume 25 per cent.; 
 how many 'gallons must now hi; withdrawn, so that the water may 
 find its fornn-r level { 
 
 lo. Find the value of 728 Ihs. of rye and barley mixed efpmily by 
 measure, when rye is 70 cents, and barley is 80 cents, per bushel. 
 
 Exercise LXXXII. 
 
 1. 'rh(f sum of 8118.75 was paid for a certain piece of work. A 
 antl B W(jrked toijjellier at it for a certain time ; .after which B fin- 
 ished it alone in 7j days. It A and B, when workini,' toj.(eth< r, 
 received $5 a day, how many days did each work ? {AoU. — A — - B 
 in work, throughout.) 
 
^.^°' 
 
 s^ V> \> 
 
 V] 
 
 Vl 
 
 /: 
 
 
 /A 
 
 7 
 
 V 
 
 IMAGE EVALUATION 
 TEST TARGET (MT-3) 
 
 '1.0 
 
 ■fill! 12.5 
 ■U 1^ 122 
 
 t ld& 12.0 
 
 u JIJlBE 
 
 I.I 
 
 
 
 1.25 
 
 1'-^ IJ4 
 
 Photographic 
 
 Sdences 
 
 Corporation 
 
 
 •^ 
 
 \ 
 
 iV 
 
 \\ 
 
 ^q> 
 
 V 
 
 
 \ 
 
 23 WEST MAIN STREET 
 
 WEBSTER, N.Y. 14580 
 
 (716)872-4503 
 
 ■^ 
 

n 
 
 BXUR0ISE8 IN ARITUMBTIO. 
 
 2. Simplify I ( — of— I -r I — x- I of (2.^ of U+— . 
 
 I \ J U' / ^ 14]* 26 / \ ■ Hi ') 27 
 
 3. Two cogged wheels work togttlKH' ; one wheel lias 90 and the 
 other 40 cogs ; the larger revolves 100 times in a second ; how often 
 will the wheels be in contact, in the same position, every second 'il 
 
 4. A has $3 more than \ of a certain sum of momy ; B has ^12 
 more than j*^ of the same sum, and C has $10 less tlum ^ of it ; find 
 the sum. 
 
 5. Bought fruit for $120 ; sold 00 per c<;nt. of it at 8) per cent, 
 of the cost price, and the rest at 20 pur ctnt. advance on the cost 
 price. Find my gain or loss ptsr cent, on the whole. 
 
 6. A boy has 9 coins in his purse; there are twice as many 
 twenty cent pieces as five-cent pieces, and half as many ten- 
 cent pieces as lives and twenties together. How much money has 
 the boy in his purse ? 
 
 7. A and B have together $420 ; and 20 per cent, of A's is $4 
 less than 1G| per cent, of B's. How much money has each ? 
 
 8. Wheat weighs 48 lbs. to the cubic foot ; find the value of a 
 bin of wheat, 40 feet long, 20 feet Avide and 4 feet 6 inches deep, at 
 $1.05 a bushel. 
 
 9. A does f of a piece of work in 16 days, and then B joins him. 
 They work together at it for 1^ days when B leaves, and A finishes 
 the work in 41 days more. How long would it have taken B to do 
 the whole work alone ? 
 
 10. A has 7 
 
 r^x^off 
 
 -hrX' 
 
 '1 ^ 
 
 — X — of 
 
 H 9 
 
 times as much 
 
 U-|ofJfx}, 
 
 money as B, and together they have $495 ; how much money has 
 A more than B ? 
 
 11. A vat, 45 ft. long, 16 ft. wide, and 2 ft., 6 in. deep, is filled 
 with syrup ; what is it worth at $57.60 a puncheon 1 
 
 12. Find the net c^sh proceeds of the folio whig bill of produce, 
 8 per cent, being allowed otf for ready payment : ^ 
 
 76 bushels, 20 lbs. buckwheat at GO cents a bushel. 
 29 bushels, 12 lbs. wheat at 90 cents a bushel. 
 72 bushels, 16 lbs. barley at 03 cents a bushel 
 92 bushels, 24 lbs. millet at $1.72 a bushel. 
 53 bushels, 30 lbs. Hungarian at $2.40 a bushel. 
 
FOURTH CLASS. 
 
 M 
 
 13. A circular reservoir, havint; a diameter of 98 rods, is half-full 
 of water, and 8t)lti00'0ir)()26 gallons are admitted ; how much will 
 it raise the surface of the water in the reservoir 7 
 
 id 
 
 Exercise LXXXIII. 
 
 1. Of what does the L.C.M. and H.C.F. of any two numherH 
 consist? The L. 0. M. of two numhers is 1194830, and their 
 H.C.F. is 34138 ; one number is 2389(16 ; what is the other? 
 
 2. What is the difference lie^ween the simple an<l tlio compoutid 
 rules of arithinetit^ ? Tho product of two numbers is I13r»2418227, 
 and their quotient is .307 ; find the nuinberH, Reduce JJ of a tt). 
 troy + ^ of a ft), avoir, to lbs., oza., dwts. and grs. tro)j. 
 
 3. What is the difference between xnhiar and decimal fractions? 
 ' 3i ^ 2^^ 
 
 — J-TjVof 2J l+— of |]-f|. Find the sum of 
 U " J 3 
 
 6-238,4.627 and 2 1345. 
 
 Simplify : \^ of 
 
 4. Find the total cost of papering the walls and painting the 
 ceiling of a church, 120 ft. lon'4, 70 ft. wide, with a ceiling 18 ft. 
 high, the paper to be 21 imhes wide, wortli .i?1.30 a double roll, and 
 37 strips to be allowed for openinifs, the burdeihig to cost 9 cents 
 a yard, and the painting 15 cents a square yard. 
 
 6. What would be the cost of car]>eting the church in question 
 4, with 45-inch carpeting, laid down lengthwise of the church, and 
 costing $1.87 \ a yard ? 
 
 6. A rectangular field, whose length is to its breadth as 5! 4, con- 
 tains 12 acres, 80 sq. rods. A stri]) 30 rods wide and running the 
 length of the field, is sown with !• aley at a cost of $1.60 an acre, 
 and the remainder is sown with wheat at a cost of $2.40 an acre. 
 Find the entire cost of sowing the field. 
 
 7. A owned ^y of a lot, and was offered $1800 for ^ of his share. 
 B bought the whole lot at this rate, and paid a year's back taxes 
 amounting to 1^ per cent, of the value of the lot. Find B's total 
 investment. 
 
 8. In a mixture of 50 gallons of liquid, the wine is 40 per cent, 
 of the w^liole ; how much wine added will make the wine 90 pe'v 
 cent, of the whole ? 
 
 9. Divide $270 among A, B and C, giving B J as much again aa 
 A, and ^ as much again as B. 
 
H 
 
 EZEUCISKS IV ARITHMETIC. 
 
 10. A grocer bought $000 wortli of tcti, nnd by using ft false weight 
 gained |44 on tho salu of tho lot ; huw many ozs. did liu suU for 
 alb.? 
 
 11. How often does ^ {^0J^'22{',)-Uh > x ^ lO^x i^jX^^xli y 
 contain 1.')^ times 1§ ? 
 
 12. If horses and 4 oxen can consume the pasture on a field in 
 27 days, and 9 liorsos and 12 oxen can consume the pasture on the 
 same tiold iu 12 days, coni[)aro tho appetite of tho horso witli that 
 of tho ox. 
 
 13. When 1830 lbs. of hay sells for $10.47, what is hay per ton? 
 
 Exercise LXXXIV. 
 
 1. Simplify: HlxHs^f ^• 
 
 2. Have ft certain sum of money of which I spend f + $5 ; then |^ 
 of the reniaindor all but §5 ; I havo ihou left $10 ; find my money 
 at first. 
 
 3. Reduce 144 lbs. avoirdupois to ozs. troy, and express the 
 result as the fraction of 3C0 lbs., troy. 
 
 4. Sold I of ft ton of coal gjiining 8 per cent. ; what fraction of 
 the coat did the | of a ton cost me ? 
 
 6. Bought 50 lbs. of tea and codee for SL4.G0, paying 40 cents for 
 the tea anM 25 cents for the collee per lb. ; how many lbs. of each 
 were in the mixture ? 
 
 0. Sold a pile of cord wood measnrinc; 80 f"et long, by feet hiu'h, 
 getting $4.50 a cord for 10 cords of it, and $3.75 a cord for the rest; 
 haw much did I get altogether for the pile ? 
 
 7. If 2000)1 ll)s. of sugar cost £402g, how much will f\ of a ton 
 of sugar cost ? 
 
 8. Divide the L.C.M. of 1380, 1960 and 1380 by the H.C.F. of 
 1470, 4907 ftn i 507. 
 
 9. Divide $100 among A, B and C, so that B may have 1^ times 
 as much as A, and C 1^ times as much as B. 
 
 18 
 
 10. Divide 
 
 by 
 
 IT 
 
 35 
 
 3 4i^ 3A 2^ 3A 
 
 - of of 
 
 7 12^ llf 
 
 11. If f of a barrel of flour costs $1.12, what will two bags, one 
 holding y^, and the other f ^ of a barrel, cost me ? 
 
FOURTH CLASS. 
 
 95 
 
 I" 
 
 }D 
 
 of 
 
 163 
 
 12. Twelve cnlvcs are equal in value to 4 goats, ami 2 calves equal 
 to 4 pig.s, and 10 pigs co.->t $30; liucl thu vuluouf u cliuvo of 7 
 animals o( each kind. 
 
 13. Find the product of the sum and dijj'efence of 8 and 
 
 
 
 U-lJ 
 
 Exercise LXXXV. 
 
 ke 
 
 1. Find the valuo of 5J yds. cloth at SjOd. a yard, 7| yds. lace 
 at 7/8(1. yanl, and 8 qrs. 5 bushels wheat at 44/iSd. a quarter. 
 
 2. One hundred bushels of wheat ajul barley together cost 
 $70.80 ; the wheat was 87 cents, and the barley was 00 cents a 
 busliel ; how many bushels of each were there i 
 
 3. A fanner sows ^j^,l\ of an ounce of wheat to the square foot 
 in sowing a rectangular held, 00 rods long l)y 80 rods wiile ; what 
 does it cost him to sow the field when wluat is worth §1 u l»ushel ? 
 
 4. It costs $5.25 to sow a field, 40 rods long, with oats at 35 
 cents a bushel, putting on 2 bushels to the acre; how wide is the 
 field? 
 
 5. A merchant mixes IG lbs, tea, at CO cents, with 14 lbs., at 50 
 cents a lb. ; at what rate per lb. must he sell it to gain 24^^ per ct.? 
 
 6. Divide $225 among A, li and C, so tliat B may have | as much 
 again as A, and C may have J as much again as 13. 
 
 7. Find the simple interest on $470 for 6} years at 5 per cent, 
 per annum. 
 
 8. The cost of building a tight hoard fence, 40 rods long, with 
 inch-lumber, worth $10 a thousand, is $31). GO ; how liigh is the 
 fence ? 
 
 9. A lady wishes to carpet a floor 20'8" x 18'G" with 30-inch carpet- 
 ing worth 90 cents a yard, the strips to run lengthwise of the room 
 and 4 inches per strip to be allowed for waste in cutting ; find the 
 cost. 
 
 10. Express f of y^^ of a dollar as the fraction of £30 Sterling. 
 
 11. The gain at which an article is sold is 20%, and the sum of 
 the gain, cost, and selling price is $108 ; find the cost price. 
 
 12. A merchant sold a s\iit of clothes for $54, gaining thereon ^ 
 of the selling price ; find the cost of 13 dozen such suits. 
 
 ] 3. A has 14 acres, 15 sq. rods, 8| sq. yds. of land, which ho sella 
 at $22 an acre ; find his receipts. 
 
96 
 
 KXKKCIHB8 IN AUITUMKTIC. 
 
 Exercise LXXXVI. 
 
 1. A ctin do j^ of a pioco of work in 5 days, B can do j of th« 
 remriindur in 10 days, and C can tinislj it in 4 days. A and IJ work 
 togeblier ut it for 5 ilayu ; how long will it take C to finiH'i it alonol 
 
 2. Find the anioimfc of $450 for C57 days at 10 per cent, per 
 annum, simple inturust. 
 
 3. If 5 men or 8 women or 12 boys can do a piece of work in 40 
 days, how long will it take 20 men, 9, women and 9 boys working 
 together to do it ? 
 
 4. Find the total cost of ])ainling the outside of a box, (with lid), 
 4 ft. lonj;, 3 ft. wide and 4 fr. duoi), with paint at 18 cents a square 
 yard, and of lining it inside with lead worth $4.50 a cwt., j^iven 
 that 2 lbs., 4 ozs. of lead lines a 8(iuare foot of surface, and that 
 the box is 90 per cent, as large inside as outside. 
 
 5. A boy harrows, lengthwise, a roctanc;ular field containing 15 
 acres ; if the field is (50 rods lon»j, an. I the liurrovv is 15 ft. wide, how 
 far does the boy walk in going once over the field 7 
 
 6^ Simplify 
 
 : V) -^ — of 
 
 e^+iorj-?-? 
 
 of J 
 
 
 7. Find the value of a mixture of 15 gallons of brandy, wine 
 and whiskey, mixed in the ratio of 3 I 2 ; 1 respectively, when 
 brandy is $8, wine $3, and v.hiskey fl. GO a gallon. 
 
 8. A produce dealer sells 16 cwt., 30 lbs flour at $2.60 a cwt., 
 4 tons, 150 lbs. hay at $12 a ton, 4 cwt. 42 lbs. oats at 33 cents 
 a bushel, and 50 lbs. corn, at $8.86 a cwt. Find the cash receipts 
 on the sale, there being 10 per cent, off for cash. 
 
 9. Show that '4 of an acre + '3 of a square rod + "45 of a square 
 yard + 39*6 square inches—" '2 of 2 acres, 1 square rod, 17 square 
 yards, 4 square feet, 108 square inclies. 
 
 10. A and B start together from M. and tj'avel directly east, A 
 at 4 miles and B at 3 miles an hour. C starts, at the same moment, 
 from N., 64 miles directly east of M., and travels icest at 2^ miles 
 an hour. In how many hours will C be midway between A and B 1 
 
 11. Find the quotient of the L.C.M. and the H.C.F. of 444, 1480 
 and 1065. 
 
 12. By ' ow much does the sum of the following numbers exceed 
 
 2i 
 their product ? — f» I. H> I o^ 1l!J» ~"» '^h 
 
 8| 
 
FOUUTU CLAUa. 
 
 9T 
 
 I 
 
 I 
 
 If]. B lias son, which is 00 por cont. of C's motioy, which is 91 § 
 pur cunt, uf D's. Find thu siun total uf thiur ni>>nuy. 
 
 Exercise LXXXVIL 
 
 1. A cnn do a piece of work ftlone in 10 days, B in 12 days, and 
 C in '20 days. A and iJ work toj^'utlor at it for 2 dayn ; then Bund 
 C woik toj^'uther at it for li days ; utter which ull threu work toi,'t!ther 
 at it until tiiu work is fniished ; how luui^ is tlio work iindir contract? 
 
 2. A mail rom-ivus ^37. HO per diy for workiti'^ 10 liours a day 
 for 15 days ; wiiat is tlie unit oi work used in the coiii|iutution / 
 
 3. A, B aiitl C are joint owners of a rec^^uni^nlar piece of land, 70 
 cliuins h)ni( by 40 rods wide ; it has on it a standin^' crop of wheat 
 estiuiated at 3r> bushi-ls per acre, C sells the land witli the crop as ib 
 stands, receivi!i<^ ."JliOan acre for the laniland HO cents a bushel for 
 the wheat. He retains 5 per cent, of the receipts for his coinniission 
 
 as salesman, and the balance in then divided us 1.3*3;5, respuctivuly. 
 Find each luan'a share. 
 
 4. A clothier buys 15 cases of roaly-made chT^liingof 20 suits 
 each ; he sells § of the lot at an advance of 20 per cent, on cost, and 
 the remainder at 30 per cent, discoinit. What is his gain or lo^s por 
 cent, on the whole lot ? 
 
 5. A tank is ft'd by an inexhaustible supply of water which flows 
 out thnniyh an openini^, 7 inches in diameter, at the rate of 10 miles 
 an hour. ITow many barrels, gallons, pounds and ounces of water 
 [lass through the o])ening every 15 minutes ? 
 
 C. Nine bushels of rye and nine bushels of barley together cost 
 $11.34 ; the rve cost 70 cents mort! for every 5 bushels than the 
 barley ; find the value of each per bushel. 
 
 7. Simplify: 
 
 31-G-f042 
 
 •378 X 420 X 12| 
 
 of 
 
 (2i + i)-(3|-J) 
 
 + -4V. 
 
 iV J 
 
 8. Nine bells which toll at intervals of 3, 9, 12, 15, 18, 21, 24, 
 27 and 30 seconds respectively, all bi'gin tolling simultaneously with 
 the hour of one o'clock, p.m., as struck by a clock which strikes the 
 hours and half-hours. What o'clock is it when the bells all toll 
 again simultaneously with the striking of the clock ? 
 
 9. In a bag of 341 marbles, Tom's share is to Will's as ■{ ^ of 
 *of4}>-;<liof — }■• How many marbles has Tom more 
 
 I uJ 
 
 than Will ? 
 
 13^ of 5 
 
RXEItOlHKS IN AniTIIHF/nO. 
 
 10. Find tho square roof of Mm L.O.M. of IJ, in J and 9. 
 
 11. A man Hpont 8100 uml had Htill loffc 40 por cont. of wimb he 
 spoilt, which was 8w Ilhh than ^'^q of wliab hu had lib tirat. llow 
 much had h«) at lir.st? 
 
 12. A man biiys applos at, tho nvto of 3 for 6 cents, and bgUm 
 thum at thu ratu of 4 for |0 cunts ; what in hit) gain on the sale of 
 144 dozi n apples? 
 
 1.3. A, H and C toijothor, ha\ o 8-70. M has |^ os much m >noy 
 as C, an I for uvory 84.50 tliat A has, IJ and toijuthor have $11. 
 How much munuy lias each? 
 
 Exercise LXXXVIIL 
 
 1. If 20 mon, .32 wonuMi or 40 hoys can do a pi(M!o of work in 16 
 days, how lung will it taku 11 niun, 24 women and 8 hoys to do it { 
 
 2. Divide the sum of i 
 
 and 
 
 i-i 
 
 by their difference. 
 
 3. Divide $06. GO amonr; A, B and 0, so that A shall get twice as 
 much as B, and as auoh as A and B together. 
 
 4. Find the cost of lathing tho walls and coiling of a room IC x 
 12' X 9', an allowance being made for ono door (>' x 3' and for two 
 windows 5' x 3', the lath being worth 12^ cents a bunch. 
 
 6. The roof of a building is 40 feet long, and each side, from the 
 eave to the ridge, 15 feet wide ; find the oost to shingle at $3.20 a 
 thousand shingles. 
 
 6. It costs $720 to build a bridge at 18 cents a 8q|uare foot of 
 surface; tho bridge is 13 ft., 4 inches wide ; how long is it ? 
 
 7. Find the value of the following crop : 16 acres, 120 square 
 rods of oats, 19 acres, 100 square rods of wheat, and 10 acres, 76 
 square rods of barley ; the oats yielding CO bushels to tho acre, 
 worth 36 cents a bushel, the wheat 45 biishels to the acre, worth 
 $1.12 a bushel, and the barley 50 bushels to the acre, worth 56 
 cents a bushel. 
 
 8. Out of a cistern, containing 57 gallons of water, 14 pails were 
 taken. If the pail held 2 gallons, 3 quarts, how much water (in 
 gallons and quarts), still remained in the cistern ? 
 
 9. Gentlemen's neck-ties are bought at $3.50 a dozen, and Hold at 
 35 cents each. What is the gain on the sale of 300 such ties ? 
 
rOUKTtI CLASS. 
 
 99 
 
 10. If 839.12 wore paid for ft load of wlioat at 31.00 a bushel, liow 
 many bushuls niu\ Wm. did tliu load contain / 
 
 11. Find thofn.dnotcf tho L.C.M. of 0, 12, 20, 24,54, 81, 03, 14, 
 and tlio II.C.F. ot J)45, 840, aud lL'ii5. 
 
 12. Simplify: ^ i + !^ + l + ^ + ^, + ^„ ^ x i,A,-^ + ^,),. 
 
 13. Dividu V.VM) among A, Band 0, «o that for ovory !i:5 that A 
 gets, B Hhall get iglO and C ;jjf8. 
 
 i 
 
 Exercise LXXXIX. 
 
 1. A man earns $040 a year and .spends 8400; how Ion-' will it 
 take him to pay for a roctanguhir plot of grt)nnd, 40 hy 'M md.*, worth 
 $80 an acre i 
 
 2. Find the net roceipt.s of the following hill, 6 per cent, hoing 
 allowed oil' the face valuu tor cash : 
 
 13 hushols, 1 pock j^ra.ss-sood at !?C a bu.shel. 
 
 20 Ib.s., 1.") o/s. oheisso at §16 a cwt. 
 
 50 11)3. hay, lit .^18 a ton. 
 
 30 07.S. gold dust at !i<'J0O a lb. 
 
 51b.s. leadat .«!0.i:ia lb. 
 81 lbs. nails at $0.05 a lb. 
 
 3. Paid $22.50 for buckwheat at CO cents a bushel ; how many 
 bushels and lbs. did I buy / 
 
 4. If $78.75 are paid for flour at $3.75 a barrel ; how many cwt. 
 and lbs. are there ? 
 
 5. A soils land for $310.10 at $22 an acre ; how many acres, rods, 
 yards, feet, and inches does he sell i 
 
 6. Divide $108 among A, B, and C, so that A shall have | as much 
 as B, and that B shall have ^ as much as C. 
 
 7. A merchant sold velvet at $0.50, and lost thereby 7} per cent. ; 
 find the cost price of the velvet per yard. 
 
 8. The cost price of a rectangular piece of land, 10 by 18 chains, 
 was $4250. It was sold at $80 an acre ; find the gain on the wile of 
 the land. 
 
 9. How often does the square of 890040 contain 873 x 441 -r- 03 / 
 10. Simplify : ■[ / ^ \ x \ - — - + f of | 
 
 r ^x 
 
 lAof 
 
 ^ofuoiy u-i 
 
 of ll 
 
100 
 
 KXEUCIHRfl IN AUITIIMRTIC. 
 
 f. II. Roiii^lit luMiiils fur ^.-jT-OO lit 3 crtifH (i «1m/.i|| ; if | of tliciii 
 \V(iru Hold at tlic into of 'JO for Tt cents, wliiit did tliu huliiiicu Null for 
 |ii)r do/A'ti, Ho HH to incur licit licr guiii nor [vhh i 
 
 I'J. If II lo.iii of ^VrU) hrin^s in ^■l.'2iVfi inforcst h month, wimt in 
 tho rutu per cent, ut wliidi tlic money ih luuiiud / 
 
 13. Fin(' tlio Mim of tlm thirr f|Motii'ntH urisintj from the diviHJon 
 of tho L.C.M. vi ob04, 4biiO and 4*>.»'4 by each of tiio given numbers. 
 
 Exercise XO. 
 
 |~-7 + i| X L\ X 1^) + S + ir»i?.^ 1. 
 
 1 
 
 2. Find tho L. C. M. of (a) 4(1'-', 5:i4, 023, r,93, 728 ami 930 ; and 
 
 3. A certain niiinhiir of lbs. of cotlee cost J?32. It was hoM a<^ain 
 at 62 centM u 11*., giving u piolit of 30% ; iiud thu nuiubur of puundN 
 bought. 
 
 4. TiiO amount of a curtain 8um at interest for 8 years at U pur 
 cent, is $404.40 ; find the sum. 
 
 5. An article is soM at 12\ per cent, advance on tho cost i)rico, 
 <ind the siunoi the gain amd HuiiiuK price if* $1050 ; find the seilin^ 
 price. 
 
 6. Nine men receive 8''»33.()0 in H\ (lays, working 8 hours a day; 
 what are each man's hunrhj waycs ? 
 
 7. The amount of a certain sum is .ii<(»5rt.2(), the time 7 years, 
 and tho interest jrijj of the sum ; Hnd the rate percent. 
 
 8. Find the amount of $500 for 10 years at 4% simjde interest. 
 
 9. A farmer sold an equal number of horses, cows and pigs for 
 $1755, receiving $32 for eucii cow, $90 for each horse, and ^13 for 
 each pig. Find the total number of animals sold. 
 
 10. A has a farm | of a mile long and 20 chains wide. What is 
 it worth at $03 an acre ? 
 
 11. Divide !fC7.10 among four boys, giving each one ^ less than 
 the one beftne hiui. 
 
 12. Divide $25.20 between two boys, so that <;ne may receive GO 
 cents more than twice what the other receives? 
 
 13. A cart-wheel makes 2(i40 revctlutions ingoing 11 miles ; how 
 uiany inches in the wheel in diameter i 
 
FOURTH t'\.\nn. 
 BxercisB XOL 
 
 101 
 
 t. Simplify 
 
 ^^x5■^i!x^ 
 
 i|of l^^+2J..f :n 
 
 xni of £3, null., 8(1. 
 
 7 
 
 2. A boivrcl JM IS foot \>m<i hihI in iridion wido ; whiifc ih i^ wurHi 
 wliiMi liiiiilKtr IH H()lliii)4 lit ffU\ ti tli'MiMaihl fuot? 
 
 M. Il inr|iiirt'(l HRLMU) nntU, oixcU 2 - foot by — foot, toturf aror- 
 
 V2 12 
 
 b<iiii plot of groiiiitl ; find tliu valnu of tiie plot at $145 an Hore. 
 
 ^. 
 
 4. Eff'^'M rost 13 crntM ft (Inznn, mid 1(5 of tljoni are hoM for 20 
 V>ntH ; linw iiiiuiy dn/.m sold will pt'udiico u i^Min of 91 05 '/ 
 
 5. Urown's fmiii cntisists of 10 uniform, rm't.inv'nlar Molds, oai'h 
 53]^ roil.s long by 31) rods wido ; how in.iny acro.sof i.md has lirown/ 
 
 rt. Simplify 
 
 r>iof 4^-2|of 3 
 
 h 
 
 r2iu ) 1 
 
 7. Dividt^ ^1200 umojiif A, R nud C, so Miit "R shall roocivo " an 
 much as A, and that C «hiill rccnivo I as niiH'h us \\. 
 
 8. A morchant bou'jflit .suj^ar at .Sir)0 a ton, and sohl it out ftt 4 
 lbs. for 33 cents ; find his gain por cent. 
 
 9. A room, 31 \ foot lonpf and 15 foot, iiichos wido, will ro(]uiro 
 how much lo.>s than 100 s(|uaro yards of cnrpot to cover its floor? 
 
 "0. How often does tho L.O.M. of 2, 4, 21, 3C, 46, 91 and 180 
 contain tho H.C.F. of 5(542 and 74G2? 
 
 11. When tho minute hand has travelled 330® on the dial-plate 
 of a clock since 3 o'clock p.m., what time is it ( 
 
 V 12. Find the L.CM. and tiio H.C.F. of tho following numbers 
 
 f\y rcsolcvK) each of thom into its prime factors, and thon selecting 
 
 the L.CM. and H.C.F. from those factors : T.'idO, 8820, and 44100. 
 
 13. (rt) Tom's age 5 years ago is to his age 3 yoars hence as 2; 3. 
 How old is Tom now ? (/>) A owos a grocery bill of $750.00, pay- 
 able in 3 months. What sum should A now put out at interest so 
 that the sum, together with the interest thereon at 8 per cent., 
 shall exactly meet the bill ? 
 
102 
 
 BIRRCISRS IN AUlTUUKTia 
 
 Exorolae XCIL 
 
 1. If 613.50 buy il uf a tun uf tlax. what fraction of a ton will $30 
 hny ? 
 
 2. A piiioo of I.ukI (v><«f h $ IOSO .it $80 un aero ; it is 20 chains -^0 
 links wiilu, how h>n.( in it in ri»tU / 
 
 M. I tow iimuy '2\ innh riihoH c;i?j hn rut o>it of A block of ntonn 6 ft 
 loii'^, 'l fi't't, 1.^ inohitu wiilu, nuA 10 iiichoM iloop ? 
 
 4. 'I'hf r(Mimiii(1<>r, 9, ia f of thu divisor And } of thu quotlonfc ; 
 wliiit is Lhi) (livhltMnl f 
 
 5. Fiii.l tho I.e. INT of: 
 
 (m) 4, 'JH. HJ. 72. on and 108. 
 (/>) 8, 1>, L'T.^ii, .'U>, 45muir)2. 
 
 0, Thu cost to fonouH road on both nidei, at 15 oontsA rod| is 
 
 f28.SO.()t). How many iiiihi.s lonu iH it? 
 
 7. At what rate, in milos and roiU per hour, will C2 miles, 200 
 rods 1)0 tnivtllrd ovor in hours, HJ mimitfs, 40 Hocond.s ? 
 
 8. Divi.lo tho L.C.M. of 18, 48, 04, 72, 28, 00, 132 and 244 by the 
 II.C.F. uf 275781 and 27<1025. 
 
 0. Find t]\t) t.ot.;vl cost of : 
 
 32 tons. 000 lbs. middlinp's at Si 5 a ton. 
 7044 Ih.s. b.-irli'y atoli cunts a bushol. 
 
 10. A p(M-.sMn hi>ii;ht 4 bii.shol.s, 12 p[.illons of whoat at 2cnntsa lb. 
 and 5 bushols and a oiTtaiii niiinhor of piUons of oats at con>ji a 
 
 II !ck, payiii'4 for the whoht ^\). 12. ilow many gallons uf oats did he 
 my altogothur ? 
 
 11. Whoii 20 lbs. of potatoes cost 25 cents, what is tho value of 
 76 bti.sliols ? 
 
 12. Divide tho L.C.M. of 21, 42, 18, 36, 9, 46, 180, 90 and 040 by 
 tho G.C.M. of 3232 and 1952. 
 
 13. Sirjplify-{ ^g + JJ + ,itj + |f-?3)x 
 
 U(48Jx9). 
 
 Exercise XCIII. 
 
 1. If six score is a "lojijr" hundred, how many dozen herrings 
 are there in 132 b(/\os of 2 " hmtj" hnndrods each? 
 
 2. Simplify : 
 
 ^ga-ll)of8xUH-6U 81^31 
 
 of 
 
 1 + 5 + U + H 12x4 
 
rOURTll CLAHH 
 
 103 
 
 130 
 40 
 ft, 
 t} 
 
 )0 
 
 a 
 e 
 
 3. If 40 rnili of h tologrA|)h lino cost $00, fltid tho valu* of 40 
 AilluM of tltu Nuiito lino. 
 
 4. It cowtN 91R-) t'> fi^<^<l in horfloi nn oiitn for (( wuokM, giving uach 
 hurMu 3 p«''kN Uuily ; tind tint piicu of ouls prr htisliul. 
 
 6. How ninny liarndn n fluur, ut fRu hun**!, mIioiiM Ih* i«x(*lmnii{ed 
 fur 'trio |MiMiiiN of oiitNnt 3r> cuntM a IhihIu'I, •)'.'(;() |ioiin<iH of wluut 
 At 81.10 li I)iinIm*I, Mo jxMitiiU (if oliivor NiHul ut )iilll.(«0 u hunhul, aud 
 610 (KMiiuU of huuf ul clO a huiidiod weiglit'/ 
 
 6. A hoy taI<o« 13'J0 Rfo{»^, oaoh 2 ft., fl in. lonjf, in i^oinj^ round 
 
 X 
 
 roctjinuulur Hold 00 ludi bng. ilow niuny aciiis doua tliu Hold 
 contain i 
 
 7. Out of a H\\u\ r* SCfM^.OO. 8702.20 aro allotted to a chiritablo 
 inHtirMtioM, and of tl o runiaindor M i;t<ts 20 per (;unt. nioru than A, 
 and C 20 per cmt. nioru than it. Find C'h hharc 
 
 8. t)ivi(U) ^.'{0(1 anifnitj .lann's. Androw and Uohort, giving An- 
 drew $13 Ivsn thiiii iluniu.s, and 1^13 ituirt' thiiii Koli(>rt. 
 
 0. Find thu cost of paperinj? a room 40' 2" hy 10' 4" with paper 
 worth 05 cunts u single roll, uU iwing, fur windowtt and doorH, 9 
 ■ti-ijiN. 
 
 10. Wluit will it co«t to paper tho walls of an opera h«ins»>, flO'x 
 40', with p:i|i('r worth 81.(10 a donl>io roll, allowing fur 1.3 windows, 
 each 4' wide and 3 door.s oadi 8' wide, iho coiliiij.? being :J7j'nt hiyhf 
 
 11. Find the cost of carpotincif tho opera house, in qiustion 10, 
 with 45 inch wido carpeting at $1.20u yoi'd, thu HtripH tu run length- 
 wise ot the house. 
 
 12. Find tho cost of itapcrinif ft room 70 by 30 feet, with paper 
 wortli 85 cents a double roll, allowing 14 strips for windows and 
 duors. 
 
 13. Have a certain sum of which I spend ^^+82, then \ reiiiuin- 
 der + $3; after which I have still left $3. iluw much was tlte 
 original sum ? 
 
 Exercise XOIV. 
 
 1. Sold 80 yards cotton at 12 cents a yard, gaining | of the sell- 
 ing price : Show that 20 per cent of tho number of yards at cost 
 price is equal to the gain at which the cotton wa.s sold. 
 
 2. Find tho sum of all the odd numbers from 781 to 797, in- 
 clusive. 
 
 3. A, B and C can do a work in ISJ^ff days working together. A 
 and B together can do it in 24 days. In what time can C do it 
 aluno 7 
 
: 
 
 ^•'^ 
 
 ii 
 
 KXEKC18E» IN AUllilMETlC. 
 
 4. A merclmnfc buys 640 yards of cloth at 80 cents a yard. He 
 Bells ^ of it at V2^% advaticu on cost, and the rest at 10% advance 
 on cost ; find his entire gain. 
 
 5. Simplify: 4< - 
 
 Hof^\ X 7J 
 
 }- 
 
 of lif Vof lllBhUling8,Sterlmg, 
 
 * X § of U 
 and reduce the result to dollars and cents. 
 
 6. A rectangular farm contains ^ of a square mile of land. It is 
 93J chains long ; how many rods wide is it ? 
 
 7. A house and lot toLjether cost 8^90, and the house cost 25% 
 more than the lot ; Hnd the cost of each. 
 
 8. A merchant sold 3 tons, 120 lbs. of yarn in 7-lb. and 10-lb. 
 packages, selling an equal number of each, and getting IS»37.50 a 
 dozen for the larger packai;;es, and $27 50ad(»:^en for the smaller 
 packages. How mucli did he receive for the yarn ? 
 
 9. A pile of 20-inch wood, 80 feet long, and 4 ft. 6 in. high, is 
 Bold at $2.40 a cord ; fiiid the receipts for wood. 
 
 10. Find the total value of 15 bushels 12 lbs. wheat at $1.20 a 
 bushel, 16 gallons })ea3 at 7') cents a bushel, 24 pounds of potatoes 
 at 35 cents a busiiel, and 72 pints of rye at 72 cents a bushel. 
 
 11. The amount of a certain sum of money for 5 years, at 9 per 
 cent., is ^263.90 ; find the sum. 
 
 12. Multiply the difference between 67x85 and 50 (07 +85) by 
 -{ (896 times 987)4-141 )-, 
 
 13. (o) Find the product of the sum and 20% of the sum of 402 
 
 and 63. Divide the product thus obtained by 156^ 
 
 ■ 22H ^ 
 
 of m|. 
 
 (&) In 1892 a merchant's profits were ^ of his receipts. 
 At what rate per cent, profit were his goods marked 1 
 
 Exercise XCV. 
 
 1 . On what sum is the interest for 8 years at 5 per cent, equal 
 to the interest on $202.50 for 20 years, at 4 per cent. ? 
 
 2. If ^ of a number plus 3 is equal to ^i; ot the same number 
 filiis 8, what is the number ? 
 
 
FOURTH CLASS. 
 
 105 
 
 lal 
 
 >er 
 
 3. (a) What iimst we do ^vith fractiona before we can compare 
 tliem ? (b) liy Iiow mucli docs tlie (jreatest of tho fnllowinj; frnc- 
 tions exceed the least •''-iVsj iU *"^^^ i^j* (0 AiTungo them in order 
 of iiiiigiiitudc. 
 
 4. Tho (jnotient is 10 times the divisor, and tho latter is 17 times 
 tho remainder, and the .sun of tho three i.s UliHO ; find tho dividend. 
 
 5. The snm of 82')0t is divicUul amon*^ A, B and C, so th.it B 
 shall receive 5 times as much as A, ami that G shall receive 7 times 
 as much as A and B together. lIow many times A's money is B's 
 and C's together ? 
 
 6. Tho amount of $021 for 9 years is $900.45 ; find the yearhj 
 rate of intfrest. 
 
 7. On S")12, $7 10.. SO is due at the end of a certain time at 5 per 
 cent, per annum ; find the time. 
 
 8. When 60 tons, 870 lbs (jf hay sold for $!)0C.9G, what was hay 
 per ton ? 
 
 9. A farmer sold tubs of butt(!r of 30 lbs. each at 30 cents a lb., 
 and 50 dozon eggs at 37A cents a dozen ; he then bought with tho 
 money, 93 lbs., ^^ of an oz. butter ; what was butter per lb. ? 
 
 10. One man travels 10 miles, 120 rods per hour for 8 hours a 
 day, and another man travels 140 miles, 30 rods per day. How 
 much longer will it take one man than the other to complete a jour- 
 ney of 5S7273 miles, counting days to a week ? 
 
 11. Find the square of the sum of all the odd numbers between 
 780 and 798. 
 
 12. Sold fifty-four dolhirs' worth of eggs at 10 cents a dozen ; if I 
 had bought the eggs at 9 for 10 cents, find my loss. 
 
 13. (a) What is the total amount of the following bill : 72 dozen 
 fish at 3 for 5 cents ; 21 oranres at 20 cents a dozen ; 114 lbs. sugar 
 at 19 11)8. for a dollar. (6) What is the balance due on a note for 
 $250 at C per cent, interest for two years, on which a partial 
 payment of $05 is made every six months '( 
 
 Exercise XCVI. 
 
 1. What is 25 ])er cent, of $640 ? Invest it in oranges at 3 for 
 ten cents, and find the number of dozens b;)Ught. 
 
 2. Three -fourths of a dollar is what fraction of 340 cents? 
 
 3. A boy takes 5420 steps in going from X to Y. If 6 steps 
 are equal to one rod, how many miles, rods, yards, feet and 
 inches is it from X to Y? 
 
106 
 
 EXERCISES IN ARITHMETia 
 
 4. Forty per confc. of a barrel of 9fi dozens of egj»s was sold 
 at 3 fur 10 cunts, and the re»t at 15 cents a dozen. Find receipts. 
 
 5. If 13 dozens suits of clothes cost $7488, and the selling 
 price of a suit is $54, find the <;uin per cunt. 
 
 6. If 5 lbs. tea at 78 cents a lb. be mixed with 8 lbs. at 65 cents 
 II lb. and the mixture be sold ut 80 cents a lb., find the gain per cent. 
 
 7. Cloth, which cost $1.00 a yard, is marked 40 per cent, below 
 cost ; find the soiling price of 700 yards. 
 
 8. Subtract ^f + ii + i'j + A + T^'^fy) from 3 J, and multiply the 
 difference by 342J^ ; then, divide the product by 84^^. 
 
 9. Arrange in order of magnitude : f, gg, f j^ and J. 
 
 10. Simplify : 15 
 
 2Jx7^x^ 
 
 •} 
 
 11. Find the intermediate fraction between ff J} and ||^, whose 
 denominator is 2613. 
 
 12. By how much does a barrel of wator exceed a barrel of fish in 
 weight ? 
 
 13. (a) A stationer bought 20 bales of paper at $20 a bale; he 
 then sold it again at 12^ cents a quire ; find the gain per cent. 
 (b) How much tea at 30 cents a lb. must I mix with 18 lbs. at 45 
 cents a lb. iu order to produce a mixture of tea worth 39 cents a 
 lb? 
 
 Exercise XCVII. 
 
 1. In going from A toB a man takes 5,400 steps, each 2 feet 
 3i inches long. How many miles, rods, yards, feet and inches does 
 he travel ? 
 
 2. Divide 3 acres, 240 square rods by 2 square feet, 36 sq. inches. 
 
 3. At 20 cents a rod, it costs $92.40 to enclose a circular plot of 
 ground with a fence ; find the value of the plot at $3.20 an acre. 
 
 4. Divide $7098 among A, B and C in the proportion of 2, 6 
 and 7. 
 
 6. A boy has 91 coins in his purse, made up of 5-cent, 10-cent 
 and 25-cent pieces. He has twice as many 1 0's as 25*8, and 5 times 
 as many 5's as lO's. How much money has he ? 
 
rouRTo CLASai 
 
 107 
 
 fl. A rectfingnlar farm is 50 chains loncf by 50 rods wirle ; a strip 
 40 rods in width is sold otl' tlie entire Icnyth of the fjiiiii. (a) How 
 many acres and sc|uaro rods jire sold ? (6) Wliat is the remainder of 
 the farm worLli at ^05 an acre I 
 
 7. Find the value 
 land at $(>9 an acre. 
 
 •■{ 
 
 lllH-^ofA 
 74| 
 
 ofisjof 
 
 a square mile of 
 
 8. Find the cost of 29 lbs., 0}i of an ounce of tea at 60c. a Ib.f 
 and 45 ll)S., 2 02:3. butter at 20c. a lb. 
 
 9. If $3i;0 amounts to $1101 in 6 years, at what rate per cent 
 per annum is it loaned ? 
 
 10. Find the value of 29040x30405-100002045-^-0031. 
 
 11. A can walk 3 miles an liour, and starts on a journey at 
 G.30 a.m. B starts 2 liours, 45 minut«^s, afterwards for thu Maine 
 place, and along the same road, and they, together, arrive at their 
 destination at 4.45 p.m. How fast did B walk per hour, if they 
 both stopped 1 hour, 30 minutes for dinner ? 
 
 12. Find the value of ^ of 2 pecks of beans at $3 a bushel, /t- (4 
 4 quarts of onions at i;^0 a bushel, ^V of 8 gallons of beets at $1.80 a 
 bushel, and 7 lbs. of potatoes at 23j cents a lb. 
 
 13. A can do a work in 5 days, B in 6 days, and C in 15 days. 
 They work together at the work until it is finished. If $13.20 is 
 paid for the work, find each man's share. 
 
 6 
 
 nt 
 
 169 
 
 Exercise XCVIII. 
 
 1. Find the total cost of 16 bush., 18 lbs. peas at 70 cents a 
 bushel, 42 lbs., 12 ozs. butter at 28 cents a lb., 13 bush., 15 lbs. par- 
 snips at 36 cents a bushel, and 6 bush. , 40 lbs. onions at 90 cents h 
 bushel. 
 
 2. Simplify: 
 
 r3fX9 ^-(Hi)l 
 
 ^_ — _^ Uif 
 
 L f ot 
 
 4 _ 7 
 "ft T F 
 
 
 ^13. 
 
 3. Divide ^609 between John and Robert, giving .John (3f § x 
 2^1 X i^j X 2^^) times as much as Robert, 
 
 4. Had a certain sum of money of wliich I gave away $3 more 
 than I; then $1 more than /y of the remainder; then $5 less than 
 f of what now remained ; after which I had still left $15. How 
 much money had I at first ? 
 
log 
 
 R1BKCISR8 \S ARITIIMETIO. 
 
 5. A farmer soils 40 i,'oe.so and a certain nmnl)er of turkeys at 
 the average price of U() cciitH each. Ho reroivcs 75 cciitH each for 
 tlio gecHu, and $1.20 each for the turkeys. How many turkeys 
 does lie sell / 
 
 0. A merchant buys CO wobs of cotton of 42 yards each at cents 
 a yard ; he then sells \ of it at 25 |»er cent, atlvanco on cost and the 
 rest at 8 cents a yard ; lind his total gain on the sixty wubs. 
 
 7. A sj)eculator bought 5 acres of land on the confines of a city 
 at^lOO an acre. Ho divided it into lots, each 12 rods long and 2 
 rods, 3 yards, 2 feet wide. He then sold the lots at $75 each ; tind 
 his gain, if it cost .^75 to survey the lots. 
 
 r 3,Vx§xlixf 113x81 
 
 8. Simplify : -^ x 
 
 LC,-Vof l2%of Klflof I 14 
 
 9. Find the <listance, in miles, rods, yards and ft et, that a man 
 travels in 13 days, l;{ hours, 40 minutes, at tlie average rato of 35 
 miles an hour, 8 hours constituting a day's walk. 
 
 10. Find the value of 5 
 
 Hi' 
 
 yards of scalette at $7 
 
 
 a yd. 
 
 11. Find the L.C.M. of 14, 15, 20, 12, 30, 7, 8, 4, 21, and divide 
 it by the H.C.F. of 30 and 75. 
 
 12. Find the prodnct of the L CM. of 3, 9, 17, 81 and the L.C.M. 
 of C, 7, 8, I), 5(>, 252; incre.ise it by 30 and divide the result by the 
 L.C.M. of 13, 39, 12 and 78. 
 
 13. The amount of a certain siim for 5 years* at 6 percent, simple 
 interest is $191.10; tind the sum. 
 
 Exercise XCIX. 
 
 1. Simplify : 
 
 7i + 6HlA 1 riV + 7'o+3'*(I 
 
 vn-^'^h-ii) Ux§xSx2t. 
 
 2. A man owns ^ of a potato plot, and B the rest, and \ of the 
 difference between their shares is 42 bushels, 2 pks. Find the 
 value of the potatoes in the plot at GO cents a bag. 
 
 3. When 28C0 lbs. of hay sells for U1.44,, what is hay per ton ? 
 
 4. Find the L.C M. and G CM. of (7-iJ-r4i-V) and (14^4-9^1). 
 
 5. How many s<][uare rods in | of '1 of an acre 9 
 
FOURTH OLABS. 
 
 109 
 
 |l? 
 
 fi. If $133 gives 5 per cent, giun, what is the gain per cent, at 
 1158} ? 
 
 7. Dividt! 8510 among A, B and C, giving B half as much as C, 
 and A I as much as B. 
 
 8. It takes A and li 1^ days to mow a certain field. A alone 
 can mow it in 4 days. How long will it talvo B alone to do it ? 
 
 9. It reqiiiri'd 3.5n424 sods, o.ich 2 ft, .*»), inches long by 8} inches 
 bi'oiid, to tiiif a Curtain lot ; tind the size of the lot in acfes. 
 
 10. Tlio amount of a certain sum for a certain time at 7 per 
 C(!nt. is 8508.20, and the amount of the same sum for the same time 
 at 12 per cent, is $571.20 ; tiud ihu .sum and the time. 
 
 11. If 20 boys or 15 men can do n work in 19 days, in how many 
 days could 24 boys and 20 men do it ? 
 
 12. Find the cost of p.ipering tht; walls, and painting the ceilings 
 of a room 30 ft. 2 in. by 24 ft., 4 in., there being 3 doors, each 3 ft. 
 wide, 6 windows, each 2 ft., 8 in. wide, the papur costing 8 cents a 
 single roll, and the painting 18 cents for every g of a sq. yard. 
 
 13. Find the amount of the following bill of goods : 
 
 24 yards, 9 inches carpeting at 80 cents a yard, 
 62 yards, 2 feet car[)eting at 1)0 cents a yard. 
 3G yards, 2 ft., G inches linen at 30 cents a yard. 
 73 yards, 4 inches hump carpet at 18 cents a yard. 
 
 Exercise 0. 
 
 1. Find the greatest factor common to 209 and 312 and the least 
 number into which they will each divide withojit a remainder. 
 
 2. At 3 J cents a square yard for material and labor to hang, 
 what will it cost to employ a paper-hanger to hang 5'J double rolls 
 of Canadian wall-paper, each roll IG yards long ami 21 inches wide? 
 
 3. Using the 'iii.e<iii. berwetm 8750 .iiid 33 J2 as a co-factor of 11466 
 find the rtsiUt and write it out in ivorUs. 
 
 4. A man bou'^htafarm for 
 and twenty-dollar gold pieces. 
 many were there of each ? 
 
 L3000, payin^^ for it with ten-doliar 
 If he paid in all 825 coins, how 
 
 6. Simplify: 
 
 r, 5 
 
 X 41 
 
 
 7t5 
 
 
 2 a0fx2}na 
 
 X 
 
 G 
 
 6. Have 30 gallons ale worth 20 cents a gallon ; hew much water 
 must I add to lower the price to 15 cents a gallon ? 
 
no 
 
 EXKUCISRS IS ARITIIMBTIO. 
 
 7. HajM^ worth $5 a ton anfloat.s35c«!its ii l)tisliel, and ahorse 
 eata 20 Ibn. of hay and 2 t,MllouH of oats dnibj from Fobrnary l.'ith, 
 1802, till July .'Ust in tho saino yuar. both days inckisivo. Find 
 the total cost of fending tho horsu during that time. 
 
 8. Two-fifths of fi section of land is sown to wheat, ^ of the .3- 
 maindnr to oats, and tho remaining 102 acres to l)arley. (a) Find 
 th»! value of the whole section for land and crop thereon, at ^40 an 
 acre, (h) Jf tho land cost $17U2 more than tho crop, what is tho 
 land worth per acre ' 
 
 9. Find the dlferenre between 08 x 46 - 8 -J- (91 - 40) an'' 40 X 35 
 + 2025-r5, and S(piaro tho tifth part of it. 
 
 10. Sold 80 bnshels of ajifjlos at 00 cents a bag, and gained there- 
 by ^IG ; what did I pay per bushel for tiiem ? 
 
 11. (d) Write a fraction that will ox[)rea3 the Fignro A C T) 13 us 
 a part of H C D F, as a part of E G D F, referring to tho following 
 diagram : — 
 
 H F 
 
 (6) What kind of a fraction have you ? (c) Show that the Fig. 
 A D B is three-eighths of the Fig. E G D F. 
 
 12. Divide $100 among A B and 0, giving A ^ as much as B, and 
 B 3 times as much as 0. 
 
 13. Find the cost of carpeting a room 31'6" by 2410", with 30- 
 inch carpet, laid down lengthwise of the room, and costing $1.20 a 
 yard, nothing allowed for waste in cutting. 
 
 Exercise CI. 
 
 1. A debt of $368.35 is due at the end of nine months. What 
 sum of money put out immediately at 8 per cent, interest, will at 
 the end of the nine months liquidate the debt? 
 
 2. Bought a certain number of cows and sold them again at 
 $40 each, thereby gaining $135 on the lot ; but, had I sold them at 
 $21 each, I would have lost $378 on the lot. How many cows did 
 I buy, and what did they cost me per head f 
 
 ■ s. ■ 
 
rOUHTH CLAHvS. 
 
 .111 
 
 ^ 
 
 3. Find tho cost of papering tl\o walls of n room, 48 ft. by 32 ft., 
 at 81.05 u (loulilo roll, m\ uUowanco buing made for 8 windows each 
 2' 7" wido, ttud for 2 doors ouch S 2" wide. 
 
 4. What is tho bal.mco duo on a noto for 8250 to run for 2 years 
 at C pur cunt, pur ainnnii, a j)arlud piujmod of '^iJb buin;^ nmdu on 
 tiio nutu ovury six mouths I 
 
 5. A and B toj^other can do a pioco of work in 81 Ijours, A and 
 C can do it in 10 hours, and Band C can (K> it iu 12 hours. Out of 
 80 paid for tho work, what is tho sharo of ouch, whon tiioy all work 
 toguther at it? 
 
 6. When tho sum of 8500 amounts to 8710 in 7 years, what is 
 tho rate per cent., pi;r aunnum, at which it is loaned 'I 
 
 7. (n) Draw a note for 8205 at nine months payable by yourself 
 to A. T. Moody or order and bearing interest at 5 per cent, per 
 annam. 
 
 {h) B does H as mueli work as A when they woik to-j^ethcr, and 
 they both together take 2'i days to do a piece of work. Ilow long 
 would it take each one win-king alone to do it? 
 
 8. A man spent \ of his inoncy + 810 and ho then lacked 820 
 of having tho half of his money left. How much money had he at 
 first ? 
 
 9. I bought goods for 8240, and sold them again at 15 per cent, 
 advance on cost. What did I get for the' goods / 
 
 10. When 16 ILs. of tea cost !?G.80, what is the value of ^^^ ozs. 
 of tea ? 
 
 11. When 18 bushels of wheat cost 815.93 more than 18 lbs. of 
 vvlieat, what is wheat per bushel ? 
 
 12. If f of A's money=§ of B's in a purse of 8132, find the share 
 of each. 
 
 13. If 10 caps are exchanged for 25 hats, what per cent, are caps 
 dearer than hats ? 
 
 hat 
 at 
 
 at 
 
 at 
 
 Idid 
 
 Exercise OIL 
 
 1. Bought 45 bushels, 2 pks., 1 gal. wheat for 847.45, and sold 
 16 bushels, 1 peck, 3 qts. of it for 820.92. Find my gain per bushel 
 on all I sold. 
 
 2. Find the L.C.M. and H.C.F of 130^ 7| xlU x tI x4A )- and 
 Jof ^16§xl|x2^x6Ax22|.. 
 
 1 1 
 
112< 
 
 KXKKCIUKN IN AKII'llMKTIC. 
 
 3. A nnd B rent a pnstiirc for 9fi2. A puts in 10 oown for 4 
 montliM, unci B a certain numlHr for & nioiitliH ; B payn ^bO ol the 
 rent; huw nmny cuvvs hu<l hu in tlip pastnru i 
 
 4. What number boars the sanio relation to IJl, as 61 doeH to 17 ? 
 
 B. A fanner, " brcakin;;," on the |ti'aiii(», hnlf the lon^^th of a 
 ** qudyfi'V-sei tiiin,^' vsnrks 18 liours, 45 niimito.s a day f(»r one week. 
 ITow inui h prairie docs lii> turn over in that time if his plow cutn u 
 14-incli furrow, and his team truveU 2A miles an hour, an allowance 
 bein;4 nuule of 1^ niinutcH every time in turning' aro\ind '/ 
 
 fi. Flour sold at S0.80 a barnd gave a profit of 42^ percent.; 
 find the cost of the Hour pur cwt. 
 
 7. What is tlio name of the Rule by whi(;li "ire fdJcr ane nvmher 
 as man 1 1 tivics (tx tlnttr are imUs in <iii()tlit'.r' '. (Jive an cjxaniple to 
 show that you undtrHland the (picstion. Mxplain your example. 
 
 8. Define intf'.o.sl. Find the Kiniple interest on §.'JliO for 511 
 days at 5 pel ct*nt. per annum. 
 
 9. What time past 12 o'clock will the hands of » watch be 240 
 degrees apart ? 
 
 10. Reduce 40 cents to the decimal of $2Jj. 
 
 11. Tom lost 2 more than ^ of his marbles, and liad still left 6 
 more than f of them. How many marbles did Tom lose i 
 
 12. A can mow 9 acres (tf hay in days. B can mow 6 acres in 
 4 days, and C can mow 18 acres in 10 days. How lonji^ will they 
 jointly take to mow 130 acres, 80 rods '/ 
 
 13. The net cost of a bill of goods is S.')()7.54, after two successive 
 discounts of G percent, and 8 per c(!nt. have been deducted from 
 the invoiced price. Find the invoiced prico. 
 
 Exercise CIII. 
 
 The old par of exchange on Sterling money is 84.44J[ to the £. 
 What does an Englishman benent by the iioiv par of exchange over 
 the oldy in exchanging £900 Sterling for Canadian currency ? 
 
 2. What per cent, is the new par of exchange in advance of the 
 old? 
 
 3. A rabbit is 376 of its own leaps ahead of a dog, and it takes 
 12 leaps while the dog takes 6, l)ut the dog covers as much ground 
 in 2 leaps as the rabbit does in (5 leaps. How many leaps does the 
 dog take in catching the rabbit ? 
 
rolfRTIf ('LA8><. 
 
 113 
 
 28 
 (d 
 
 •I. If >\ ^iiiiu-a he worth l?.">. 1 1 , :in<l a Kontlonmn has 8*'286.iJO in 
 CaiiiuU.'in ciiiTi'iicy, whiit is hu wnith in Kii-^hsh luotiuy ? 
 
 5. By ri'Hohitioii into piimn fditors (no Inn<^ (livision to h» used) 
 find the L.C.M und tho (J. CM 'of l().';:.(). 1 l.'JO^'J Jind hWKuVX 
 
 (i. Divide !?l()r).:t() hotwoon A an<l II (I) so th.if A shall have 
 twice as iniuih as li, and (li) so that A shall havu .*::<; 10. '{() more than 
 tivice the half of iJ's ; {',)) Which is thu l)i!ttoi' division for A, and by 
 how iiMich i 
 
 7. Twelve rolls of carpot, wei.,diin</ in all ('» tons, I HO Ihs., 
 cover a sni'faci) of 'J'J.'iO siiuhh! yanls. IInw many cwt. and llis. oif 
 Hiu.h carpel mj^ would a strip 50 yanU long and 2 tout, l\ inches wide, 
 woij^li ? 
 
 8. An eg(^ inorchant huys ej^ijH at ') cents a dozen ; liow nmny 
 ouj^ht hu to sell for .^l(>2.3i> to yain 10 per cent, hy the transiictionl 
 
 :;. 9. A rectanjjjnlar <,'ra veiled plot is 12 yards, 3 feet, G inclie» long 
 hy ,i yards, 1 foot, !) inches wide. I*'ind its area. ' 
 
 10. Simplify: (a) 'Sf 2;{8 + j;,«/^ ; and (6) -238-?- -701, givinj? the 
 results in vidgar frictions. 
 
 11. If (> lbs. of tea are wortli us much as 20 Ihs. of cofFoe, and 
 2 Ihs. of cotroe are worth 4 ll)s of rice, and 8 l])3. of rice are worth 
 6 lbs. of l)utter, what is hutter a Ih., when 50 lbs. of the tea soil 
 for ^3. 75? 
 
 12. (a) A wood dealer buys wood at $3.50 ft conl. At what price 
 ])er C'>rd must he sell it in order to realize a profit of 20 per cent., 
 after allowing 12\ per cent, of his .sales us worthless ? (b) A urcjcer 
 buys sugar at 4 cents a pound. Allowing liiij per cent, of all the 
 sugar bought for loss by waste and through shrinkage in weight, 
 hovv many lbs. must he sell for the dollar to ensure a gain of 25 per 
 uont, 1 
 
 d\-^2;\ ( 15| ^ 
 
 13. Simplify (a) . x 38 ; (6) { — + -IG ^ x 7. 
 
 7ixl-2G ( 2i J 
 
 Fxerciee CIV. 
 
 1. On a certain day an egg-merchant bought eggs at 25 cents a 
 score, and sold them again at 20 cenis a dozen, thereby clearing 
 $40.50 ; how many dozen did he handle that day ? 
 
 2. A man took a cargo of apj)les in his boat from Annapolis to 
 Dii,'by. Tho boat held 75 barrels and 3^ bushels each. Find the 
 weight of hlB cargo in tons and lbs., if each barrel weighed 18 Iba 
 
114 
 
 BXKROISEil IN ARITOMRTia 
 
 3. Closfiify : (a) 23 ; nnd (b) ^ of nn inch. 
 
 4. A nmn takos 100 sfo|m pnr mimito, each wtop boincf 2 ft. 9 in. 
 long on thu uvuni^'u. How lon;^ will it tuku him to wulk 3U miloH, 
 80ru<lHl 
 
 r>. Miiko out, noatly and corrc»cHy, tho following hill, and fln«l 
 tho totjil junouMt, of It : May 1st, l^'.Kl, A. H. IUuiih & Co , Ihirn 
 Hide, Kold to.Fnliii A. Ilnico, .'{'J 1)uh!ju1h A0\\ ll)s. wheat at (»2j| cents 
 a hiishul ; 4'i() lo.s. hiirloy at .'17;. cont.s a l)ii.sliid ; 2 pucks, 'A Ih.s , l 
 ozH. ryo at Hi cents u hu.Mhul ; 17 owt., 05 lbs., 10^^ oza. flour ut 
 $1.80 ucwt. 
 
 Write receipt for payniunt in full. May 13th, 1893. 
 
 6. Divide 4 acres, 10 stjuaro rods hy 27, usin'^ factors, and no 
 reduction before boj^inning the operation of dividing. 
 
 7. A sum of money is made up of 4 times as many crowns ua 
 shilHngs, and there uro 75 coins in all. What is thu sum ? 
 
 8. Tun percent, of a coitain sum of money increased by $21 is 
 equal to ^ of GiJij per cunn. of the sum. Find t'.j sum. 
 
 9. Find tho cost of carpetini^ a hall-way, 40 feet long and 7 feet 
 wide, witlk 30 inch carpeting, laid len<4tliwise of the room, and wortii 
 76 cents a yard, allowin'4 4 inches per strip for waste in matching. 
 
 10. A field, 20 rods loii'.,' by 10 rods wide, is bordered by orna- 
 mental trees, set 11 feet apart and worth 15 cunts each, the tree' 
 being included in tlu' area of the Held. It is suiroutuled also by a 
 ditch 7 ft. wide and 3 ft. deep (tin; ditch being no part of tho area 
 of tho Held) at a cost of 4.|sct;ntsa cubic yard to excavate. Find 
 the total cost of the property (including improvements) land being 
 worth $70 an acre. 
 
 11. A and B own a farm of 320 acres which they have rented. 
 Of tho rent, A gets 50 per oon*^, .md B 40 per cent., tho rest going 
 for tivxes. A's share is i-^iS more than B's. Find the amount of the 
 rental per acre, and tho number of acres B owns. 
 
 12. Two men, A and B, hire a boat for $2.80, to go from X. to Y. 
 and return. One-third of tho way to Y. thoy take in C, who agrees 
 to share the expenses fairly for the distance ho goes. C. gets off 
 at Y., paying his share of the fare, and A and B return to X. How 
 much does C pay ? 
 
 13. Find the amount of $4451 }^} at simple interest for 8 months 
 at *< per cent, per annum. 
 
rOUKTII CLAM. 
 
 lib 
 
 Bxeroise OV. 
 
 1. A, B »nd undurtako A j(»b()f work, for whirh tho ■um of 
 914.40 ia tu 1)1) piu<l. A couM do it aloiu) in (> tlnyH, H in 7^ diiyH, 
 ftnd C in 1) diiys. Tlmy ull wuik togotlu-r .ii, it for 1| tl.iys, wlion H 
 and C luiive, and A UniHhos it ulonu. li<jw much uf thu mum7 
 Hhould oauh rocuivu 1 
 
 91)| 
 
 2. If a gill uf wntor wui^lis 5 ozs., >ind ah iiuporinl gnlloti 
 
 contnini 277*274 ciihio indues, how niuny tons of wuttir wonMu Uink, 
 48 foot long, fuut widu nml 4 fiiot doup, Ixld 1 
 
 3. A boIIh u wutch to B nt u lo8S of 20 por cent. ; B tlion hoIIh it 
 to for 16(2(3.88, i^.iining thort'l»y 5 \wr oont. Find what tliti watch 
 cost A. 
 
 4. On January lst,l802,a dopositor pl.itrd in tho S/ivln-^'s' B/mk 
 3202.00. On May LMith, 18!)2, ho withdrow tliu diipusit witli intorust 
 at thu rate of 4 pur cunt, pur annum, \\ hat amount diil ho with- 
 draw ? 
 
 6. A has £40, lOsh. Sterling', B has £20, 18sh., Od., Halifax 
 currency, C has 7oO Vork fshillin^'s. How many dollars and cents 
 has A more than B and C toguthur i 
 
 C. A has $44.97, B KH York shilling's, C £10, 48., (Id., Halifax 
 currency, and L) £1.'), i8s., Stt'rlin>4. Tluy put their money t(»j,'etlior 
 and buy orjiumuntal trees at 75 cents uuch. Huw many do ihuy yut? 
 
 of lill I +12iV 
 
 7. Simplify : J 
 
 in-n i-f 
 
 8. The followinfj rpicstion is given nt i'n examination : ** How 
 often have 1 /[ nf aceiit in £21, 15.s.. Od.'W A works it, usint^ Halifax 
 currt-ncy, and B works it, using (Sterling money. What i.s thu 
 ditl'urencu in their answers ? 
 
 0. A can row a mile in 20 nnnutos, B in 15 minutes, C in 13 
 minutes, 20 seconds, and D in 12 niinuten n-spectively. If tlioy all 
 start from tho pier at tho same timi; and row directly out into tho 
 lake, how far must each go, so that returning they may ull reach the 
 pier again together? 
 
 10. " Multiplication is the i)roccs3 of taking one number as an 
 addend as many times as there are units in anorlier." (o) Wliat is 
 the one numlter, here referred t(j, called i (/;) What is the otlier 
 called? (c) When is this true, if we interchange thu ' uml)ers ? 
 ((/) Take two numbers and prove this rule, (e) Indicato tho multi- 
 plication of *^iiix times stutn." 
 
116 
 
 BZBKOIIU IN AUlTltMKTia 
 
 11. If tliu aum of '7, '27 and 'hj of * nuinhor b« 3070, w)i»t it 
 tho numl)or 7 
 
 12. A mull HoM <;r)() harnUof upjilff for 8<»<57.^0, tli<'r>'hy cli>nrin({ 
 r> por cent, "f tliu Cost. If lio |)niil si u liurri>l t-ir thu Nortlutrii 
 Spu*M, uiiil IN) ccntit u l>iiirt!l for tlni IMiodu iMluitd (iiueiiiiigii, liow 
 iiiuiiy hiinoU of vai'li did ti«i lniy niid Null / 
 
 13. Whttt (lucinml part of } ui u Nqimro rod i« 121 itqiiaro iiichuNt 
 
 I 
 
 Exorcise CVI. 
 
 1. (a) Dividci Mio aum of 7n!W x 210;i mid HVM x HfiOl by 2.110 by 
 nhnrt division, nnuig «// /Ac ititlm-.i of tin- divisor (/<) Find tliu 
 contimi. d pioilncfc of : ('.irtMH : 7H) (rM<>'.>74 - 44G -I- 1472) 
 
 (i(U>uu2!>270-T-4r.»i728;;) (4:ni;!r)i7:{ '••i : 7;{m215). 
 
 2. H(.w much in •{ (087 i:m -2^11) 4- (7<1847."»-7 + 12) ).-f-4«2? 
 In dividinff uhu (a) loiii; division, and (h) hliorl division liy uli tliu 
 fncturn unci uxplmn oiitli fmitinl ronrdndDr. 
 
 3. A, B und C di<.' a dniin for which tiny, toj^utlier, receive ^*X\. 
 A work« lit it for 7i il.iyM und ili'^'s tiO rods. It works ut it U8 iiiuiiv 
 duyH us A d'v^H rods por (\iiy, und (' works us muny (hiys us A nud B 
 together. If tlicyuU work iiniformly, und urc nuul uccordii g to the 
 niunber of rods euch dig' what is ituch iiiiiHH sliure of the receipts ? 
 
 4. A nwin, by his will, left his property, whit h wus then vulm-d 
 at 016,3<H), to be divided uiiion'^' A, It und O., ho that B should get 
 01000 iiioro than A, and C !ii<l:;(IO more tliun B. On tho deuth of 
 the testator, the property was found to have depii'ciutid in vulno 
 l()^ per cent. What is tho jn^i apportioiinu'iit of the bulunco of the 
 property, after a legal (l.iini <jf ^510 is paid out of it ( 
 
 5. If in eggs wei<:,'h 2 Iba., 2 ozs., what will (16 dozen and 8 of the 
 xunie sized eggs weigh ? 
 
 6. A nmn puid .$25 80 for 85 dozen oranges and lemons, there 
 being ^''2 ^^ niany oranges as lemons, und the lemons costing 8 cents 
 per dozen less than tlio oranges ; lind the cost price of ouch per 
 dozen. 
 
 7. An estate consists of 18 rectangular fields, of vnilhim size, 
 each containing 11 acres, 17 rods, 23 yds., 4 ft., 108 inches. Uow 
 many acres aro there in it ? 
 
 8. T sow 2h bushels of wheal to tho aero, and grow 720 bushola 
 on 18 acres ; bow uxany bushels have I for each bushel sown ? 
 
FOURTH OLAtt. 
 
 HI 
 
 9. A mnn tnsvoU M miloH. 2U0 nwU. in U hut»n j how lu^iiv 
 • hftiiiii and (<vi ,\„vn h.. truvul ptr miutitol * 
 
 10 Find tl>o .«.r;rij;, /„„ , ,h.,. h,. pf y,^ fuUuwing J 
 21J II.M. at 72 c.nfH ft lb. 
 
 lO.i II.H. 5t 46 CIMlU A lb. 
 
 8.^ IbH. Ht .'15 ntH 11 lb. 
 20,S Urn. HtnOcont-iftlb. 
 6j"o Ibi. lit lL'«l,"„"o cntM/i lb. 
 
 11. On » cortmnday.u nM-rdiant gained |13 by biiyini^ effvs At 
 10 c«nt« A do/,., uiul M.liinj^ tlu-ni u^mjh at 50 ouuU a Moro. Uu^r 
 many U<)Z«tn i.f ok^m did liw hiindio that day 1 
 
 12. Simplify: 2i -fJI of g-f-^o^ of ft x iJ. 
 
 13. If ^ of a lb. of t.A l)« worth 22 ccntM more than 40 por o«nL ol 
 A lb., what would bo the \uluo of 70 lbs. of ihuiamettial 
 
FIFTH CLASS. 
 
 Exercise I. 
 
 1, The product of two numbers is 324, nnd their qfiotient is 9 ; 
 find the nuniburs. 
 
 2. What will it cost to paint the outside walls and both floors of 
 a two-storey cottayo, 30 feet, in. long, 26 feet, (> in. wide, and 18 
 foet high, at 15 couts a s(iuare yard, the walls to be 15 inches thick 
 and no allowance boing made for cornices, partitions or openiugs ] 
 
 3. Simplify 
 
 51 of 71 
 
 n n of 4-j 
 
 1 
 
 3+- 
 3i 
 
 + 
 
 1 'I of 31^ 
 
 4. Friid gave away 812.60, and had still /^ of his money left ; 
 
 how many jjuirs of ducks at 34 cents a puir could he have bought 
 with his money before he gave any of it away 1 
 
 5. A river is 10 feet deep and 125 feet wide, and flows at the 
 rate of 5 miles an hour ; how many tons and lbs. of water will tiow, 
 over a fall t)n it, every minute 'i 
 
 (). Bontrht 8 lbs. tea at 50 cents, 15 lbs. at 58 cents, and 28 lbs. 
 at 05 cents ; mixed it together and sold it so as to gain 50 per cent. 
 At what rate ])er lb. was the mixture sold ? 
 
 7. The sum of the cost, gain, and selling price, of an article is 
 $00. and the gain at wliieh it was sold is 12^ per cent. ; find the 
 sellimj prica of the article. 
 
 8. If Ifi men can split a pile of wood in 10 days, how many men 
 could split /uu/' times as nuich wood in one-third of the time I 
 
 9. A rectangular field, 180 rods long and 8 chainr? wide, is 
 rented for one year for 372. Seven acres of it are sown to wheat, 
 yielding 30 bushels j)er acre, worth $1.08 a bushel ; 18 acres to 
 oats, yielding 70 bushels I'er acre, worth 40 cunts a bushel ; and the 
 rest to barley, yieliling (iO bushels per acre, v.'orth 05 cents a bushel. 
 AN'hat is the net gain on the entire crop, if it costs $87.80 to 
 market it ? 
 
 118 
 
FIFTH CLAM. 
 
 119 
 
 10. How fast is a locoinotivu running when the truck wheel, 
 which is 2{^ fcot in diameter, makes, every 3 minutos, 440 turns 
 more than the driving-whoel, which is of^ feet in diameter? 
 
 11. B paid $57.00 for 29 lbs. of tea ; what wa.s that for every 4 J 
 ounces ? 
 
 12. Find the L.C.M. and H.C.F. of (19}|-r7|) and (8/5 x 1^). 
 
 13. How often does the L.C.M. of (7i-^8^) and (lin-ij^) contain 
 their H.C.F. ? 
 
 Exercise II. 
 
 1. How fast is an engine runnini^ per hour, when the truck 
 wheel which is 2^^ feet in diameter, turns 330 times a minute more 
 than tlie driving wheel, which is b-^j^ feet in diameter ? 
 
 2. How many cubic feet of iron are required for 3 water-pipes, 
 each 30 inches in diameter and 24 feet long, tlie iron being 2 inclies 
 thick ? 
 
 3. A spent § of his money on Tuesday, ^ of the remainder on 
 Wednesday, and f of what he had then left on Thursday ; after 
 which he had $72. How much money had he at first ? 
 
 4. Divide $142 among A, B and C, in tlie proportion of ^, ^, ^. 
 
 5. The distance between two towns is 840 miles, and is represented 
 on a certain map by 1 ft. 9 inches. Find the distance between two 
 places, if the distance between them on the same map is 3*6 inches. 
 
 6. Bought 200 bushels wheat for $173.50, part at 90 cents and the 
 rest at 85 cents a bushel. How many bushels at each rate did I buy ? 
 
 7. A can do a work in 12 days, and B in 20 days, (a) How 
 long will it take both, working together, to do it ? (b) After A has 
 worked alone at it for 3 days, how long will it take B, alone, to 
 finish it ? (c) If A's w.iges are $3.25 a day, and B'sare $4.25 a day, 
 how much more does the work cost when A works 3 days and B 
 finishes, than when both work together at it ? 
 
 8. Rode to town at the rate of G miles an hour, and walked back 
 at the rate of 4 miles an hour, which occupied mo 5 hours ; how 
 far is it to town ? 
 
 9. A has < "--T" + 5 of I -r ^ - ^»5 V times as much money as B, 
 
 who has half as much as C, who has | as much as D, and altogether 
 they have $380 ; how much money has each ) 
 
120 
 
 LIXKHCISES IN AUiTUMttTlC. 
 
 10. A can do a piece of work in 15 days, and B in 26 dn.yn^ A 
 works alone at it for 3 days, then B works nlone at it for 6 days, 
 after which they I'oth together tiuish the work ; how long was the 
 work under contract ? 
 
 11. Bought 120 bushels wheat for $87, part at 60 cents and the 
 rest at 80 cents a bushel; how many bushels at each price did I buy? 
 
 12. A man throw 20% oflf the price of a horse ; then, 15% oflf that 
 again : the next day, he sold another horse of the same value, at 
 the same selling price as the former ; what per cent, did he throw 
 oflf the latter horse ? 
 
 13. Simplify: 
 
 20 
 
 |-ofi,ii-Hia| 
 
 ^of4J -fjcflif-ijl 
 
 Exercise III. 
 
 1. Find the net cash value of bill of merchandise, 8 per cent 
 boing allowed oflf for cash : 
 
 76 bushels 20 lbs. buckwheat at 60 cents a bushel 
 29 bushels 12 lbs. wheat at 90 cents a bushel. 
 72 bushels 16 lbs. barley at G3 cents a bushel. 
 92 bushels 24 IbH. millet at 172 cents a bushel. 
 53 bushels 30 ll>s. Hungarian at 240 cents a bushel. 
 
 2. Sold a pile of 20-inch wood at $1.45 a cord ; the pile was 80 
 feet long and feet high. Received in payment $11. 25 in cash, and 
 the balance in potatoes at 35 cents a bag ; how many bushels did 
 I receive? 
 
 3. Bought 40 tons coal at $4.32 per *' long ton" and sold the 
 whole again at $4.25 per *^ short ton"; find my gain. 
 
 4. Four-sevenths of a ton of hay cost $28, and ^ of 2§ tons of 
 such hay are exchanged for 7 sheep ; what are sheep a head ? 
 
 5. If § of a irross of brooms cost $18.90, how many broomjs should 
 be given for 5^ dozen eggs at 3 for 5 ?ents ? 
 
 6. Two-sevenths of the vinegar in a cask leaked out, and it was 
 then found to contain 9 gallons more than ^ of the original quan- 
 tity when full ; find the size of the cask. 
 
 7. A, B and C can do a certain work in 4^^ hours. A and B can 
 do it in 6<^ hours. In what time can C do it alone ? 
 
 8. Divide the L.C.M. of 24713 and 26614 by their H.aF. 
 
lid 
 
 FIFTH GLASS. 
 
 121 
 
 9. A boy spent 8G more than ^ of his money, after which he had 
 $6 more tlian lialf of it lufb. How much money had he at first ? 
 
 10. Divide the L.C.M. of ^'iOlOl and 440908 by their II.C F. 
 
 11. H.vd a cortiiin sum of money of which I spent 84 more than 
 the I, I thou had left $20 more than ^ of the original sum; find that 
 sum ? 
 
 12. Square the quotient of the L.C.M. of 43923 and 46254 and 
 their H.C.F. 
 
 13. Invested 
 I get? 
 
 in hay at '5 of a cent a lb. ; how many tons did 
 
 Exercise IV. 
 
 1. A mixture of 28 lbs. of chicory and coffee top^ether costs $3.G4, 
 the chicory being 9 ce»its a lb, and the cofl'ee 25 cents a lb. ; find the 
 number of lbs. of each in the mixture. 
 
 2. A merchant sold his stock of goods for $5308.90, realizing 6 
 per cent, more than he woubl have done, had ho sold the week before 
 he did. Find the value of 80 per cent, of his stock the week before 
 he sold. 
 
 i- of m- 
 
 121x02, 
 
 of $0105; find the sum 
 
 3. A received 
 
 which A received . 
 
 4. Reduce $[5 -{ 12| + 15| + 30J )- of 5] to £ Sterling. 
 
 r: T^' ^ .-, , . * X, ... ,L.C.\r. of 9,18,20 
 
 5. Find the product of the quotients oi,^ ^T.r — . .. . ^-, - 
 
 ^ ^ G.C.M. of 14, 20 
 
 L.C.M. of 3, 6, 9, 20. 
 G.C.M. of 14, 22. • 
 
 6. Express as the product of the powers of prime factors : 
 
 1, 2, 3, 4, 6 , 2 5, 26, 27, 28. 
 
 ' 13, 33, 93, 103. 
 
 :n of if 
 
 7. (a) A boy ploughed 5 
 
 and 
 
 6^-3^ 
 
 acres of land at 7 mills 
 
 per sq. rod ; how much did he get for his work ? (b) Sold 75 sheep 
 for what 120 sheep cost me ; what rate per cent, did I gain ( 
 
 8. Simplify, as the product of the powers of the prime facton 
 arising from : 
 
 1-2-3-4 17-18'19-20. 
 
 13 ^S 
 
 4»-53. 
 
 s 
 
 i 
 
129 
 
 iziacxsBS nr ARiTHMBTxa 
 
 9. Two wheels of a toy carriage are 3 feet, 8 inches, and 4 feet 
 10 inches, respcctivoly, in circumference. Ho\7 far will the carriage 
 have gone when the smaller wheel has gained 7 revolutions on the 
 larger? 
 
 10. The price of 60 lbs. of a mixture of black and green tea is 
 $31.20. If the black tea costs 57^^ cents and the green tea 37^ cents 
 a lb., how many lbs. of each were m the mixture ? 
 
 11. If 20 apples = 12 pears and 8 pears = 6 oranges, and IS 
 oranges -= 15 lemons, and 6 doz. lemons = 2 lbs. tea, how many lbs. 
 of tea should be exchanged for CO doz. apples 1 
 
 12. A note of $750 amounted to $759 from January 1 st, to March 
 14th, 1892. At what rate of interest was the note drawn ? 
 
 13. A regiment of 840 men walking 5 abreast and 4 feet apart, takes 
 13 minutes, 38^^ seconds to cross a bridge Y^^n *^f^ "^ile long. If 
 each soldier steps 80 times a minute, what is the Itn^'th of each step ? 
 
 Exercise V. 
 
 1. Sixty lbs. of tea at 40 cents a lb. and a certain number of 
 lbs. at 56|f cents a lb., avor.iged 50 cents a lb., when mixed together 
 and sold. Find the total amount received for the tea. 
 
 2. At 18 mills on the dollar, a man pays $27 income tax, when 
 20 per cent, of his income is exempt from taxation. Find his 
 income. . 
 
 3. John Pines rents a farm for $520 a year. If he does not 
 pay the rent for 3 years, when money is worth 5 per cent, per 
 annum, what will be the sum due then ? 
 
 4. A Canadian tourist goes to Vienna with $2500.66, which he 
 exchanges for Jlorins at 97 cents for 2 florins, lie spends 17(> 
 florins in Vienna, and thence goes to Santiago, where he exchanges 
 the remainder of his florins for rials, at the rate of 2 florins for 7 rials. 
 He spends 2100 rials in Santiago, and thence goes to Paris, where he 
 exchanges the remainder of his rials for francs, at the rate of 10 rials 
 for 7 francs. He now spends 511 francs in Paris, and thence goes to 
 Glasgow, whore he exchanLjes the remainder of his francs for Sterliiuf 
 money at 73 francs for 55 shillings. He spends £10 in C .asgow, and 
 then exchunges the rest of his Sterling money for C.inailian money at 
 the ordinary rate of exchange. How much money does he bring home 
 after paying $73 for a ticket to Montreal ? 
 
 5. A farmer has horses worth $75 each and sheep worth $15. He 
 has 42 head in all, valued at $1470. How many sheep has he 1 
 
FIFTH OLASa. 
 
 123 
 
 6. Atnne merchant bought 70 gallons of wine at $4 a gallon, 
 mixed with it 14^ per cent, ot itself of water, and then sold tlie mix- 
 ture at $4.75 a galluii. Find his giiiu. 
 
 7. A and B have equal shares in a certain sum of money. A 
 spends GO per cent, of Ills share and li spends 45 per cent, of his 
 Khare. Now, one-third of the dillerfnco between what tliey each 
 liave Icfbis ii;=28. Find tiie sum in which both together had equal 
 shares. 
 
 8. A tank containing 45 barrels of water is emptied by a pail 
 which hokls 10 quarts, 2 pints, (a) How many full pails are re- 
 moved? {!)) How many (luavts reuiain in the tank to bo removed 
 after the last full pail is taken out i 
 
 9. (rt) Simplify -{ (2}i + ]}i + 3\)^loi ;J of 1^ }» xl5. (6) From 
 ^\ of a certain number j'^^ of j of it is taken and 43 remains ; what is 
 th'.j number? 
 
 10. A's apples are worth 3 for 5 cents, and B's i o.wS 2 for 5 cents. 
 U:)th together th.'y have between 1^ and 2 dozens. They exchange 
 without loss to either party. How many had .mch at tirst ? 
 
 11. Sold 18 lbs., 12 ozs. of butter at IG cents a lb., and 59109 lbs. of 
 oata at 18jj cents a bushel. Put the proceed.s out at interest for 5 
 years at 6 per cent. ; iind the total amount due at the end of that 
 period. 
 
 12. Spent ^ of my money and S5 more, then f of the remainder all 
 but $5 ; after which I had still $10 left. How much had 1 at first ? 
 
 13. Using the measure, ^^ 25 quarts to the cubic footy** for wheat, 
 how many lbs. should be reckoned to the measured bushel to make it 
 correct by iceiylU ? 
 
 Exercise VI. 
 
 1. What times after 9 o'clock are the hands of a clock 144° 
 apart ? 
 
 2. (a) Add 760, 240, 516, 829, using the Roman symbols. 
 (6) Subtract 1725 from 2069, 
 
 (c) Multiply 42 by 95 
 
 (d) Divide 1825 by 26 
 
 3. A farm of 100 acres runs back ^ of a mile across a concession ; 
 what is the farm worth at $7.42J| 2^^'*' foot frontage ? 
 
 4. It takes a boy 21yV minutes to walk around a circular race- 
 course whose radius is 315 yards ; how many uiiles and rods per 
 hour does the boy walk ? 
 
 u 
 
 « 
 
 i% 
 
 (( 
 
 ({ 
 
 (t 
 
 (* 
 
 <» 
 
 (( 
 
124 
 
 KXBRCI8R8 IN ARITUMKTir. 
 
 i I 
 
 5. Find the value of tho land, enclosed within a circtdar hedgo- 
 row 1J>80 yards in circiiintoiunco, at ^.S8 uu aero. 
 
 G. At ^O.GO an acre, a cinnilar plot of ground costs $3883.11 ; 
 rtnd tho cost of onclosijig it with a fonce at 65 cents a rod. 
 
 7. A does J^ of a [)ioco of work, and B, who works half as fast as 
 A, finishes tho work in G days. Find the value of tho work, if A is 
 paid $2.25 a day. 
 
 8. How long will it take a man, who travels at the rate of 2 yds., 
 7 "2 inches pur second, to complete a jouiiiey of 72 miles 'i 
 
 9. A weaver sold GO per cent, of his Rtock of cloth at 80 cents a 
 yard, realizing thereon ^2784 ; he then sold tlio remainder at 20 
 per cent, advance on his former price ; find iiis entire receipts f<»r 
 cloth. 
 
 10. Buy COO bushels peas at 90 cents a bushel, payable at tho 
 end of 8 months. Sell immeiUatoly at 85 cents a bushel, and put 
 I of tho proceeds out at G per cent, and the rest at 12 per cent, per 
 annum. How much do I gain or lose ? 
 
 11. Had a flock of sheep of which 40 more than J died ; then, 50 
 less than j| of the number left strayed off and 1 sold ^ of what I 
 had still left. I then had 20 sheep ; find the original number in my 
 flock. 
 
 12. Simplify : 
 
 52-r-3i 39 
 
 52 
 
 -^9| of 4^ 
 
 I3i 
 
 1 l^(2023jj-.7Hs\j)- 
 
 13. If 10 bbls. of sugar of 300 lbs. each cost $4 50 a barrel, and 
 the merchant sells it out at 20 lbs. for a dollar, find his gain per cent. 
 
 Exercise VII. 
 
 1. Had a certain sum of which I spent $2 more than f and had 
 left $2 ; find the sum. 
 
 2. Had a certain sum ; spent $2 more than ^ of it on Monday , 
 then $4 more than ^ of the remainder on Tuesday, and had left $20; 
 find the original sum. 
 
 3. Of a certain sum, I spent g plus $3 ; then ^ of the ^jmainder 
 minus $1, and have left $13 ; find the sum. 
 
 4. Have the half of my money left, after spending $5 more than 
 i^a of it i find my money at first. 
 
riFTH CLASH. 
 
 125 
 
 5. Rn ■* a certain sjim of which T npont 60 cenU more Hmn ^ ; 
 thi'n 30 cents nioio than ^ (»f tho roiniiindur ; then 25 coiit.sluHs than 
 h of whiit was still luft. I found I hud left $1. Ilow much had 
 I at Hi'Ht ? 
 
 (5. Annie gave away \ of her apples ; then J of tlie remainder ; 
 then 2 nioru than 'I of what sliu hatl still left. She found that Hhi> 
 now had 4 ap[ilos Uft. lIow mnny dozens had she at tirst V 
 
 7. Two t^allons mort! than i^ of all the li(iuiil in a barrel leaked 
 out ; then § of the rcruainder and 5 gallons iiii>ro wtMe taken out ; 
 then ^ of tlio reiiiaiiitler all but; 2 gallons ovapoiuted ; after which 
 there were 7 gallons loft in it. How many gallons of li(juid were in 
 the barrel at tirst? 
 
 8. Had a certain sum of whieh I s[)ent $14 more than -J ; then 
 $5 less than -j of tho remainder; then §<.'» more than 1 of what still 
 remained. 1 then had left $6 ; how much money had 1 at first? 
 
 1). hoiight goods for $ltiGCg and sold them for ifrlbGOJI ; find my 
 gain per cent. 
 
 10. Divide the diflerence between \^ and JJ by their sum, and 
 multiply the quotient by 111). 
 
 11. Divide $120 between A and B, so that | of A's money is i 
 of B's. 
 
 12. Out of a certain sum I take $2 more than the fifth ; then $10 
 less than it of the remainder ; then, ^2 less than i| of what still re- 
 mained ; after which I had left $10 ; find the original sum. 
 
 13. Bought 70 lbs. of green tea at 42 cents a lb., and 80 lbs. of 
 black tea at 03^ cents a lb., and on selling the mixture 1 gained 1^ 
 per cent. ; find the selling price, per lb., of the mixture. 
 
 ay, 
 ?20; 
 
 der 
 
 lan 
 
 Exercise VIII. 
 
 1. A circular tank, 6 ft. li inches in diameter, and of uniform 
 size, is 16 ft. long ; how many barrels of water will it contain ? 
 
 2. Simplify: 60 
 
 
 -r-Uof 
 
 ^xfi 
 
 off 
 
 ^1 X Itt 
 
 62| 
 
 } 
 
 + 36. 
 
 3. Find the exact amount (in quarts) that a bucket 14 inches i>i 
 diameter, ami 14 inches deep, will hold. 
 
 4. Divide $325 between A and B, so that 25 per cent, of A's 
 share shall be equal to 40 per cent, of B'a. 
 
126 
 
 SZER0I8I8 Ilf 4RITUMlfiTia 
 
 6. A tank Is 9 feet iluep, 7 ft. wirlo and 12^ ft. long, and U filled 
 with wfttcr ; how many barroU docs it hold ? 
 
 6. ITow many barrels and ^^allons will a circular tank, 10 feet long 
 and 3 ft. G in. in diiunutor, hold ? 
 
 7. Spent I of a curtain Hum and $2 more, and had loft § of thu 
 Hiimand $10 ; find thu sum. 
 
 8. Find the difloronco between tlm bank discount and the true 
 discount on $1040 duo in 4 months at 7h pur cunt. 
 
 9. TIio amount of aci-rtain principal for a certain time i\f pur 
 cunt, is $45.5, ami at 8 pur cunt. , the amount is $tUO; iiii i the pritici[ial 
 and the time. 
 
 10. Wlicn 72cwt. 15 lbs. wheat brings $141.30, what is wheat (a) 
 per bushel t (6) i)or cental ? 
 
 11. What must bo the mailccd price of clotli that cost .$1.50 a 
 yartl, so that the seller may ruiluco hia price 10 per cent., and still 
 make a profit of 20 per cent.? 
 
 12. The amount of a certain principal for certain time at per 
 cent, is $102!).r)0, and at 9 per cunt, the amount is $1181.75 ; find 
 the principal and time. 
 
 13. Divide $108 atnong A, B and 0, so that A shall get | of B's 
 share, and B | of C'b share. 
 
 Exercise IX. 
 
 1. If i*j- of the value of a house is exempt from taxation, and 
 $21 is the tax levied on the remainder ut 4 per cunt., what is tho 
 value of the house ? 
 
 2. Divide $800 into two parts, so that 4 times G per cent, of one 
 part shall be equal to 5 times 8 per cunt, of the other. 
 
 3. Divide $04 into two parts, .so that tlie interest on one part for 
 5 years at 4 per cunt, shall equal the interest on the otlier part for 
 4 years at 3 per cent. 
 
 4. A chest of tea weighs 90 lbs., and a grocer puts it up into 
 caddies of equal size ; tho next day Im puts up an S8-pound chest 
 into the same sized caddies, and has l.'i lbs. luft. If tho selling price 
 of a caddie is $10 50, what is the value of what he has left, from 
 filling the caddie, the second day ? 
 
 5. Simplif)' :- 
 
 ^ 
 
 7 
 
 Uxt^ttx2| 
 
 x38 
 
FIFTH CIAHB. 
 
 l'J7 
 
 ami 
 
 tliO 
 
 one 
 
 into 
 bhest 
 )rice 
 troni 
 
 6. Find the 'luotient of tlie L.O.M. >iw\ fJ.CM. of :j()401 »uul 
 12341. 
 
 7. A'h rnpo is.'} timoH j of nn inch + i <>f ij of a y.ird + Cj",, ft. 
 -)-2A yiinls li)ii<4, iiiid H M is ."> bimoH iiH lonj,; ; tiitd tlu) totil valuo if 
 thuir ro|u>H at 5 nulls a toot. 
 
 8. If '20 pur cunt, of tlio cost of a Imrso is 0(Hiul to \2\ per cent, 
 of thu Hulling i>rio4-, find tho ^iiin pur cunt, at whirli it in hdM. 
 
 9. A lodger pays his hill of 8*2!). 50 with 2u cunt t.iiri lO-ct-nt 
 pieCL'8. If tliui'o Were IGO coins, how many of thuso w jro 25-cunt 
 pieces 1 
 
 10. Pure milk is worth 32 cents a ;,'illoii, hut hy watering it th»i 
 pricu is reducod to cuntu a quart. N\ hat fraction of the milk is 
 thu watur in thu mi.\turo / 
 
 r2*+u-2i 1- 
 
 33 
 X — of a yard of cloth 
 40 
 
 11. Find tho value of 
 
 'tta ^(2|of3|)-f3g}^ ayanl. 
 
 12. (a) What is the lead numl>or which, as a co-factor of 21, will 
 give a product which shall he a nmltiplu of 45 i (/>) Which mnUijile 
 is it ? 
 
 13. The dianietor of a circle is 3 miles, 77 rods, 1 yard, 1 foot, 
 inches ; find the length of a deyree in Ike circumJerMnce of the 
 circle. 
 
 Exercise X. 
 
 1. Paid 40 per cent, duty on a horse, and sold it at a loss of 10 
 jier cent.; hut if I had sold it for .^To.OO more, 1 wouhl have gaincil 
 '20 per cent. Find the cost price of tli(i horse. 
 
 2. Six boys hired a boat for an hour, bub two of thein failud to 
 pay, and the expense of each of thcf others was incruast d 15 
 cents. What was charged for the boat ? 
 
 3. An American grain-dealer paid 20 per cent, duty on Cfinadiaii 
 barley, and sold it to a brewer at 5 per cent, loss ; but hud ho re- 
 ceived 12ji cents a bushel more for it than ho did, he would I'uve 
 gainetl 12^ per cent. Find the cost price in Canada of 836 buaiioljy 
 of the barley. 
 
 i. Simplify 
 
 S 
 
 iofgxJofH 
 
 f 
 
 10 
 
 I of A 
 
 of f X9> >-r^ 
 
128 
 
 v.x?.ncinr.n in AniTiiMKTin. 
 
 5. FiiKl tlio .vim of three iimiUntn of ilTHUR, 7«H''7 undCllOl ami 
 thoii' I..(J.M. 
 
 0. Af M «-ontn a Ih., nil nuitnl, C iiKirki-tod III Iimi^h— 7 ff»r A, 
 AV('rii;,'iii;,' I.M) Ihs. »';i' li, /iinl <> f'-r U, iiviTii;4iii',' *JI<> His. oiicli. A, 
 however I'liiitiM'il tliiit his line's witru wortii liiilf ii cent u II). iiioru 
 iliaii (I'm vvliitli nuIluWJMl. C I licinlivitlt tl llu) pincii<li iiccnriliiij^ly. 
 Fiml t lie uiiioiiiit ili.it v.tii-li roiiHVi'd and tlm arfnuL .seUimj jniif of 
 carli III Ill's liD'^'s |h'i' poiiiid, 
 
 7. A iiinl 15, in H diy^, ri\n fmlsh a })iooo of Work of wliicli A alono 
 did jj III 1 days. Ill what hiiio luiild 1 1, alono, liavu dotiu it t 
 
 8. A nial d aliT lias a bin, 1*3 f«'ot li»n'^', 14 feut wido and 12 foot 
 denp, wliii'i lie lilts witli hard and solt oo.-d in the ratio of 2!5 
 respectively. If the hard coal eusts .^tLf)!) a toll, and tliu buf t cuul 
 $1 1.75 a toll, iind lliu cost of lilling tliu bin. 
 
 J) A ami li li.ivi; cortain sums out, at intir.st at 4 and 5 percent, 
 per unniim, ii'spectivtjly, and >i7( *'^ A'siiu-ome isiipial to j| t)f \Vn ; 
 also, tliu Hinii ot their iiiuonieit is !{<1().*.IU. Find tliu sums out at 
 interest. 
 
 JO. A and H liavu certain Huins out at 5 and (> per cent., 
 
 respectively, piT anmini and ij of A'h iiicoine is equal to ^'\^(^ of IVa 
 also, the diU'eicncu between their incoines is J$iL'4 ; tiiid thesuniHou 
 
 ut 
 
 at interest. 
 
 11. How far may a pcrsMH ride at 1.'» miles .an hour, so that ho may 
 walk back at '6.^ luiles an hour, anil l)e away 7 hours, %-k niinutus / 
 
 12. A and l», in days, can tinisha work of which A alone did ,^o 
 in 4^ days. In what time would li, alone, have done it i 
 
 ■ 13. Find the product of the thirteenth tnuLHide i)i iJOS and the 
 seventh poirxr of seven. 
 
 Exercise XI. 
 
 1. Find tho L.C.M. of all the composile numbers between 204 and 
 220 inclusive. 
 
 2. Find the L.C.M. of all the evisn numbers from 67 to 81. 
 
 3. A man borrows $72, on the first day of every tnontli during the 
 year, on which he pays A a cent a month on every dollar he borrows 
 How much docs he owe at the end of the year 1 
 
PIFTU ri.ASS. 
 
 129 
 
 lie 
 
 4. Fiiul tlio nqunre root of o.icli of tlio following numbow , 
 
 (.,) 7ii;(i<!HHi. 
 
 (D '.M;|'UH!>r>U. 
 
 (•) .'{(ilW.U'.Sl. 
 (/•) HOTI-JHl. 
 
 ()/) •;isi)!ii:;rt. 
 
 5. FiXfr.u't till' rnlhi root of each of tho following nuniborpi : 
 
 ((») l'J!»rM('Jl(>. 
 
 (<•) <.M(»l()l7r):i23. 
 ((/) 07ir.Mi:ioo(). 
 
 C. Fin<l tho siiiii»lo intoroaton "^ "5 for 2yiJHrH nt C por cont. pt-r 
 ivnniiiii. 
 
 7. Find tliu {itiiouut of I8M20 for 5 yuurs at 8 per cunt. >}iiit|)lt« 
 inti-ri'st. 
 
 8. NVliiit sum of ninnt'y will aninmit t<) !5ir»37.t»0 in 8 yours ut 
 '^\ pur cent. , pur unnuiii, 8iin[)lo iiituiu^it i 
 
 9. WliuM ^1 1() is tlio simpio iiitrrust on %f5.S0 for 5 years, what is 
 thu r.'itu [turcent. at which it is loanuil? 
 
 10. In wiiat time will .■?»'» 10 amount to $7<>8, at the rate of 4 piT 
 cunt, pur annum, siniplu inturust 7 
 
 11. What principal will amoimt to ^87.<)0 in 4 years at 6 pur 
 cent, pur annum, simplu inturust ? 
 
 12. In what time will §154 amount to $21)4.14 at 7 per cent, pur 
 annum, 8imi»lo inturust '/ 
 
 l.'i. A had .$118:30, B J? 12740, and C had !i<i;j(i50 ; thuy investnl 
 thuir money in city lots at thu hiijhvd |)ricu pur lot, ho as to allow 
 uac'h om^ to invust all his iiiniicy. Thuy then sold tht; lots to 1), 
 gaining $5400 ou tho wholu. Find uach man's bharo of thu gain. 
 
 I. 
 
 he 
 
 Exercise XII. 
 
 1. The dilFurence butweon thu inturust on a certiiin sum, at 5 per 
 cent, for ono year and at 15 pur cunt, for the same time, is $8.40 ; 
 find thu sum. 
 
 2. (a) Increase $740 by 5 per cent, of itself ; (6) A has $893, 
 after losing (5 per cent, of his income ; what is his income ? 
 
130 
 
 MSKH(JI>4HH IN AHITMMKriO. 
 
 •'t. \ iiihii'n |».i,y hoiiii^ iiMTiUHPil *2tt pt i i*i itt, in lliurolty IntTinnoil 
 to JJ?.S.7"» u wi'tik ; wriuii wuh litH f-Mfiitr }••• iily Hnlury ? 
 
 4 Diviilii f^*.>Hl itiimn^ A, I) utiil <!, uivin'4 It tliruu tiiiioN tin much 
 M A, Hit<l (! twiro HN tniK'li liM A Hiid H to^itthor. 
 
 5. Wh/it is tli4* li>aHt iiiiiuhttr wliicli us » co/nclor ot (V) will ((ive u 
 prodiirl wliicll mIihII l)i))i innlfiplr of Tt'i? 
 
 «». Ill till' ox|>r«Hsi.»n j^ of II lb. : (i.) Wluit ttiu'H i| of u ll». o\|)r.)HHt 
 (ii.) VVIiiit <loois tlu) 4 ox|>rnHH ? (irr. Wlmt, «lo«"^ Hn» 5 fXpiotH? 
 (iv.) \N li.if is l\ir niiin'' unit ' (v.j Niiiin- ull flio j'i<i' liminl iniiiiburtt 
 in uoMii' lion with llin i;x|iri*^-4ion, (vi.) Wlmt tmiiKi in uppliud to 
 thu niiiiicrat'ir iiml <l*<ii'iiiini.itor of h friictinu^ (vii.) Ih h fnirtiun a 
 nmnher 1 (iivo rurtHoii for your uiiswor. 
 
 7. Fiml tho (liffbroticp, in inclutM, iMitwuoti a minfifc on ft droit 
 wliosi) <Miciinifor«j»ico in iJ imluH, 21 loih, 4 yanU, I foot, (J inohe«, 
 and on onu whoso ciioiimft'nMjoo is 4 iiiilos, UiM) rotjs, 6 yanla. 
 
 8. Olio fotoih of tho cost of rt horso in }^ of tho h»(I1imj( price, and 
 tho KHinat whirh it is sold Ih ijjIlHO ; find thu conb of throu car-loadf 
 uf 17 Buch horsi'H each. 
 
 ». liou.^ht (;i25 ll)H, Hiiuar at 4 cents a lb. ; p.iid .*<(l0.r.O froight, 
 and l,\ cont.s a lb. duty. I lost 4% of tho (.'ntiro w»'i;(ht in waste, 
 and sold tint roin.iiiidor so as tu gain oi^^jj pur cent. ; how many 
 lbs. did I HoU for tht) dollar ? 
 
 ,-*ii + n 
 
 10. By how much does { 
 
 oxccod \ + fl 
 
 If + i^r H?J 
 
 11. Find tlio smalh'st cnfnotor of .30r>l whicV will form a product 
 that Hhall bo a miilti})U of L".Ki8. Which nviU '• is it ? 
 
 12. A yroci-r had two b.nrels of su-^ar, ono wrij^diing '67)0 antl tho 
 (»thor .'](tO lbs., vvliii h ho put up into ;in i-von ninnbi-r of tho largest 
 si/ud dollar parcels. In putting up thu [)arcolH, he found that he 
 had loft 8 lbs. in the tirst barit^l, but nothing in tho 8u<!ond, tho 
 parcels cxaiitly emptying it. Jlosv many lbs. did he sell for the 
 dollar ? 
 
 13. (a) Find the L.C.M. of 24 and 42 by three difForent methods. 
 (6) Find the G.O.M. (H.O.F.) of 96 and 240 by three diflforent 
 methods. 
 
 Exercise XIII. 
 
 1. A regiment of soldiers is bilUtud in three towns as follows : 
 In the largest %\ of the nuinbrr in the smallest, and in the smallest 
 ^ of the whole regiment, the remaining 880 being quartered in the 
 other town. How many men are in the regiment ? 
 
 
rtrrif oi.am. 
 
 131 
 
 |B : 
 
 Ihe 
 
 2. Tht'«« omVh of tho NAiiiA Nixo ATo iIIIimI with win* ; in thn t]r*«t 
 cmik 8() jior ri-nt. ft" tlm inntrtits i« |mih> ; III l|(i< Mm ml 7*' per 
 eoiit., Hint ill ilio tliml \Kt \>or i^i iit. Fiom tlm tirMt rank tU) per 
 Ofiit. of till) (Miiiti'tiU iH witliijiituii ; t'n>Mi till) Mi*('i*nil !N> |)(>r uunt. 
 Aiid ftoiii tlm tliii'd 10 |>«i I t'tit Wltiii i>ur uiiiit nf tliti ori^iiml 
 coiittjiaN JH ihu puru >viiiu iii*^ li.fi in lliu lliivu ciiNkt / 
 
 8. Tf 1 ll». HVnlfilnpoiii «)f gold be coinud iiiko KM, fin., whftt 
 wuiglit (troy) is u Movi'i'iugn 7 
 
 4. A n'MtTvoir, conliuiiiiiK WTftOO Itiu rcUof wiiti«r, U i>iiipti<'d hy 
 A |>ip''. tliu Hoctjuii of vvliicli in 7 inclxM in diiiiiK t* r, atiil tliion^h 
 wliicli ili<> vvdifi' IliwH witli u vflority of 1 iiiIIih uit hour, in liow 
 iiiiiny diiyn uiid Iioiiim will tho ro^^orvoir Ih* «>)iipti«!d i 
 
 5. VVIi;it Hiiiu of iiioiioy will utiiount to ;?lH.'l7r).({4^ ni thi'uo yuan 
 at 7 p*<r (DUt. (-oiiipoiiiid intui'i'Ht I 
 
 6. A, n JiU'l <', Hf:irt tov'tfthnr fioni tin- mjumo point, nt tlie mimo 
 tiiiir, liud tr ivel in tlio s^iuw diinctioii, i'imiikI :iii island 'JO niili's in 
 circniiifuroncu. A ^'ocs 4 niiliH un hour, it 7, itnd C I'J. (n) \u 
 what tiniu iiftor st irlin'4 will they all \h> lirsf lum'th«'nif<iiin '/ (/>) At 
 whiil point \>ill thiH \ni ( (') How oftun will oHch havi) gonu round 
 ihe i.MliuKU 
 
 • • * 
 
 7. nividti 'M'i\ by •;J78 without Jird ihanyinj^ tlm dttciniaU t<» 
 
 vulj^ar fniitioii.s. 
 
 8. Find corrcrrly to tivo duciutul plucun tho value of tho HerieH: 
 
 111 
 
 1 + — + + 4-otc. 
 
 1 1x2 1x2x3 
 
 9. A nuuclr'til boui^ht two pioces of tweed of e<pud l«Mii,'tli8 
 Contuinin<4 to-^- tin r as many yards as it c>>s\. hiui cents per yar«l to 
 buy it. Ho sold it all for H? I HO at a ^a in of iT) per cent. ; tind the 
 number of yaids in oauh piocu b<>uglit, and tho .selling prico [)or 
 yard. 
 
 10. Tlmro is a n'etanj^lo wlioso lenjjjth is \\ times its breadth, and 
 which may bo planked either way with planks of longths JO, J 2 or 
 14 ft. What is tho least sizo of tho recLanglo i 
 
 11. At what rate j)or cont. will .Sl,9i>- for 2^ years amount to as 
 much as .i?l, (»<)() for 8 years at 5 per cent./ 
 
 12. A person investing in tho 4 J per cents, pays ^ brokerage and 
 makes 5 por cent, on his money. In what priced stock does he 
 invi'st i 
 
132 
 
 EXERCISES IN AUITHMKTIC. 
 
 13. (a) A conical pieco of marblo, tho diameter of whoso base is 
 2 ft., 4 inches, contains 7 i:nl)ic feet, 145t» cubic inches of n>aibk(. 
 I{e<niii'C'd Llie altitU'lo of the cone (b) If 1 sell my farm for §1440 
 and my stock for ^(iOO, I shall i^ain 20 per cent, on the orij^'iiml cost 
 of both ; and if 1 sell the farm for •^r'lTlO and tho stock for cost, 1 
 shall gain 30 per cent.; find the original cost of each. 
 
 Exercise XIV. 
 
 1. A bill due 4 months hence u discounted at 7 per cent, per 
 ann\nu (true disc<»unt) and i$Ii8t)1.00 is received for it. What is its 
 face value 1 
 
 2. How much money must be invested in stock at 80^, paying an 
 annual di\ idi iid of 5 per cent., in order to realize an income of $720 
 per annum, brokerage being ^ ? 
 
 3. In the middle of a rectangular jtlot, 348 ft., 2,^- inches long 
 by "iS ft. wide, is dug a circular pit 25 ft., 8 inches in diameter and 
 18 ft. dee[) , and the earth so removed is then spread evenly over 
 the remain<]er of the plot. Find by how much the level of tho plot 
 is raided ? (Area of a circle — ol x r.'-^). 
 
 4. Two drovers, A and B, go to a market and buy together 800 
 sheep at $10 a head. A takes 500 of the sheep and 13 the remainder ; 
 but upon examination tliey agree tiiat A's sheep are wortli a dollar 
 a head more than li's. How much should each pay for the sheep? 
 
 5. If an ounce of pure gold be worth £3, IG sh. and | in weight 
 of a gold coin be pure gold and the remainder an alloy 40 times less 
 valuable, what is the weight of the pure gold in (a) a guinea? (6) a 
 sovereign ? 
 
 6. A license to kill game costs $20 ; a cartridge costs ?> cents and 
 a sportsujan kills his bird every fourth shot on an average ; when 
 birds are worth 40 cents a brace, how many must the sportsman 
 shoot to pay expenses and buy a license for next season 'i 
 
 7. A spec'dator buys 371 sheep at $3 a head due a year hence. 
 He immediately sells 271 of them at $2.75 per luiad for cash, and 
 the remainder at $4.10 a head due in month.s hence. How much 
 does he gain by the transaction, money being worth 5 per cent.? 
 
 8. A snail begins to crawl 12 inches per minute, up a pole, and 
 is folloived 21 minutes afterwards by a potato-beetle, whose rate is 
 to that of the s'nail as 8 is to '*.), and they are together 2 ft. from 
 the top of the pole. Find the length of the pole. 
 
 9. A railway train travels 40 miles an hour when it does not stop 
 and 35 miles an hour including stoppages. In what distance will 
 the train be 45 minutes late ou account of stoppages? 
 
FIFTH 'LASS. 
 
 133 
 
 10. A contrnctor n:;rec(l to do a cor(-ain work in days. Hu 
 employed 2 iiicii and .'! l)oys who did i of tlio woik m 4 days. He 
 then put on two mort; men and ono more ])oy and /j; more of tliu 
 Work was done the next day. lie now took oil' all the mm, and 
 employed ono'.iyli hoy.s tn linisli the centra t on time, lluw many 
 additional boys were employed the last day ? 
 
 0-li 1.3,\) 
 
 of of ...f 
 
 11. Simplify : — 11 x 
 
 \ 
 
 
 O 
 
 1 
 
 [' 
 
 ."> I «>! .-1 
 
 o'r} 
 
 3c) f 
 
 4-5 
 
 f 
 
 of 18LJi,'r>0 fartliings. 
 
 14+14+14 
 
 12. A garden contains .'j8,4L0,ft20 stpiaro inehe.s, and it.s length is 
 35 rods. How wiile is it i 
 
 13, I take 2l0.^teps in walkiii'^ round the four .sidts of a rectangu- 
 lar lawn ; find the area of tlie lawn, if (J steps are C(|uivalent to 5 
 yards and the shorter side takes 48 steio. 
 
 Exercise XV. 
 
 1. A clock lo.sos 10 S'.'conds every 12 minutes and is set right at 
 a.m., what will l>e the true time wlien tlie clock indicates 5 uU p.m.? 
 
 2. A watch loses ?>('> secnds in 10 minutes, and is s(>t right at 10 
 o'clock a.m.; what will he the true time when the hands are coinci- 
 dent between and 7 p.m.? 
 
 3. A clock whi(!h gains 10 seconds in 1.^) min.. is set ri'jjht at 6 
 a.m.; what will 1)0 the true time when theclock iudicales U'iOp.m.? 
 
 4. What is the second time after 4 o'clock that the second hand 
 is midway between the hour and niinute hands on a clock having 3 
 hands all moviuLj about the same centre ] 
 
 5. Wiiat is the tirst time 5 o'clock when the second hand is 
 midway bi'tween the oher two hands on a clo k with a minute, a 
 second and an hour hand all moving about the same centre 'i 
 
 6. At what tinie after 9 o'clock will the hour hand be midway 
 betw'en the other two, on a clock having three haudr' all nioving 
 about tilt! same centre ? 
 
 7. What is the first time after one o'clock that the minute hand 
 is midway between the other t.vo, on a clock with three hands — a 
 minute, a second, and an hour — all moving around the same centre? 
 
 8. At what time after two o'clock will the minute hand be first 
 midway between the second and hour hands on a clo<;k, on which 
 there are three hands all revolving round the same centre ? 
 
 ;i 
 
 I.; 
 
134 
 
 EXEl{(;iSES IN ARITHMETK!. 
 
 9. Afc wljafc times after 8 o'clock are the hands of a watch 10 
 lainuteH apart ? 
 
 10. A |)(!raon slarled at half-past two in the afternoon and walked 
 to a villii^'e, ai-rivini,' there! when the villat^o clock inilicated a quar- 
 ter past tliKii!, After Htf'yiiig in tlu; villiis^ci 25 iuinutt;s, he drove 
 homo hy ;i ro.td iUKt-foiuih an loui; auaiii, at a rate twice as fast as 
 
 he liad walked, and reached home at 4 o'clock p.m. 
 was the viil!i,''e cluck wroni; ? 
 
 How much 
 
 11. A man left iiomo at 3 o'clock p.m. for a village, arriving there 
 when the vIHm^o clock pointed to 4.30 p.m. After .staying 20 
 minutes in the villaL,'(!, he returned iiome by a road ^ longer than 
 the one by which ho went, antl at a rate twice as fast as he went, 
 arriving at home at 6 o'clock p.m. Ilow much was the village clock 
 wrong ? 
 
 12. A m.in left home at 2 o'clock p.m. and walked to a village, 
 arriving there whi'U the village chjck indicated 4 o'clock p.m. After 
 staying in the village 15 miinites, he returned home by another 
 road, wiiich was h;t,lF as long again, at a rate three times as fast as 
 he went, and arrived at home ar 4.30 p.m. How far was it to the 
 village, if ids rate in was 6 mile.s an hour ? 
 
 13. At what time after 7 o'clock are the hands of a watch 13 
 minutes apart ? 
 
 Exercise XVI. 
 
 1. Tea at 50 cents a lb. is mixed with 4 lbs. at 70 cents a lb. 
 and 20 per cont. is gained by selling the mixture at 68 cents a lb. 
 How many lbs. of fifty-cent tea were in the mixture ? 
 
 2. ^old sugar at \)^ cents a lb., gainhig thereby 14f per cent, of 
 the sales. Find my gain per cent, on cost when the selling price is 
 10 cents a lb. 
 
 3. The road between two villages, AandB, 9 miles apart, is over 
 a mountain, the summit of which is 3^- miles from A, and two per- 
 sons set out from A and B at the same time, the formcx walking at 
 the rate of 2 miles an hour up hill and 5 iniles an hour down, and 
 the latter 3 miles an hour up hill and 6 miles an hour down. How 
 far from B will they meet 1 
 
 4. Bought a piece of cloth at $4.60 a yard. It shrank 16§ per 
 cen\;. in length. Sold it at $7.20 a yard ; find my gain per cent, on 
 the whole. 
 
 5. A bought an article for $40 and sold it to B at a certain gain 
 
 fier cent., B sold :t to (J, C to D, and 1) disposed of it for $82,944. 
 f each gained the same percentage on what the article cost him, 
 find that percentage. 
 
 \ 
 
FIFTH CLASS. 
 
 135 
 
 lb. 
 lb. 
 
 of 
 is 
 
 0. A's capital, B's capital and O's capital are to one another as 
 the iiunibtas .'5, 4 and 5 ; and As time is to \Vh tinio as .^);0. A's 
 gain is !?7<K) find C's g.'iin i3 §900. Find (a) ratio of BstiuiutoC's 
 time, and (b) 15'.s g.iin. 
 
 7. A hoMs a note aj^'ainst B at 9 months, drawini^ interest at 
 
 8 per cent, per unn\nn. , C buys the noti; at a discount of 6 per ct'nt. 
 otf the face of the note. What percent, per annuu' does C make 
 on the money invested ? 
 
 8. At what rate per cent, discount oti the face of a note must a 
 broker l»uy notes bi-aring intevestat 10 per cent, in order to make 
 26 per cent, on his investment i 
 
 9. I s(dl 40 lbs. of tea at a gain of 25 per cent., and 50 lbs. afc a 
 gain of 12^ ]»er cent. Had I sold tlie whole h t at a gain of 10 per 
 cent., I wouM have received §2.1)0 less tlian 1 did. What waa the 
 cost price per lb ? 
 
 10. The cost at 14 cents a square yard is $479. 16 for gravelling a 
 circular plot. Find ti;e diameter in rods. 
 
 11. If the specific gravity of silver is 10"5, and a silver ball 1 ft., 
 
 9 in., in diameter is to be considered, find (a) its weight in lbs. and 
 ozs., and (6) its .surface in square feet and inches. 
 
 12. A fruit-dealer bought a quantity of cherries, apples and 
 grapes, paying for the whole .§120.00. The grapes cost him CO per 
 cent as much as the clua'ries, and the apples cost him 44| per cent, 
 as nmch as the apples and cherries toge.ier. How much did each 
 kind of fruit cost him 1 
 
 13. A man bought a hide of leather in the United States, and 
 smuggled it across into Canada, where he sold it, gaining .§15. Had 
 he paid the import duty of 15 per cent., he would have gained in 
 selling it, 19^^ per cent, of the cost to import into Canada. What 
 did it cost him 'n the United States ? 
 
 U 
 
 at 
 ,nd 
 ow 
 
 )er 
 Ion 
 
 Exercise XVII. 
 
 1. Sold a coat for ^20, 1. ising thereby 20 per cent, of the pro- 
 ceeds. From this find the cost of 40 dozen coats. 
 
 2. A horse cost 6| times as imch as a saddle. By selling i he 
 saddle at 11^ per cent, loss and the horse at 1 1| per cent, gain, $224 
 is realized. Find the cost of the horse. 
 
 3. I take 1452 steps in going round a field in the form of a 
 rectangle. Find the area of the field, in acres and sq. rods, if 6| 
 steps are equivalent to a rod, and the longer side takes 396 steps. 
 
 t 
 
136 
 
 EXfiRClHES IN AUITIIMETIC. 
 
 4. An excursion party of men, women and children purpose 
 going on Jin excursion, ugrt-ein;,' to pay expenses in ratio, 6;3;2 ; 
 but on account t;f 10 tneii, 5 women and la children heing ahscnfc, 
 the ratio of expenses was 1();3;2. llow many chil<lren purposed 
 going on the excursion, if tlu> whole party who purposed going 
 numbered DO ? ILnv many children went I 
 
 5. Sold tea at lbs. for a certain sum and gained thereby 50 
 
 Sir cent. I afterwards reduced the gain on tea to 33^ per cent, 
 ow many lbs. did I give for that sum? 
 
 C. A j)erson discounts a note duo in 15 months so as to make 10 
 percent, peranninn -tn his mon >. What rate per cent, on the 
 face of the note docs 'lo exact ? 
 
 7. The true dist;. nt on a sum of money for one ye;ir, at 7^ per 
 cent, is $40. Find lie true discount on the same sum at 3^ per 
 cent, for the same time ) 
 
 8. Bought cloth at $4 in gold, and sold it at ."?6 in currency. 
 Did 1 gain or lose and how much per cent., gold being at 120 / 
 
 9. I received an eight per cent, dividend on railroad stock, 
 piii'chased at 20 per cent, discount. What per cent, did my invest- 
 ment pay ? 
 
 10. How many bricks 9 inches long, 4J inches broad, and 4 inches 
 thick, will be required for a wall 30 feet long, 20 feet high, and 4 
 feet thick, allowing the mortar to make up one-sixteenth of the 
 entire wall ? By what per cent, does the mortar increase the volume 
 of each brick ? 
 
 11. A company of boys is met by A who gives each boy 25 cents. 
 Afterwards tliey are joined by 4 more boys and the money equally 
 divided among all the boys, who are then met by B and he gives 
 each boy 25 cents. The boys are then joined by 10 others and the 
 money again equally divided among them, when it is found that each 
 boy has 20 cents. Had all these boys been- met by A his donation, 
 divided equally among them, would have been 7^ cents each. How 
 many boys did A meet 1 
 
 12. Two numbers are to each other as 13117, and their sum is 
 16230 ; find the numbers. 
 
 13. For what must I insure property at IJ per cent, to cover a 
 loss of $4710? 
 
FIFTH CLASS. 
 
 137 
 
 IB 
 
 3r a 
 
 Exercise XVIII. 
 
 1. From ft unifnrin cyliiulric.il wuter-t.ink, 14 feet in dianioter 
 ftiid Stan liiiL,' vertically \j[)riLrlil, water is <lra\vn, till tlu> surface is 
 liwcrcMl ;i fcot, 4 inclu'H. Find the number of gallons romovod, 
 given tiiat a quart is <tO cubic inches. 
 
 l.tii 
 
 2. Into how many (qwil parts must '6 of 3.3 H of 17 + 
 
 2.<i2."i 
 •4 of 5*75 be divided, so that 13 of such parts may auiount to 1083? 
 
 3. Find the L.CM. of all the (len)i, numbers between 107 and 181 
 
 4. A contractor employs 5 men to di<4 a ditch in 40 days, each 
 man doin;^ an averai,'e day's woik ; but he timls that <»nly one of his 
 men does an average day's work and that two of them do respect- 
 ively I and _^ /(!>s, and the other two respectively ,ij and .j',^ more than 
 an averai^c days work. IIow many men, doin;^ an .iverai^e day's 
 work each, nnist he employ the 40th day in order to complete the 
 contract on time 1 
 
 5. A merchant in Montroid, who wishes to transtiit 400 pistoles 
 to Malaga, finds that direct exchau'^e from Montreal on Malaga is 
 $.'3. (15 for 1 I'istole, and that circuitous excliange from Montreal on 
 Malaga, through Lombui and Pai'is, is as follows ; Fror.i Montreal 
 on London ^4.8!» for £1 Sterling; from Lon(b)U on Paris 2">.\ francs 
 for £i Sterling, and froui Paris to Malaga 19 francs for 1 pistole. 
 What course of exchange should he adopt ? 
 
 0. How much water must be added to a mixtme of 55 gallons of 
 wine yj pure, to make the mixture 80 per cent, pure ? 
 
 7. A feed merchant mixes 40 bushels of oats at .35 cents a bushel, 
 20 bushels of rye at 60 cents a bushel, with 10 bushels of bran at 15 
 cents a bushel, and grinds it al together into chop. If ihe bran de- 
 crease 10 [icr cent, and the rest of the mixture nicrease 10 f>er 
 cent, hi the grinding, what will be the value and what the vveig.it, 
 by measure, of a bushel of the chop ? 
 
 20^ 
 
 8. A cask contains 7 parts brandy and 5 parts water ; of the 
 
 144 
 mixture is now di > wn off and it is filled with water ; what is the 
 strength of the mixture then ? 
 
 9. A person had a certain capital, J of which he invested in 3 per 
 cents, at 90, and the remainiler in the ^h per cents at 110. What 
 was his capital, if his total income is $28U i 
 
 1! t 
 
138 
 
 RXKKOISRS IN ARITHMRTIC. 
 
 10. The (lifTnronco between th«^ bank and true disoouiit on a cer- 
 tain Sinn of rnonoy for '» yt«arM at 6 per <X!nt. per finniim is S76.0r>. 
 What, i.s the sum ? 
 
 1 1. Divide $720 between A and B, K'vitig A ()0|{ per oe-xt. of both 
 
 sharos. 
 
 12. Tlio area of an ollipHo in 308 sq. inches, and its major axis is 
 2 ft., 4 in. Find it^' minor axis. 
 
 l'{. How many })all.s, each 7 inohcis in diaiiu^ter, can be made from 
 a piece of luad 14 inches long, 11 inches wide and 7 inches thick ? 
 
 !l 
 
 Exercise XIX. 
 
 1. A doah'r sent his atjont to sell 500 bushels of pease at 90 
 cents a bushel and 800 bushels l)arl(3y at GO cents a bushel. The 
 aj^oMl sold tin; poasci at $1, and the barloy at 75 cents a bushel, took 
 bis conniiiNsion of 2h per cient. and paid expenses of !i?30.'.)0, remit- 
 ting the balance. What per cent, profit did the dealer realize? 
 
 2. Find the cost of enclosing a circubir park whose area is 85 
 acres, 99 sq. rods, 21 s(i. yds., 5 sq. ft., 130^ sq. inches, with fencing 
 at 05 cents a rod. ( tt — 3f , ) 
 
 3. What woidd a dishonest dealer gain per cent, by using a 
 weight 15 ozs. to the Ih.'i 
 
 4. Water rises 9 inches per hour, in a circular tank 28 ft. in 
 diameter. If the water stand 2 ft., 9 inches doo[» in the tank, and 
 a pump which empties 1000 ftubic feet per hour be set in motion, in 
 what time will the tank be empty ? 
 
 5. Which is the better investment, to pay $3125, for a farm, due 
 5 years hence, or to pay $(>200 cash, money being worth 6 per cent, 
 per annum t 
 
 6. I sold a quantity of Bank of Commerce Stock at 120 and in- 
 vested in Montreal Bank Stock at 88 which I afterwards sold at 90, 
 and repurchasing my Bank of Commerce Stock which had risen to 
 125, I found I had lost $180 by the operation. How much Bank 
 of Commerce Stock had I at first ? 
 
 7. Divide $1875 among A, B, 0, D and E, giving D $190 more 
 than E, C $295 less than E and D, B $10 less than E, and A $235 
 more than B and together. 
 
 8. How many cords of stone will be required to curb 96 circular 
 wells, each 5 ft. 10 inches in diameter, and 30 ft. deep, the thick- 
 ness of the curb being 1 ft., 2 in.? 
 
FIFTH (!LAS8. 
 
 139 
 
 I more 
 1235 
 
 pcular 
 tliick- 
 
 U. A {XTHoii sells out 'STtiKM) .»tnck in tliu throe pur eunta. at 96 
 un*l invests in I'iiuk stocU ut. 75| which pays an annual dividond of 
 2^ por cont What is hi.s iinivaso in income/ 
 
 10. l)ivi(lo ij^'JOHO auion^ Hvo nu-n, seven women and fourteen 
 hoys, HO that each woman may have i^' of a man's share and each boy 
 ^ of a woman's shari;. 
 
 11. At what ral(! per cent, discount on the face of a n(>te nnist a 
 broker buy notes Ixaiiii'^ interest at 8 percent, per annum, 8o an to 
 make 20 percent, on his investment y 
 
 12. A man's inoome is drrivod from ^1500 it a certain rate per 
 cent., and i!i»730O at 2 por cent, more than inc former rate. Hia 
 whole income isJSflODO. Find the rates. 
 
 13. (a) liy selling tea which cost a certain jn ice per lb. a merchant 
 gains 12^ [ler cent, of the proceed.s. Me now raises his sdlini,' [)rice 
 to $1.00 alb., by which lie trains lj^3() on the sale of i!i«.,'hty-four dol- 
 lars' worth of tea. Kind the original ci>.st price per lb. (b) Tour 
 por cent, of A multiplied by b is greater than A by 400 ; and 6 i)er 
 cent, of A multiplied by ja is less than A by 315 ; find A. 
 
 Exercise XX 
 
 1. How much money must be invested in the 5 per cents, at 80, 
 brokerage 1 per cent., in order to give an income of $4G0 after de- 
 ducting an income tax of 4^ cents in the dollar ? 
 
 2. A per.son sells out $4000 stock in the 4 per cents, at 1)2, and 
 invests in the 3i per cents., gaining thereby 840 por annum by a 
 change in his income. At what price did he purchase the latter 
 stock 1 
 
 3. If liC of a farm be worth $1600, what is tlie value of 7-2 of it? 
 
 4. C's daily wages are $1.20, and he receives $17 for finishing a 
 piece of work at which A and B had worked together for 6 <hiys ; 
 find the sum paid A, B and C for the work, given that A and B to- 
 gether can earn as much in 6 days as C can earn alone in 19 days. 
 
 5. How many lbs. of tea at 45 cents, CO cents and 90 cents a lb. 
 must be taken to form a mixture of 500 lbs., worth 75 cents a lb.? 
 
 6. Simplify % (4i + 3i) of a £ + of 83 of 16 sh. -|- 
 
 *of3-4 + t? 
 5-571428d. 
 
 7. A st(»re-room will hold 1G| bales of cotton and 20 casks of 
 rum ; but 13.\^ bales and 2 casks will fill ^ of it. How many casks 
 would alone till it i 
 
140 
 
 IZEItCISFS IN AllITIIMiniO. 
 
 8. If tliotrue discftunt on ^'1H7 for 2 ycnri h(«.?17, in liow many 
 years would the truo diMCdUiit on Jjjlllil) bu ^WJ iit ihu Jiaiuc lutu { 
 
 {). A cr \v cm row from A to Fl, witli tin- ,-t umih, in 2 lioiir.s, iind 
 it ciin row from H to A, ii.;.'iinHt tliu Htrtiiiiu, in 4 liuuru. Cuuii'uro 
 tlio rutuH of tho built und Htiuum. 
 
 10. A l»uck(^t bo;^inH to discciid inio h mine nt the siimr time tlmt 
 another i)c><^ins to ll^(■(>lt<l fr<im tlio bottom. Tliu btukct iit tlut top 
 ruiicht'H tbi;l)ott Mil Hi minntos, und tbcbucUi!! iit tbo li'ttom ruucliuH 
 tliu to|) U\i, minutcH, uftiti- iiiissint^ eiicb oihur. W'hut timo wiis 
 occupiud by each in porformin^ thu di-stunco I 
 
 11. What is tlio dillotonco in co.st of fi-Mcinj,' tw" ost.itos of 4000 
 acruH each, oiiu in the fnnn of a .s({ii uc, uihl tbu other in thu fr)rm of 
 a roctanglu who.so .sides aro as lb : S), thu fun u costing u7J^ cents a 
 rod I 
 
 12. A merchant .suniliu his a'jent .*?'.)(:()!) in tlonr to Hull on a com 
 mission of 'A^ [h'.v cunt, ami insrructs limi fiirtlitrmoiu to invcni thu 
 balance in ajipK-s on a commis.sion of 5 per cent. Kind his total 
 commi.ssion, and the number of barrels, at $2 per b.nrul, uciit the 
 merchant i 
 
 13. Forty-nine piocts of load, each llj inches thick, and in tho form 
 of an ellip.se whoso majoi- and minor axis are iusi)uctivuly 2 tt. 11 
 in., and 1 ft. 9 in., an; multcd and ru ci.st into bails, each o^ inches 
 in diameter. Find the number of balls re-cast. 
 
 Exercise XXI. 
 
 1. A man leaves homu at 4 o'clock p.m., to walk to a town where ho 
 arrives at (). 15 p.m., by the town clock. After stayini,' in town li 
 hours, he a_Ljain starts for lujiui' at a rati; 4 thnes J'uster than ho went 
 and along a road twice as long as the former, aniving at home as 
 tho clock there indicated 9. li) p.m. Find ((<) how much the town 
 clock was wrong ; (6) thu distance to town, supposing his rate in 
 going to town was 4 miios an hour. 
 
 2. A man bought a quantity of oats at 40 cents a bushel, and 
 three times as many pease at 00 cents a bushel, paying altogether 
 $55, which was $5 more than he would iii'vu p;ud h.ul hu bought 
 thu whole quantity at 60 cents a bushel. U >w many bushels of pease 
 did he get ? 
 
 3. A gives B 9 yds. the start in a race of 108 yards. B gives C 
 12 yds. the start in the same distance, llow many yds, could A 
 give in a race of 210 yards ? 
 
riFTII CLABS. 
 
 U\ 
 
 4. A pmnp, vrhich Mont] still ^ mi!lu^o« in 15 min., oc(Mii)io(l 12 
 hours in diainin,' n ci-llir 10 ft. hy .'«) tt. If tli»> \via«r r«>so tJinclios 
 |iL'r lionr in tliu crll.u- ami tli% piiin]) t-niptifil IfiOO ciiliie ft. pur lioiir 
 while »V(»rkii.u', how <li'0|) was tiio wuturin tho collar whon tho piunp 
 wiiH^first Hot in motion / 
 
 6. How lonj^ will it tikkn u train ,V <>f ** ">i'o '""i?, t^f>'n'n' at tho 
 rate of 10 niilos an hour, to crr>.s.s a hridgo 2 niilos 80 rods Ion-.,' ? 
 
 6. 'rhroe-two-huiHlri<l-;iii(l-tiftiuths of onofifth of a numhor in 
 If of 100. Whfit is tho inimlu'r < 
 
 7. Reaice 1} to a docimal, hy tho rontnicfcd method. 
 
 8. A docs }\ of a pioco of work; H, f of th(! rcmainilMr ; 0, 3 '^f 
 what \\",\K thoM U'ft ; and I) this ic-tt,. How should ii^OOli.OO, which 
 was givon for tho work, ho f.iirly divided auiom,' thorn I 
 
 9. By iLMiding a sum of moiu-y at 5 per cont. and another Hum at 
 4percont. tho total f-iti-n-st is JgJiO. I'.ut, if tho huius are intor- 
 cliangod, tho intorost is $01.50. Find tho two hmius lent. 
 
 10. A and B ngtoo to have a pioco of work finishod in 15 <1ays ; 
 but A hoinjLj dolayod 5 da\H tiftcr l> startod to work at it, tho work 
 was prolon^'od 1 j^ days. How should !i^50.7O which was paid for tho 
 work bo fairly divided botwoon them? 
 
 11. If i of (x + l of x)—l of (j/- ^ of y), find a: in terms of y. 
 
 .( 
 
 3i 
 
 12. Simplify:{ | + — 1- +.247J^ - of 
 
 GO 
 
 7 I r.t 
 
 I 005 
 
 8-8 
 
 IJ. 
 
 
 J,,: 
 
 wont 
 
 |uo as 
 town 
 
 Ite in 
 
 13. (a) A man 1ms two kinds of gin. The first is worth 80 cents a 
 galltni more than tho second, and 5 j)ints of the second are worth 4 
 pints of tho first. Find tho price of a gallon of each kind, (b) Tho 
 rate of a man's rowing is 3 times the rate of the stroan: on which ho 
 rows, and he can row 10 miles down stream and up again in 3 hours. 
 Find his rate of rowing, and the rate of the strt-am. 
 
 jind 
 
 luthcr 
 
 iught 
 
 Ijease 
 
 res C 
 ddA 
 
 Exercise XXII. 
 
 1. Twelve turkeys and 12 geeso cost together, |24.fiO, and the 
 turkeys cost 45 cents each more than the goose. Find tho value of 
 a score of turkeys. 
 
 2 The radius of the innc# circle of a race-course is 122 yards, 
 and the course covers an area of 14 acres, 154 sq. yards. Find the 
 width of the track. 
 
H2 
 
 RJCFnnsRM IN ArmiiMiTio. 
 
 • I. Till- liri^ht of a I'Muiii i-. h.iir III!' w i<IMi .mil iU roinpuss in 120 
 fook. KiimI tin' riiiiiil»ff of yiii<ls <>f |.iipi r. \i\ jim'Iu'h wi<lr, iiMjuinMl 
 to oovor it« walU, {^ivyii f liif. 5 f)«'i' n-nt. of Mjn mcwi in ullowud for 
 windo vs and <loorH, nw\ tliuf, thu Iriii^'tli of tho room in to thu widtli 
 lis 3:2. 
 
 4. A oyliii<l<'r, LM iiicluw \><\\'X, fiftefl wiMi ii f)i'<ton ut ono «'inl. 
 Hiid with Ii v;tl\(i .'it Uiu otln'r cihI, vvliicli opiiis with a pn'ssiiro of 
 (»0 ll>s. to tint si|ii.iro iii.ii, liHs, Mil iJs imiiTMinfiici', 20 Ibn. pri«H.sm»! 
 to tli''s»pmr»' iiM-li on st-irtin;,' tlu" piston ; how f.ir niii>*t tlio piston 
 1h» fi.rci'il into tlio cyliinU'r to upcii tlu; valvo if thu |iii!s,siir») (»f coni- 
 presHiid iii' viu'ios invcrs«>ly iis tho .spiic(» it occupios? 
 
 6. A fiininT ImysT sh.ircs in ii chocsn factory ut .^(10 ;i .^hiro ; iit 
 the end of thusi-cdnd yt»ar.sto(!k rintiH to JJiTO u Hhiiro, iind hcHollsout 
 (nut hUiuo ; tho Htocic now falls S^i") ;i shur»! I'dch HUcct'cdinfjj ytuir, and 
 }io K'lls otit a .shari' uach year till ail hix .sfi.civ i.s t,!m.s di.sp(»,s»Ml of, 
 when lit! liiids hi! Iiiih iit>iilM!i- 'j;,iint'<l nor lost. What p«!r cent, inter- 
 est on invcstiiiont did the factory pay ? 
 
 6. A cylindrical vat fccf in dianiotor and 4 foot, 8 inchos deep, 
 contains l850*jr»;,'allonM. ll<»w many t;nl»ic iniiho.s are e(inivalent to 
 a gallon i 
 
 7. What fraction of an anj,do of a regular hexaj^on is an angle of 
 an c<[uilateral trianglo ? 
 
 8. A person wislios to cover a piece of ground 00 feet squaro by 
 a pyramidal t(!nt 40 fret in ,)cr{)('ndicidar liel<^dit. What will the 
 canvas rofpnred coat him at 21 cents a square yard ? 
 
 9. A ])yramid of hy.xA, altitude .'5 fci!t, and having a regular hexa- 
 gon for il.s l)as(!, »!ach side being 4 v^.-T inches, is melted and re-cast 
 into balls, each jf of an inch in diameter. Find (a) the number of 
 balls cast and (h) the weight, in o/.s., of the portion of lead left after 
 casting the last ball, if the specific gravity of the lead is 130. 
 (tt =3f). 
 
 10. A merchant in Minneapolis sends his agent in Halifax a 
 consignment of thmr which ho sells at ^0 a barrel on a commission of 
 l.\ per cent, and invests the proceeds in National Bank Stock at 
 1141 on a commi.ssion of :,' perctMit. If the National Bank Stoi-U j)ay 
 11 J per cent, yearly dividends, and his first dividend l)e $U)84.cJ5, 
 Iind the number of barrels of Hour shipped from Miinieaixdis. 
 
 11. A l)oy swims two miles doivn a stream and up again in 2 
 hours, 40 minutes. His rate of swimming in .still water is twice as 
 great as that of the stream. Findhisi-ale of swimming in still water. 
 
 12. How many balls, each 7 inches in diameter, can be made from 
 apiece of lead 14 inches Icmg, 11 inches wide, and 7 inches thick ? 
 
riFTH «LAs§. 
 
 143 
 
 rlo of 
 
 U.35, 
 
 in 2 
 
 fee as 
 rater. 
 
 from 
 lick? 
 
 l.'l. A otfors 834n0t for a firm, Imlf of tho purchnne rnonoy to be 
 {mid in tlituo ycurn, mid thr haliiiu'ii in tliruu ycurs iitti i w ndrt , B 
 otlurs iiil'jr)(5M0, hidf chhIi, and lln' lialiim-o in oiio ycur. Wliioli ofFor 
 Hhould be uccuptud, iitonuy \ivu\n worth 7 pur uunt. puruunuia'} 
 
 Exorcise XXIII 
 
 1. On a voHHol from Sun Friiruisco to Midhourno, tho cjihin 
 pa8.st'n>4i)rH wv.m oim third tho nuiuhur of Htiitiiii^ii pussiMi^'trs, hut 
 2() luurt) oaliiii puHHiiii^urH wen! takuii on ))oiird iit Aiddaiid, uhiMi it 
 was found that tho cahii'i pa.ssoii;^«M*.s worn t-t tho stt'ora^o passfni^rrs 
 an 5; 14. Kind thu nuiiiltur on hoard wliun thu vumhuI roacliud 
 Mulhournu. 
 
 2. Acylindriral tunk, 7 foot indianiotor and i?5 foot Ion.', is lillod 
 with coal-oil ; how many gaUons, (ptartn and pints doeti it contain Y 
 
 3. A morehant Honds his agont poi k to soil on a (^onunisnion of 
 2 per cont. with instructions to invost the not |irocoods in toa at 
 $14 a box, attor doducting hi;s foininixsion of '.V^ ptn'otMit. for buying. 
 How many boxes of tua doos tho morehant rocoivo, both conuni.Hsions 
 being %$:>57 i 
 
 4. A and 13 enter into purtnorship, tlioir capitals being in the 
 ratio of 7;i). After throo months A withdraws a part of his capital so 
 that the ratio is as 2;.'i. At tho oiid of tho year A 'f, share of the 
 profit is ^1600. Find tho whole profit and lis shaio thoruof. 
 
 6. A customor bought, as ho sui)p()sod, tho value of $24.80 in toa 
 from his grocer who usol a weight loi o/,r. for a lb. (a) What did 
 the grocer gain on the salu ? (b) What did the custoiaor lose on his 
 purchase 1 
 
 6. A tiink, 3^ feet in diameter and 4 feet deep, had 45 inches 
 of water in it. It bocauio frozen to tho <lopth of 9 inciioa ; 
 the water was then drawn o»V by a tap in tlio bottom of the tank, 
 and tho ice allowed to melt, (iivon that water expands 10 per tent. 
 in freezing into ic(% find the number of gallons of water in the 
 n.elted ice, half a gill being V)8t, by evaporation, lUiring the process 
 ot melting. 
 
 7. How many cubic yards of clay will be required to make GI30 
 sections of six-inch sewerage tile each 14 inches in diameter (external 
 measurement) and 10 foot long ? ( 7r = 3f ). 
 
 8. Find the cost of maKiag an enclosed box, 12 ft. 6 in. long, 
 4 ft. 2 in. wide, and 2 ft. ti inches deep, with inch lumber at $24 a 
 thousand. 
 
 6i-3t il i 
 
 9. Simplify + — of 2 + i of — . 
 
 6|+3i lli 0| 
 
 X 
 
t 14 
 
 RXBItniNRN IN AltllllMKTIO. 
 
 10. A tunk :t|^ t'l-it. ill iti:Miu>U<r hihI 4 f<itt tiuup, }\m 45 inchcn of 
 wutiT btaiitliim ill it. 8u|)|ioN0 It lo fno/.o ovur wiili ico t<> ilt<« 
 fluplh of U itu'tioM, witnt will Imi the wuiglit of thu iuu in Ihu t/uik if 
 icu ill I y an lifuvy iim wntor 7 
 
 11. A cominiMaion nifrcliiwit huIIm 500 l)l>U. Hult lU 91.40 a burnl 
 on a ooiiiiiiisNioii of \j por cent.; what fIo«m hu iviiiit ( 
 
 12. A'm ctittlu arc ^ Iumh in iiuniinr tiiuii \Vh, but iru 12^ pur uunt. 
 I>«<ttt<r ill ^iMil<>. If U'h licid iiuiiiliuiM :;67 lu>a<l worth ^7*2 uuuli, 
 what iH tliu value of A'n lu'id / « 
 
 l.'l. Fiml tliu voliiuit' of tlht fniHttirn of a coni< whone vortiail 
 lii'i^lit IH t'J iiioliuH ; tilt) «liani)<t('r of tlio liir.;< i- ))hn(> uf fruHtuiii 
 l)t)iii({ 28 iiichuH and the Uiuiuntur ot tiiu luiuiler baMe being 21 
 inches. 
 
 Exerciae XXIV. 
 1. Prove ilio corructuesH of the following ntntemrnts : 
 
 Frincihal. 
 
 Uatr. 
 
 $72 
 
 «. % 
 
 9510 
 
 ^7% 
 
 !|12()0 
 
 91 KK) 
 
 12200 
 
 6% 
 
 9720 
 
 25% 
 
 TiMK. 
 
 HiMI'LK IntKKUT. 
 
 Thu I DiROOCMT. 
 
 2 yrtj. 
 
 99. 
 
 98. 
 
 2 yis. 
 
 980. 
 
 970. 
 
 lyr. 
 
 940. 
 
 9:{0. 
 
 |yr. 
 
 9100. 
 
 9'JO. 
 
 5 yrn. 
 
 *550. 
 
 9140. 
 
 lyr. 
 
 9180. 
 
 9144. 
 
 2. Find tli« himim.k inteiikst on the tnie disctmnt in each of the 
 foregoing I'XiiuiploB for tho i<iv(Ui tiino at thc3 givisn into por ount., 
 and in (■.'•';h «'a.su hIiow that the intcrust is ucjual to thu (liffeieiice bu- 
 twuun thu simple intertst and the true dUcuunty as given in the fore* 
 going tahlu. 
 
 3. From the last uxaraplo in quoHtioii No. 1 Hhow that : 
 
 («) The Simplu Interu8t= ^ of tlio Principal. 
 
 1 
 (b) 'Iho True Discount — of the Principal. 
 
 1+4 
 (c) The difference between iSini. Int. and T. Dia = 
 
 of 
 
 tho Principal, 
 ((i) Thu Interest on the T. Discount 
 
 4x6 
 
 4x6 
 
 of the Principal. 
 
 (e) The Simple Interest is greater than True Discount by 
 Simple Interest on the True Discount 
 
 ! 
 
rirrii ci ah«. 
 
 14A 
 
 of 
 
 pal. 
 by 
 
 4. Ri<'ltioo the Siiniili' Tiitur«Ht| iii enoh caM in (]ui*<«ti<in No. 1. 
 til tlitt li'Ktiun of tliii rrim'i|ml, hikI from thin fnu;tioii form ihu 
 fruotiuti \vhi(;h the 'rriiu Dinoouiit \h ot tho l*riii< ipul in ••uih cami«. 
 
 5. ((t) Provu the oorrHctnuHiH of tho foUowiii^ ; 
 
 BiMPLR IntKKP.HT. 
 
 TiiiK DiMCorwr. 
 
 
 I'HINtirAI.. 
 
 FUTk. 
 
 TiMH. 
 
 iNrr.KMr. 
 
 $57.00 
 
 $28.80 
 
 $jV).4() 
 
 .^100.80 
 
 $100.80 
 
 $14.10 
 
 I'MINUICAb. 
 
 Katn. 
 
 I'lMK, 
 
 iMaoiUNr. 
 
 $288 
 
 ft% 
 
 4 yiH. 
 4 yrM. 
 
 $288 
 1144 
 
 5% 
 fi% 
 
 4 yi ♦. 
 4 yvH. 
 4 yn. 
 
 $48 
 
 $144 
 
 r>% 
 
 $24 
 
 $114 
 
 B% 
 
 7 yiM. 
 
 7 y»"<. 
 
 n yn*. 
 
 2 yiH. 
 
 1144 
 
 5% 
 
 $84 
 
 $144 
 
 10% 
 
 $144 
 
 107. 
 
 4 yi'H. 
 
 $41| 
 
 81I4 
 
 B% 
 
 $144 
 
 6*/o 
 
 4 yrs. 
 2yM. 
 
 $24 
 
 $144 
 
 $144 
 
 67o 
 
 $1V, 
 
 (/)) .Show that Siiii|tl»! Intm-o^t U jnnpmHnnol to i'ltiNCii'Ai., ratk 
 or TIME. 
 
 (<;) Show that Truo Discount is propm'timxal to imiincipal when 
 KATK and TiMK remain uiudtered. 
 
 {(l) Show that Truo Discount in nnt propovtiomtl to katb oftimb. 
 
 6. (a) If thu sini|>K3 inteivst oi ii cuitHin huiii ho .j\^ of the prin- 
 cipal, what fiaciion of the princip!\l would rupifsiunt the truo 
 discount. 
 
 (6)(}ivon that $106 is the tnio discount on i^'MOb f<»r 1^ yrs. 
 at 10 per cent. piT annum, find the interest, witliout working 
 out as a question in interest. 
 
 7. Tho simple interest on $420 is $21. Find (a) the truo dis- 
 count ; {!)) tho diUcionco ln'tvveon tho simple intorest and truo dis- 
 count ; and (<;) tho interest on tho true disc(»uut. 
 
 8. If tho simplo inturost on $7272 for a cortain timo at a certain 
 rato, 1)0 .S'.)0".», what is tho true discount on samo sum for the same 
 time at tho .samo rate i 
 
 9. In what timo will $650 gain $241.80 if, at the same rate, tho 
 gain on $750 for one year and 14G days is $03? What is the rate 
 per cent, per annum charged ? (365 daytt=* year). 
 
146 
 
 BXEKCISUS IN ARITHMB'rrC. 
 
 ! 1^! 
 
 1 
 
 
 
 
 1 
 
 :i; 
 
 
 :l| 
 
 ■ .11 
 
 ■]'. 
 
 j 
 
 i 
 
 10. Tf Mie true disc iiiiih on |14()0 for a rortain time at 13 |)er cent, 
 is $260, what is tho true disoount >;n sumu sura for one lifth of that 
 time at same rate per cent.? 
 
 11. If the tmu discount on $743.40 for 2;J- years is 8113.40, in 
 how nrmy years will tho discount on $570 bo $70, at half the rate ? 
 
 12. If the true discount on $1089 at 3 {)er cent, be $189, at what 
 rate prr cent, would tin- true discount on $1150 be $150 for ^ of the 
 time ? 
 
 13. T'^ tho true discount on $210 for 4 years at 4 per cent, be 
 on what sum would $80 be the true discount for same time at satne 
 rate? 
 
 1. Simplify 
 
 ifyrja 
 
 Exercise XXV. 
 
 3 05 5491 
 
 875 of 3-5 X 5-03 -^ x — 
 
 305 62 
 
 6-3 
 of — of 1t\. 
 
 2-i 
 
 2. If 13 hours are rcMjuircd for travelling a givon distance at a 
 given rate, what will be rec)uir(jd when the distance ia diminished by 
 f and the rate increased by 225 per cent. ? 
 
 3. In what proportion must a grocer mix sugars which cost re- 
 spectively, 0, 8, 16 and 19 cents a lb., in order that he may realize 
 a profit of 30 per cent, by selling the mixture at 13 cents a lb. ? 
 
 4. Bought 2 horses for S200. Sold them again gaining 5 per cent, 
 on the second, and losin.; 5 per cent, on the first. If I gained on 
 the whole transaction one per cent., find the cost price of each 
 horse. 
 
 5. What will it cost to make a gravel walk, 7 ft. 6 inches wide, 
 along the sides of a squar.; field containing 2 acres, 80 sq. rods, at 
 37'i cents a square yard, tlie walk being part of the field ? 
 
 6. Divide $870 among A, B and C, so that '75 of C's share =*5 
 of A's stare, = '6 of B's share. 
 
 7. I intended to gain 20 per cent, on a stock of tea and fixed my 
 price accordingly ; after selling ^ of the stock I was obliged to re- 
 duce my price 5 cents per lb., and gained {f as much as I had in- 
 tended. What was tlie original cost price of the tea per lb. ? 
 
 8. A speculator sells out $5000 alock of Uie 3 per cents, at 96, 
 and invests tlie proceeds in bank stock at 75, which pays an annual 
 dividend of 2 J per cent. What is his iiicrease in income ? 
 
 9. A train has 380 miles to rim. After running 200 miles, its 
 rate is reduced one-seventh, and it arrives 51^ nn'nutes behind 
 
 time. Find its first rate of running. 
 
FIFTH CLASS. 
 
 117 
 
 =•5 
 
 96, 
 
 Lnual 
 
 ,, its 
 
 Ihind 
 
 10. Owing a man $538.06, I gave him a sixty-day note ; what 
 must be tho fucc of the note to pay him tho oxact debt wheii dia- 
 eounted ut fchu bunk at ten per cent, per iuinum ? CDaya of grace 
 allowed, and 3(>5 days = a year.) 
 
 11. Eighty Ib.s. of aeu water cental h 8 lbs. of salt. Find how 
 much fresh water must be added so that 1()0 Iba. of tlir inixMifc 
 shall contain 4 lbs. of salt. 
 
 12. The sum of two numbers added to the sum of their squares is 
 922, and their product is 400. Find the numbers. 
 
 13. Find the number of yards of ril>bon, one inch wide, it will 
 take to wind the surface of a couo i4 inches in diameter, and slant 
 height 12 feet. 
 
 Exercise XXVI. 
 
 1. A grain buyer made a profit of 4| ^ per cent, on a shipment of 
 500 bushels of wheat at .SI. 15, and 1275 bushels of barley at 75 
 cents a bushel, which he shipped his agent to sell on a coimiiission of 
 2i per cent. The a^eiit sold the whent at .$1.30 a bushel, and the 
 barley at 80 cents a l)ushel, and paid $28,25 for expenses, remitting 
 the balance. Find his remittanje. 
 
 2. What is the rate i»er cent, discount on the face of a note, 
 which a broker buys, bearing interest at 10 per cent, per annum, so 
 %a to make 25 per cent, on his investment ? 
 
 3. There are two sums of money, one being 4 times the other, 
 discounted, (true dis.), tlie smaller sum for two years and 6 months 
 at 4 per cent, per annum, and the larger for 3 years and 4 months 
 at 6 per cent. The sum of the present worths is $1400. Find 
 she original sums. 
 
 4. Two sums of money, one being three times tho other, are 
 discounted (true discount), the smaller at 8 per cent, per annum 
 for 9 months, and the otlierat 6 per cent, per aunuui for 4 months. 
 The sum of the present worths is i$10,500. Find the sums. 
 
 5. I shipped my agent 500 bbls. flour, vvifch instructions to sell 
 the flour on a commission of 2 per cent, and to invest the balance 
 in tea after deducting his comsnission of 1^ per cent, for buying. 
 Find the price at which he sold the flour, his whole commission 
 being $72.10. 
 
 6. The true discount on a certain sum of money for a, certain 
 time at a certain rate per cent, is $230, and the simple interest on 
 the same sum, for the same time and at the same rate is .?240. Find 
 the sum. 
 
 ^ 
 
 1 1 1 
 
148 
 
 EXERCISES IN ARITHMETIC. 
 
 ! ,1^ 
 
 ] 
 I 
 
 u 
 
 7. If the simple interest on a certain sum for a ( jrhiin time bo 
 '^n of the snni, wli.it fraction of tlie Huni will leprestjnt the triio 
 discount? (A|)i)ly the i)rinciple involved here t(. the following ques- 
 tions in the exercise.) (See PjX. 7X and 8th Qiu!h. for another 
 example.) 
 
 8. Sold a horse for ^270, gaivhig thciehy 7h\ j)er cent, of the 
 proceeds. What fractional part of the cost did I gain ? 
 
 9. Sold a coat for $30, losimj tliereby S.^.'j i>er cent, of the selling 
 price ; what })er cent, of the cost did I lose ? 
 
 10. Sold a horse, gaining .ii^f)4, which was as much per cent, as the 
 horse cost me ; what was the sellin,<^ price of the horse? 
 
 11. Sold a horse f<;r $'280, gaining therelty l-l-f per cent, of the 
 proceeds. Find my gain per cent, (m cost iiad I sold hin\ for $250. 
 
 12. If a kiln-dried piece of wood expands 4 per cent, in being 
 water-soaked, what per cent, will it <i»^ain c<jntract on ])eing kiln- 
 dried? Prove your answer to be correct i)y taking a block of kiln- 
 dried wood, measuring 050 cubic inches. 
 
 13. (a) If the bank discount on $J(i80, for a certain time at a cer- 
 tain rate, be'$210, what would be the true discount on same sum 
 for the same time at the same rate? 'h) A, B and C can do a piece 
 of work in 4| days working togetlier. B does f as much as A, and 
 C does ^ as much as B when they work together. How long will it 
 take alone to do it ? 
 
 Exercise XXVII. 
 
 1. A shed in the shape of the letter L covers an area of 13 square 
 rods, 28 square yards, 8 square feet, 108 scjuare inches. It is 20 
 feet wide, and the shorter side measures (JO feet in len</th (measured 
 from the angular point of the L) ; find the length of the longer side 
 from same point. 
 
 2. A drover spent- ^ of his money in buying hogs, | of the re- 
 mainder in buying cattle, and the rest in Ituying sheep. If the hogs 
 and cattle together cost him $375 more than the sheep, what had he 
 invested ? 
 
 3. Express in the form of a vulgar fraction the average of ^, 
 
 i 
 
 -, -4, -3^ 4f, -IGf, -OOli 
 
 31 
 
 4. Find the L.C.M. of 17^, 13f , and 15f. 
 
 5. On property worth |5000 a premium of $40 is paid on the 
 policy. Find the rate per cent, of insurance. How many cents is 
 it on the $100 ? 
 
FIFTH CLAOS. 
 
 14U 
 
 0. Ton men, 15 wotnon find 20 boys earn i?3G0 in a week, work- 
 ing in u cort.iin factory. Tho boys oiirn ojicli 75 cents a diiy, ,ind a 
 woman gets ^ as much as a man. Find tlte weekly wages of the 
 men. 
 
 7. The perimeter of a semi-circlo is 234 yards ; find its diameter. 
 
 8. (a) Reduce | of an hour to tlie decimal of a week ; (b) Reduce 
 one day to the decimal of a week ; (<■) What determines the khid 
 of a decimal ? (d) llow many kinds of decimals are there ? 
 
 9. A person invests a certuin sum (goW) in U. S. 6's, 10-30 
 which are at 10 per cent, discount, and six times as much in U. S. 
 9's, 5-40 which are at a premium of 21^ per cent,, the interest on 
 both being i)jiyubl«^ in gold, when gold is at a premium of 21^ per 
 cent. VVliat did the sureties cost him, the income from both being 
 $2070 ? 
 
 10. The perimeter of a field is '9 of a mile, and it is five times as 
 long as it is wide ; find the cost of seeding it with wheat worth 88 
 cents a bushel, when 2 bushels, 10 lbs. are sown per acre. 
 
 11. A publisher printed an edition of 1000 copies of a quarto 
 book of 1554 pages. How much paper did he use, allowing 1^ 
 quires to every ream for waste ? 
 
 12. A man has $50 ; but, after two successive discounts at the 
 same rate, he has 146.08. Find the rate of tliscount. 
 
 13. Find the square root of each of the following ; (a) f^ of 801 ; 
 (6) If of 891; (c) 17749369; (d) 7879249; (e) 25040016; 
 (/) 67912100. 
 
 Exercise XXVIII. 
 
 i. A certain room is | as wide as it is long, and requires $120 to 
 carpet it with carpeting worth $2.50 a square yard ; it also requires 
 $4.20 to paint its four walls at 5 cents a square yard ; find its 
 dimensions. 
 
 2. A merchant b'^)ught a bankrupt sto«k at 70 cents on tlie dollar 
 of the invoice price, which was $5000. He sold | of it at 20 per 
 cent, advance on tho invoice price, ^ of the remainder at 30 per 
 cent, below tlie invoice price, and the balance at 80 per cent, of the 
 invoice price. His total expenses were 5 per cent, of his invest- 
 ment for buying and 4 per cent, of his sales for selling the stock. 
 Find his loss or gain, (a) in money, (6) in rate per cent, on cost of 
 investment, (c) in rate per cent, on total cost. 
 
 ri 
 
 ■Wl 
 
 m 
 
150 
 
 EXERCISES IN ARITIIMBTIC. 
 
 ■ •! 
 
 J't 
 
 I l 
 
 3. A merchant bought goods on Jjit\u;iry 2nd, 1893, amounting 
 as per invoice to $750. Ht) t^ot succos.sivt' discounts of 16 per cent. 
 und porctnit., and was allowed iiO days to pay tho cash, after which 
 intoro.st at tlie rat(3 of 5 p^r ctint. piu- annum would be charged. 
 On February tho Ist ho pjiid .i5''{t)*Kl.*5. llow much did ho pay on 
 April IDtii, 1893, to Hottle his account I 
 
 4. A circular ciatorn is 21 ft. dooi), and holds 99 barrels, 1 ga]., 
 1 gill of wator. Find the diameter of rlio excavation whicii will 
 allow for a water-proof linin<jj 9 inches thick. (A cubic foot = 6^ 
 gauouH, and a Ixirrel 3U, gallons.) 
 
 6. Divide the L.C.M! of f, fJL and ,7^ by the H.O.F. of 9J and 24. 
 
 6. On a «um borrowed at 6 per cent, per annum, and loaned 
 immediately at 8 per cent., I gained .i^.'U.'iO in three months, 18 
 days. What do I owe the lender at the end of that period ? (A 
 month = bOdays.) 
 
 7. Jones has $80, Smith has £20, 14 sli., Sterling, and Cameron 
 has £4, U) sh., 3ii d., Halifax ciuToncy. They put their money to- 
 gethei- and invested in flour at 75 cents a sack. Find the number 
 of whole sacks bought and A's share of the money remaining. 
 
 8. A contractor bought the following : — 70 pieces of cherry scant- 
 ling, each 10 ft. long, 9 inches wide and 4 inches thick ; 120 pieces of 
 pine joisting, each 24 ft. long, 8 inches wide and 3 inches thick ; 400 
 planed and niatclu'd inch-boards (pine), each 15 inches wide and 20 
 ft. long ; and 1000 [)iecis of maj)ie flooring, eacii 24 ft. long, 6 
 inches wide and 2i incht^s thick. Find the cost of the whr' ;, when 
 cherry is worth $40, pine !p 1 5 and maple $12 a thousand feet. 
 
 9. A round stick of timber inea.sures 16 inches in diameter at the 
 larger end, 12 inches at the smaller end, and its centraHength is 
 18 feet. How many cubic feet and inches are there in the stick ? 
 
 10. I have a store worth $8775. For what amount must my in- 
 surance policy be drawn at 2i per cent, in order that I may recover, 
 in case of fire, both my premium and the value of my store ? 
 
 11. On ii?(i(X)0, my income is $370, derived from part of my cp^pital 
 being out at 7 per cent, and the rest at 5 per cent. How much had 
 I lent out at each rate ? 
 
 12. What time after 7 o'clock will (a) the minute hand of a clock 
 be midway between tho figure VII and the hour hand ? (6) the 
 hour hand be midway between the figure VII and the minute hand ? 
 
 13: Divide $2.'55 among A, B, C, D, and E, giving A $15 less than 
 B; B, .«55 less than C and D, together ; 0, $.30 more than E, and 
 D $40 less than and E together. 
 
HFTH CLASS. 
 
 151 
 
 [Hi- 
 rer, 
 
 Id? 
 an 
 
 Exercise XXIX. 
 
 1. A flum of money is S:i6; but after three successive advances are 
 made upon it at a certnin rate per cent., it ia found to be $41.0745. 
 Find the rate por cent, of advance. 
 
 2. What amount of stock in a company at 12^ per cent, below 
 par could be bought for ^1226 ? 
 
 3. For what amount should a note be drawn for 9 months, which, 
 when discounted at true discount, would produce $2000, the rate of 
 interest being 4 per cent? 
 
 4. British Columbia Mining Stock at 130 pays 10 per cent, per 
 annum, and C.P.R. Stock at 115 pays 8 per cent, per annum. What 
 would be the difference per annum in income by investing $2990 in 
 each kind of stock ? 
 
 5. A man sold out $10800 in R^iilway Stock, paying 5 per cent, 
 annual dividends, at 104, brokerage f per cent., and purchased 
 Government Brmda at 105, paying 1) per cent, annual dividends, 
 brokerage ^ per cent. Did ho gain or lose in income, and how much 
 per annum ? 
 
 6. Had 13000 in B. 0. Cattle Company's Stock, paying 10 per 
 cent, yearly. Sold out at GO, and bought in Nanaimo Coal-Mining 
 Stock at 120, paying 25% yearly dividends. Find my change in 
 income. 
 
 7. An agent is in receipt of $4300 with which to buy wheat for 
 his employer at 02^ cents a bushel, after deducting his commission 
 of 7^ per cent. H!ow many bushels of wheat does he remit ? 
 
 * 
 
 8. The net price of a piano, sold at 20 per cent, and 5 per cent, 
 off the list pric3 is $456. Find the list price. 
 
 9. The difference in time between two places on the globe, due 
 east and west of each other, is 5 hrs., 68 min., and 40 sec. Find the 
 difference in longitude. 
 
 10. Find the face value of a note drawn to fall due 2 months 
 hence, without interest, so that if discounted immediately at a bank 
 at 8 per cent, per annum, the proceeds may be $592. 
 
 11. A certain pipe is 7 inches in diameter, and water passes 
 through it from a lake at the rate of 45 miles, 6^^ rods, 2 yards, 2 
 feet, 3^Y inches per hour. How many barrels of water will be dis- 
 charged from the lake, tlirough the pipe, every 4 mins., 16 sees. ? 
 
 12. A has $600 ; but, after three successive discounts have been 
 made on it, at the same rate per cent., he has left $514.42^. What 
 was the rate per cent, of discount ? 
 
 ?i 
 
 i 
 
 IS 
 
li 
 
 ' ii. 
 
 iri2 
 
 KXEKCISKR IN AIUTIIMETIC. 
 
 13. A man has Iff76 ; but, after two succesHivo advanoos upon it, 
 at the Hame rato per cont. uf inureuoe, ht) has $84. 27. Find tli(» rate 
 per cunt, of increaue. 
 
 Exercise XXX. 
 
 1. (o) Reduce $26.40j to Jtl.s.d. Sterlinjr; (6) By dealing in tho 
 practical way in Canadian currency, what would a man lose in pay- 
 ing in falngliHh shillingu, a debt of £15. 
 
 2. Reduce 1 acre, 127 sq. rods, 21 sq. yards, 2 s((. feet, 36 sq. 
 inches to sq. yards. 
 
 3. A fruiter has 90 apples and pears in a basket, and i the num- 
 ber of apples in the basket is equal to ^ of the number of puars. If 
 pears are selling at 20 cents a dozen, and apples at 5 cents a dozen, 
 find the value of the basket of fruit. 
 
 4. From 20 sq. rods take 19 sq. rods, 30 sq. yards, 99 sq. inches, 
 using compound subtraction in working it. 
 
 5. A fruit-monger bought 70 baskets of fruit at $1.20 a basket. 
 He lost 20 per cent, of the fruit by decay, and sold the remainder 
 at 15 per cent, advance on cost. Find the total gain or loss per 
 cent. 
 
 6. From f of an acre subtract 74 sq. rods, 29 sq. yds., 16 sq. ft., 
 145 sq. in., (a) by compound subtraction, and (6) by using reduction. 
 
 7. From ^ of an acre take 38 sq. rods, 30 sq. yds., 72 sq. ft., 36 
 sq. in. 
 
 8. From ^ of an acre, a man sold 124 sq. rods, 30 sq. yds., 100 
 sq. ft., 100 sq. in. What had he left? 
 
 9. A merchant sold 560 pounds of tea, using a false weight of 14 
 ounces to the pound. If the tea cost him 87^ cents a pound, find 
 his gain by selling the tea at 20 per cent, advance on cost. 
 
 10. A cellar, the floor of which is 7 metres wide, is paved with 
 7500 paving-stones, each 20 centimetres long by 7 centimetres wide; 
 how long is the floor in metres 1 
 
 11. Find the cost of digging a trench 5 kilometres long, 3 metres 
 wide at the surface, 1 metre, 80 centimetres wide at the bottom, and 
 6 metres deep, at 15 cents per store. 
 
 12. Bought 4380 kilogrammes of prunes in Havre at 2 francs per 
 kilogramme and sold the whole quantity in Montreal at £105 Ster- 
 ling per tonneau ; find my gain, in Canadian currency, exchange in 
 Havre being 56 shillings for 73 francs. 
 
riPTII (LASS. 
 
 153 
 
 13. (a) From | of an acre a j^ardcnor sells 13 aqnare rods, 28 
 R<|iiiinj yards, 10 snmire f(u t, 150 a(juHro inchoa ; wh/it has he re- 
 tiKimini,' ? (.Vo natirflon Ih fnrc stihtriictinti). (h) Multi[)ly niiiutuen 
 hundred iiiiliioii, foiirtocii thousand and fifty thousiutd, thirty-six 
 hundred and seven by two hundred and fifty thousand and ninety 
 thousand, seven hundred and eijjht ; and tlu-n divid(» the product 
 1>y eip^hty-nine hundred and thirty one thousand, eight hundred 
 and elevan. 
 
 sq. 
 
 )f 14 
 find 
 
 I with 
 ride; 
 
 jtres 
 and 
 
 per 
 5ter- 
 ;e in 
 
 Bxeroise XXXI. 
 
 1. If ^ of l.S lbs. sugar cost as much as 2 lbs., 8 om. of coffee, 
 and 7 lbs. of coffee cnst as much «'=« 4 ll)s. of tea, and 5 lbs. of tea 
 ci>st $2.10, how many lbs. of sugar should be given for a dollar? 
 
 2. A coal bin is 35 feet long, 18 feet wide, and 11 feet deep. 
 (I) How many more tons (hif measure) of hard coed than of soft coal 
 will it hold '( (2) How many more bushels {by weight) of hard coal 
 than of soft coal will it hold ? 
 
 3. Add 6 cwt., 10 lbs., 5 ozis. ; 17 cwt., 21 lbs., 9 ozs. ; 575 cwt., 
 23 lbs., 15 ozs. Subtract 475 cwt., 75 lbs., 8 ozs. from the sum. 
 Multiply the dijf'erence by 7 ; and divide the product by 6. 
 
 4. A tank is 9 feet long, 7 feet wide and 3 feet deep ; another 
 tank is 21 feet long, 3 feet, inches wide and 3 faet deisp. How 
 many more barrels of water will the latter lutld than the former? 
 
 5. if ^ of a farm sells for $3150 less than ^ of it, how many 
 acres does a man get who buys ^ of the farm at $40 an acre ? 
 
 6. Divide the L.O.M. of 8, 12, 24, 36, 40, 90, 180, 190, 570 by 
 
 5§x7a 
 
 7. A ves«iel is said to have gone 1760 ** knots'* in going a dis- 
 tance of 2028'9 miles. How many feet are there in a '* knot'* ? 
 
 8. A cistern is 9 feet square at the top, and is sunk 13 '481 feet 
 into the ground. How many barrels of water does it hold ? 
 
 9. A mow of well settled hay is 40 feet x 20 feet, and is tilled to 
 the depth of 10 feet ; what is the hay worth at $7 a ton ? 
 
 10. A man owning ^ of a lot, sold "3 of his share for $2800 ; find 
 the value of the lot. 
 
 11. A cow is sold at a gain of 20 per cent., and the sum of the 
 cost price, gain, and selling price is $192. Find the cost price. 
 
 P 
 
 
 V. 
 
w 
 
 I i 
 
 1»4 
 
 ■XBRCISFfl llf ARITRMRTia 
 
 12. How much wator must be arMnd to 81 gallons of pure wine 
 worth $.'{.3:^^ a (gallon, ho that by soiling the mixture at $3 a gallon, 
 T may rualize a protit of $15 V 
 
 !.*{. (t) A grooor sold 18 (lo/.nri and eii^ht ej/gs for $3.f)0, thnrel>y 
 v;iiiniii^ 25 P^r ooiit. on tlu^ Halo. How iriuch did the ei^i^'H coHt the 
 j^rocer per doz. i (h) A man walking »lon.,'Hide ;i railioud, at 4A 
 miles an hour, ob.serv«*H t!>at a train, goinyr 45 milcH an hour in the 
 name direction in whicli he is walking, pasHus him in 40 seconds ; 
 tind the length of the train. 
 
 Exercise XXXII. 
 
 1. A, B, and D, four adjoining farmors, have their faniis 
 •Irainod by 960 rods of ditch, 3 feet, 6 inches deep, 5 foot wide at 
 the surface, and 2 feet wine at th») bottom. A, who benefits tho 
 most, pays half tho cost of diyj^'ing the ditch, and of the remainder 
 of the cost pays half as much as II, and D half as much as C. 
 How much does D pay, th»! cost of digging the ditcli being 7^ cents 
 a cubic yard ? 
 
 2. Divide the product of §J, I'l^, H| and }^jf by the diiference 
 between ^^^jf and f\ ; to tho result add 12 '16. 
 
 3. A bucket holds 10 pints of water when it is f full; how 
 many bucketfuls of water will fill a barrel ? 
 
 4. A has $18150 in English standard silver ; how many lbs., etc., 
 of pure silver are there in that amount of money, if pure silver is 
 $40 an (mnce ? 
 
 5. If coli'oe loses 5g per cent, of its weight in roastini:;, how 
 numy lbs. of green coffee will produce 1530 Ib.s. of roasted coffi •? 
 
 6. A stone-cutter dressed 8 stones per day for 8 days. Of these 
 62^ per cent, were circular in form, each 14 inches in diameter and 
 5 inches thick, and the remainder were rectangular in form, each 
 18"xl5"x5". How much did he earn, if ho received 9 cents a 
 square foot of surface for dressing the stones ? 
 
 7. At what price must 6 per cent, bonds, maturing in 5 years 
 from date of investment, be purchased to pay 20 per cent, on the 
 investment ? 
 
 8. Out of a cask ui brandy | is diawn, then ^ more than ^ of the 
 remainder ; the cask is then found to contain 27 gallons of liquor. 
 How much was in the cask at first ? 
 
 9. In what time will $610 amount to $1016.66 at 7 per cent, per 
 annum ? 
 
FIFTH 0LAB8. 
 
 155 
 
 these 
 
 )r and 
 
 I, each 
 
 Mits a 
 
 years 
 )n the 
 
 |of the 
 
 iquor. 
 
 It. per 
 
 10. A mow, 40 ft. lonj» atuI 20 ff. witle, is fiUed to the depth of 
 10 foct with hay woll Huttlud. Find the vahio ni thu hay at iii$7 a 
 Ion. 
 
 11. If a «hip worth .^48,000 bo inswrud for H'.i\ pn- cont. of its 
 lunl value, what will a man Iuho (in ca.se uf tiro) who has a three- 
 fifths' intoruHt in it ? 
 
 12. Th«j prouiitim paid is tlT-GO on a house insiuvd for Jii^.'ioUO ; 
 how many centn is that on thu 3100 ? What rate por ijont. in it ? 
 
 13. By using any short nujtliod you know, reduce |(} to a decimal. 
 
 Exercise XXXIII. 
 
 1. The promiiun for insuring a house was $1.3.20 at CO cents a 
 the 8100 ; for wliat sum was the house insured i 
 
 2. If the tru*' discount on SOfJO for 4 years be ^160, what will be 
 the discount for )^ears in tiie same sum at the same rate ? 
 
 3. Goods marked p.40 are sold for $4.80. What is the rate of 
 discount? 
 
 4. Average the following Ledger Account : 
 J)r* Isaac Suelden. 
 
 Or. 
 
 1887 
 
 Apr. 
 
 it 
 
 May 
 
 2 
 11 
 3 
 
 To xMdso 
 it (i 
 
 
 ( 
 
 1887 
 
 
 900 
 
 00 
 
 A})r. 
 
 5 
 
 500 
 
 00 
 
 ti 
 
 li 
 
 ,;)0 
 
 00 
 
 ( ( 
 
 25 
 
 
 
 May 
 
 lo 
 
 Hy Cash 
 
 50 
 1000 
 
 ;ioo 
 
 25 
 
 00 
 00 
 
 00 
 00 
 
 6. I receive $18030 to invest in Hour after deducting my commis- 
 nofSj . . - 
 
 each, do 
 
 sion of 3jt per cent, for investing. How many barrels, worch ^4.50 
 ) I remit? 
 
 G. If $1608 be paid for 12 acres, 90 sq. rods of land, and it be 
 immediately sold at 96 cents a sq. rod, what gain per cent, would bo 
 realized ? 
 
 7. Find the cost of 162 yards, 3*6 inches of cloth at 6s. a yard 
 
 8. Write the following in figures : Nine lii.iidrod millions, 
 twenty hundred and ninety thousand, ten hundruil and thirteen ; 
 subtract four hundred and ninety-eight hundred and fifty-seven 
 from it and extract the square root of tlie remainder. 
 
 9. The dividend is 7/^ ; the divisor 2i ; the quotient ^ ; wliat is 
 the remainder ? Make a statement of the relations among these. 
 
I* 
 
 >6 
 
 KXKU(7IHI:H in AlUTUMITKr 
 
 10. It coHt ^78.;i7j t<) tii.vo H rt'ctAMji^uldr fioM at \2\ <ont8 u 
 y/ird ; the Held wom 42 ro'lii ioii;; ; how wnU) uam it / 
 
 11. I paid $45 tu u coininiHNioii inurolmiit for Hulling uoodH ut 2^ 
 pur cunt, ooniniinhion, nud hi i otiiur ch<ir){im iinioiintfdto $\'2.7^>. 
 Kind thu nt/. fnorevih ^t thu -iuUi, 
 
 12. Ifuw many du/unH of itir^H at 10 conts a do/un wouM piiy for 
 l4U3j ouncuM uf t«a at 57 centH a pound i 
 
 13. A rual UHtatu dealer Hold a houNu and 7 tiortis of iatid for .l'4l 1, 
 iKsh. Sturlin).;. If tliu houHi; waH vnliioil at ><(i'J*.>.U<J, what was ll.«e 
 value per aero (in Canadian uiirronoy; of tin- Lmd ( 
 
 
 Exercise XXXIV. 
 
 1. For how muoh is a houiiu in^urttd, if ihu prumiuni paid in $\) 
 at j i)Or Clint.'/ 
 
 2. B and arc patnora in a grocery husinofs, B invustiMg J?40i)() 
 and ^.'{U<>0. ii is a hlei'ping partner, anW (J manages the hu.sintss 
 at a yearly walary of if^MH), Oi.t (»f a yearly g'un of !i;21MK.», what 
 should each pa' tner receive t 
 
 3. What mnst hi; the >»:Jiing price of a fjirni which cost $"8721, 
 in or ler to roali/o liO per cent, on the sale of it after allowing a 
 Heriea of discouni-s ^froni the askinj^ price) of b per cenL , iU i»er 
 cent., and 15 per cent.'/ 
 
 4. A Canadian tourist won 1/ to llaiabuig, (Jerniany, with J#250, 
 which he chanj^ed for Gerninn money at 25 cents tor a mark. He 
 spent 241 maiks in Huniburg, and then went to Li.shon where he 
 exchanged his marks for Portiiguoso moiiry ut, 2.'> marks for 4 mil- 
 rees. Ue then si)ent 12 milrees in Lislxm, .tiKl next went to Lon- 
 don, England, where ho exchanged his mihoes for English money 
 ut 5s., 9d. per milree. He then sj)ent £14, 5s. in London, and 
 this sum included the [irice of his ticket from Liverpool to Quebec. 
 Ho now exchangetl the remaii <ler ot iiis money for ('anudian Currency 
 at the ordinary rate of exchange (£ = ^4.y0j). How much money 
 had he on arriving in QuoIjoc '{ 
 
 5. A specuhitor sold stock at a discount of 10 per cent., and 
 made a protit of 20 per cent. At what rate discount had lie pur- 
 chased the stock ? 
 
 6. What sum of mon«3' put out at 6 per cent, for 4 years, and 
 compounded annually, will produce $1540.^4/^, t 
 
rinii of.AM. 
 
 167 
 
 $«.) 
 
 
 lie 
 
 ) lio 
 inii- 
 Lou- 
 )noy 
 uu*l 
 ibuc. 
 ency 
 oney 
 
 and 
 pur- 
 
 and 
 
 7. A iimii Iw^s 8ir)(HK) ill AinnricuM Ktuprlurd silver; how iimiiy 
 n»M., etc., of |)iirt< Hilv'M- lii'o thut'o in that huiii, if pure nilvur in w«>rt n 
 840 an ounce ? 
 
 8. llnw inAuy f">yH, Hftch ^\nu\^^ ? of ft inan'H work, miint >>e 
 ('iiiplov'il with S ni(ii\ to do im much work in ir) iIuvh an RO nicn 
 
 'I 
 Would do in IH dayfl 'J 
 
 'J. On a dt(}»t of iffHOO, T rocnivj^d on Jftnuary l«t, IftOl, 4.% 
 ItiihlirlH of will at, valiK'l )it JBI.Drj a Imsln-I. Tlu" Walaiioi- still tliu* 
 runiaint'd al iMt^•^»^^t,, until March I Uli. IH'.I'J. at !<> |mt o«uit. |»or 
 annum, whuii it was paid in full. Find thu ittcciptH, Munh 1 tth, 
 
 10. If hicad w»Mp:h.s .M5 por o«nt. inoro than tin- thmr frf)in whi(;h 
 it iH iiiaiUs how tnu(;h httiad can Ixnthtainod fiom L'H ImuiuIh of tlour< 
 
 1 L. A rectangular pint of j^roimd is 50 d. KaiiicttTM huig hy 50 
 niot<?rH ui«li'. How many acres, otc, aio thoro in it, an '*or«'' 
 boing .'»'".>r4 Htp rods / 
 
 12. A man buys City of Vauoouvor hontls which pay 10 per cont. 
 and wliich aro to bo riMhuMiiod at par in 5 years after purchased. 
 Monuy being worth 12 perijunt., find tlu* prici' of the bonds. 
 
 13. At what price per barrel shall an agent buy tlour at 5 per 
 cent, commission stitliat, after paying 10 cents a barrel for trann- 
 
 Iiortation, it will net a profit uf 12^ perceub. when sold at Ji^7.20 a 
 )urrel ? 
 
 Exercise XXXV. 
 
 1. Stock l)ought at 10 per cent, discount pays 16 per cent, on 
 investment ; what per cent, will a broker make who buys at 12j per 
 cont. discount, and after drawing a dividend sells out at par ? 
 
 2. On IVFaich Isb, IftO.'i, W. N. Sl.anloy bought of J. O. Doyle 
 &' Co., merchandise as per invoice, $720, on 2 montlis' credit. On 
 March 7tli, W. N. Shanloy paid ^120, March 27th, !?100, and April 
 II th, $200. What is the ofpiated time for paying the balance ? 
 
 3. A gentleman invested in stock at 90 J^ in a government road 
 paying 7 per cent, annual dividends, and received yearly $455. 
 V/hat sum did he invest in the stock, brokerage being f percent. 
 
 4. A dealer had 020 lbs. cheese, and sold a part of it at 12^ 
 cents a lb., realizing therefor $5S.7o. Find his entire receipts for 
 cheese, the remainder being disposed of at $15acwt. 
 
 6. The gross cost, of a purchase is $2342, which incIudeB a 
 comunssion of $17.25 and other charges of $24.75. What is the rate 
 per cent, of commission ? 
 
 I .111 
 
 III 
 
1A8 
 
 ■XKROlBBfl IV ARITBMina 
 
 
 6. A nmn «xcli/inmM| ](\ })nrr»An of flour ut 8B.n7i • burrol for 20 
 OOrd^of woixl. Wliut vv;ii w()< (I worth |>or cord-foot 7 
 
 7. From a Iwirrol of wutor 3'. loukoil. Fitul thu weight, in Ib«. 
 aikI oxm., of tho wiitt*r riMiimniiig in tho hurrul. 
 
 8. The cost of li |M'Aoh orchattl in !(?080. Ono-ftfth of th« vhUio 
 of tho triTs in •m|iiu1 to onu ninth of thu value of tho hind. Find thu 
 viihio of tho trcits. 
 
 \). A riid n tot(nthor I ought a bnrrol of flour ; A paid 97.36 and 
 h paid $2.15. Kovv uii^ny iba. of ilour did U gut i 
 
 (3Axl.i!|xiAx2iX 
 
 10. Multiply { 
 
 ( 1^x1^x2^x31 
 
 x24 
 
 18 
 
 by- 
 
 11 
 
 3A . 
 
 I 
 
 ^„f «:. of — 1 
 
 Ji 
 
 11. How many milos doosa nmn trav«l in phxighin^', croHMwis*', u 
 Hohl 80 rods h)ng by 00 ludn widu, his ph)tigh turning un uloven- 
 inch furitiw ? 
 
 12. Sold goodn to a curtain amount on 10 pi>r ceut. commiHNion, 
 and, having nitnittod tho not profU'CiU to th«> ownor, recuivod .f.'J<).90 
 or A per cunt, for prompt payiiiout. What wan tho amount of the 
 cominisHiuu, and tho valuo of tlie guodH sold ? 
 
 13. I sold two hoiHos, recoiving for the Bocond J as much as for tho 
 first. On the first I '^ainod 10 por cent , and on the Hocond I lost 
 81^ ])er cent. ; but gained on botti $110. Find the coat price of each 
 horse. 
 
 Exercise XXXVI. 
 
 1. A speculator bought a h)t, May Ist, 1802, for fSftO, and gave 
 in paynitiut his note with interest at 7 per cent, per annum until 
 paid. On Fob. 17th, ISO.'J, ho sold the lot for $700 cunh, and re- 
 deemed his note. What did he gain 1 
 
 2. What sum would be saved per annum, if the interest on a 
 public loan of $4,000,000 were reduced fr(»ni H^ per cent, to 3 per 
 cent. ? If, in consequence, the j)rice of the stock foil from 101 to 
 95§, how tnuch would the propyl ly of the fundholders be 
 diminished ? 
 
 3. How much miist I invest in 4 per cent, stock at 82 brokera-^'e 
 h per cent, so that in tho event of the stock falling to 78, I may 
 lose (bv selling my stock) simply the income on three hundred 
 dollars worth of stock ? (Brokerage in each transaction.^ 
 
gave 
 
 until 
 
 id re- 
 
 on a 
 
 13 per 
 101 to 
 be 
 
 n-a-,'e 
 
 may 
 
 ulred 
 
 rirrii CLA81, 
 
 160 
 
 4. Find tlie uqiiAt«'d tiin*' wltuii the l>Alanco of tliu fullnwiiig 
 liMdgt't' Account bucoiuuit tliiu : - 
 
 Dr. John Si.oam. CV. 
 
 1802 
 
 
 Due. 
 
 I 
 
 «« 
 
 2 
 
 «« 
 
 3 
 
 TolULfronioldfto't. 
 
 1 2 (H) 
 
 '* AiiioNK«)HN'<)nlur 15(10 
 
 ** A. Sinclair's 
 
 10 (H) 
 
 1892 
 IJdc. 
 
 8I»yordor on him 20 00 
 
 9, '• 1.1) 
 
 13i «« Cuih on act.. 
 
 115,7C» 
 
 5. A slii|Mnoiit of goo(U U invuioud8ir){M). At what niiin Hhoiild 
 it bo insiiiMl at ^ por cunt, hu that in ciiHuof li>Ha thu Mhippur vvouUi 
 ruottvor both the invutcu price and tliu pruinimn? 
 
 (]. What 8 tht) p.ir viihiu of stock if thu diticount is f ISoO, and 
 thu ratu of diticount 13^ pur cunt. 7 
 
 7. A Houcidator Itoiight canal stock at Ho^, and sold it a^^ain at 
 102^ ri>cuivin{{ $OL.'iO an tliu nut ca.sh proccotU of tliu huIu. What 
 wan luH nut ({am, aUowin.; jf [)ur cunt. l)rokuriijju uach way ? 
 
 8. I)ivi<lu 80 into two paiLs, hucIi that ono shall bu (2^ x jj x5^ 
 X J X ij X ^ X iih) iiioro than the othur. 
 
 0. A m'ocur Hold 240 lbs. of ttsi at 80 contd a lb., using a 15- 
 ouncu wvi^l't f<*f 1^ pound. If tliu tua co.st him 50 cunta a lb. by 
 coir'>ct weight, what was hi.s g.dn on thu nalu of thu tua 1 
 
 10. A Krocur rocuivus .^11 52 for butter wci^liod on scalua th. t 
 roijjistorud 14jj ounces to thu lb. How nmny cuntfi* worth did hu 
 cheat hi.s ciistomur? 
 
 11. A spuculator sold stock at a discount of 20j per cent, and 
 made a profit of 10 [>er cent. Find the price at which hu had in- 
 vested iu thu stock. 
 
 12. On -Ian. Ist, 1803, a not(> for 8500 is drawn up, bearing in- 
 terest at pur cent, por annum until paid, aixl to bu com[)(iundud 
 whenever payments aru niadt! tlioruon. On March 15th tliu sum of 
 8210 is paid ; on August 8tli, SOli.Ol), and on Octobur 20tli, !:'122.40. 
 What sum will redeem the note on .Jan. 1st, 1804 i 
 
 13. One-fifth of A's slieep is oquid to | of B's ; ])ut A buys 00 
 slioep, and 13 increases his tloik 17 por cent, by buying 15 por cent, 
 less sheep than A. Find the value of their united tlocks (after 
 these purchases) at $5 a head all round. 
 
 Exercise XXXVII. 
 
 1. Find the face value of the note, drawn May 1st, 189.3, to 
 mature in 90 days, which discounted May 18th, at 10%, will pro- 
 duce the net caslk proceeds of $500 ? 
 
 1 
 1 
 
 i 
 
ICO 
 
 KXBKCISES IN AIUTIIMKTIC. 
 
 r'^ 
 
 n 
 
 '' hill 
 
 2. I have 210 sovortsigiis ; what weight of pure gold have T, if 
 pure gold is worHi $440 an ounce ? 
 
 3. Find thu cash halanco due on the following account, on Sept. 
 7th, 18U3, inturost (Year- IJOO days.) the rate of per cent, per 
 annum : 
 
 J.h\ Petek K. Empty. Or. 
 
 1893 
 
 
 
 $ :c. 
 
 I118!)3 
 'lApr. 10 
 
 
 $ 
 
 c. 
 
 Mar. 
 
 1 
 
 To Mdse at .'JO (hiy.s 
 
 500 00 
 
 By Cash . . 
 
 . 500 
 
 00 
 
 (( 
 
 31 
 
 " <J0 '* 
 
 200 Ot) 
 
 , " 19 
 
 (• it 
 
 . . 100 
 
 00 
 
 May 
 
 20 
 
 « i( 4i 4JQ .c 
 
 400 (K) 
 
 Sept 2 
 
 
 ..GOO 
 
 00 
 
 Aug.l 1 
 
 (i t( u 3(j a 
 
 200 00 
 
 
 
 1 
 
 
 4. A can drivr tMund -♦circular track 5 times in 42 minutes, and 
 B can drive rouii ! . 8 tihios in 70 minutes. H they start from the 
 same point togcihLi', at the same time and fhive in the same direc- 
 tion, hew ni.iny times will A drive round the track before he over- 
 takes B ? What time will it occupy / 
 
 5. Find the cost to line tlie hotloi i and sides of a rectanyular 
 cistern, 4 fr., 3 in. scjuare at the top, and 8 ft., (> i»i. deep, innide 
 measuremeutj the lead costing 32 cents a square foot. 
 
 G. A train runs at the rate of G4 Km. per hour for 35 consecutive 
 hours. Find the approrimate number of English miles the train 
 traverses. 
 
 1 1 1 
 
 7. Express in decimals: 1 1 f- .... 
 
 50 3x50» 5x505 
 
 8. Find tho value of a cubical Idock of marble whose side meas- 
 ures 6 dm , at ^24 a cubic metre. 
 
 9. A conrt-yaid is IDm., 2 M. long by 8 M. wide ; tind the cost 
 to pave it with bricks, each of wliich is 8 cm. square, if the bricks 
 cost $7-20 a thousand. 
 
 10. If oak isj^5 as heavy as water, what length must be cut off an 
 oak plank 4 dm. wide and 30 mm. thick, in order that the portion 
 cut ofr shall weigh 21 Kg., G Hg.? 
 
 11. A room is 12 M , 8 dm. long by 8 M., 4 dm. wide. How 
 much carpet 70 cm. wide, laid down lengthwise of the room, would 
 cover the floor? Find the cost of the carpet at 75 cents a M. 
 
 12. Find correctly as a mixed circulating decimal, the value of the 
 
 4 4 4 4 
 
 series : 
 
 - + 
 
 5 3x5'^ oxb'^ 7x57 
 
 13. An accountant pays $9.10 income tax on a portion of his 
 salary. VVliat is his salary if f '4 of it is exempt from taxation, and 
 .*^^ per cent, is levied on the remainder { 
 
 
fiprn CT.Asa. 
 
 161 
 
 leaa- 
 
 uost 
 kicka 
 
 pflf an 
 ktion 
 
 I How 
 
 i^ould 
 
 If the 
 
 [f his 
 I, and 
 
 Exercise XXXVIII. 
 
 1. A millor botiglit 13500 bushels wheat, unci had it insured for jj 
 of its cost at 1| per cunt. At what ])rice per hiish(;l must he sell it 
 to gain 25 per cent., the prouiium paid for insurance being $112.50? 
 
 2. Exi>ross accurately, in decimals, the value of the series; 
 1111 
 
 + + . . . 
 
 4 3-43 5-4» 7x47 
 
 3. A square plot of land, containing 1 Da., 6 A., is covered with 
 wood to the depth of 2 INI. Find the value of the wood at 30 cents 
 a " stere." 
 
 4. Divide $300 amongst A, B and C, so that A A's = J B's = | C's. 
 
 5. Find the capacity of a cistern 3 M. , 3 dm. long, 8 dm. wide 
 and 5 dm., 5 cm. deep ; and also the weight of water it will contain. 
 
 6. Out of a pile of wood, 8 Dm. long G Dm., 5 M. wide and 8M. 
 high, a man reserved 35,000,O!)0 cu. dm. and sold the rest at 37^ 
 cents a store. What diil lie receive ? 
 
 7. If gold is 19*307 times as heavy as water, what is the 
 weight of a bar of gold 4 cm. long, 1 cm., 5 mm. wide and 5 mm. 
 thick i 
 
 8. If mercury is 13*6 as heavy as water, what is the weight of 6 
 Litres of the metal ? 
 
 9. What Rules in Arithmetic would the adoption of the Metric 
 System simplify ? 
 
 Examine the connection or relation between the units of measure 
 (capacity or volnme) and of loeight in the Metric System. 
 
 10. Find the L.C.M. of 5^, 41^^, 4i and l\h. 
 
 11. Find the compound interest and amount of $250 for 3 years 
 at 6 per cent., interest, to be compounded annually. 
 
 12. Find the greatest number which will divide 941 and 1001, and 
 leave respectively 21 and 12 as remainders. 
 
 13. How much stock at 97^ can be purchased by investing the 
 cash proceeds of $1950 of another kind of stock sold at 78 ? 
 
 METRIC SYSTEM. 
 
 The Metric System of Measurement is a decimal system which 
 has for its basis a unit, railed the ^^ metre" (me'ter). 
 
 The metre (=39 37079 in.) is the ten-millionth part of the dis- 
 tance from either pole to the equator, as measured along a meridian. 
 
 I't !; 
 
162 
 
 tXBRCISES IN ARITHMKTIC. 
 
 For the better understanding of the Metric System let u« com- 
 pare it (as far as the ni»asure is concerned) with the Decimal 
 System of Notation. 
 
 DECIMAL 8Y8TEftI OP NOTATION. 
 
 ad 
 -§ 
 
 •• 52 5 o 2 0) 
 
 
 4J ^j -M -«■? ;-! — c/: 
 t- «0 U5 -^ CO on ^ 
 
 ^1 r ^ 
 
 Integral v)rd(.TS. 
 
 (Ascending 
 
 Powers). 
 
 i 
 
 < 
 
 
 I 
 
 • fyi -- ^ -U • 
 
 j3 -^ c« ^ J, 5 ■" 
 
 r^ TS S -TJ ^ J3 
 
 . ^ = o jj ti :^ „r 
 
 •S S i c === ;3^ 
 .^ ^ 5 *j ffl a ^ 
 
 « '^ 't; ^ -r: .c -:3 
 
 ■K M M -*-i 4-) -^ -<J 
 
 -^ (M CO -^ iO C l>- 
 -< 
 
 Docinial Ordei'S. 
 (Descending 
 
 Powers). 
 
 MBTiilC SYSTEM OF ME.VSURKIMENT. 
 
 (As to Length). 
 
 ll 
 
 jS iS iS 4§ .-« 
 •S-a'3'3 2 
 
 gj SMWPS 
 
 .» 
 
 I 
 
 •xs -iJ ;-i C oQ 
 
 lO "Tj* CO <M tH 
 
 o 
 
 f— I 
 
 • ^^ 
 
 u 
 
 Ascending Powers Descending Powers 
 
 of ten. of ten. 
 
 Integral Multiples. Decimal Parts, 
 
 TENS. 
 
 TENTHS. 
 
FIFTU CLASS. 
 
 Tablb. 
 
 163 
 
 1000000 metres— 100000 Dekamotres-^ 10000 Hectometres— 1000 
 Kil()inetres=100 ]Mvriiinietres=-l Megametre. 
 10000 metre3=- 1000 Dekametres^lOO Hectomutres=10 Kilo- 
 int'tres=— 1 INIyriamet iv. 
 1000 metres=100l)ekfitnetres^=10 lloctometrea— 1 Kilometre. 
 100 metres=10 Dekamotres--l liuctometre. 
 10 metros=l Dokametre. 
 1 Metkb. 
 
 "1 metre =1 decimetre. 
 •01 metre=-'l decimetre— 1 centimetre. 
 •001 metro='01 decimetre =.1 coniimetre^^l millimetre. 
 .000001 metre=^00001decimetro-=-0001 cuntimetre=C01 milli- 
 metre=l micrometre. 
 
 In the Decimal Notation, commoncing with the decimal point 
 (which separates the inteijers from tlu; decimals or the whole rmmbers 
 from the fractio'iud parts) we sue that tlio inte'iral orders aio enum- 
 erated to the left, and the dcc'nixd orders to the right of the 2ioi')if ; 
 that the first integral order to the left of the units' phice is^en.s, and 
 that the first decimal order to the right of the units' phice is tenths, 
 etc. 
 
 Now, as far as the iiie.isiirement of length is concerned, the same 
 is true of the Metric System. 
 
 It will be observed that, for the ascending powers or multiples 
 Greek prefixes are used, and they are written with capitals : 
 
 Deka — = 10 times the Unit. 
 Hecto -=100 
 Kilo— =1000 
 Myria --=10000 
 Mega— ==1000000 *' 
 
 It will be observed also, that for the descending powers or deci- 
 MAT. PARTS, Latin prefixes are used, and these are written with smo// 
 
 letters : 
 
 deci — — tV of the Unit. 
 centi- =T^ " 
 milli — =TiTTnj 
 
 (( 
 
 <( 
 
 (> 
 
 (( 
 
 (i 
 
 it 
 
 (t 
 
 {< 
 
 <( 
 
 (( 
 
 (i 
 
 (k 
 
 (i 
 
 micro — =TTruhmiT5 
 
 n 
 
 
 ■' 
 
 The Primary Units op Mbasurbmbnt. 
 
 MBASUBBMENT. 
 
 Iiength. 
 
 PRIME UNIT. 
 
 "Metre." 
 
 WHERE USED. 
 
 Distances, lengths, 
 dry-goods, etc. 
 
I' 
 
 164 
 
 BXBBOISKS IN AklTUMEIlC. 
 
 Tablb. 
 
 (Linear.) 
 100 micrometHrs (una.) = 1 millitnetro (mm.) 
 
 10 iiiillirDotres 
 10 centimetres 
 10 deciinotios 
 10 Metres 
 10 Dekaiiietres 
 10 Hectometres 
 10 Kilometres 
 1(K) Myriametres 
 
 = 1 centimetre (cm.) 
 = 1 decimetrt' (dm.) 
 — 1 Metkk (M.) 
 = 1 Dekaiiietro (Dm.) 
 = 1 llt'ctoinetre (Hm). 
 ^ 1 Kilometre (Km.) 
 = 1 Myriametre (Mm.) 
 = 1 Megamotre (Mgm.) 
 
 ^ r Very short lengths.— decimetres, centimetres, nullimotres, etc. 
 Short distances, —metre, etc. 
 
 « 
 a 
 
 Long distuncea. — Kilometre, etc. 
 
 mkasurement. 
 Akba. 
 
 PRIMK UNIT. 
 
 Square Metre. 
 
 WHERE USED. 
 
 Floors, ceilings, 
 walls, carpets, etc. 
 
 Table. 
 
 (Ordinary Surfaces.) 
 
 100 sq. centimetres (sq. ?m.) = 1 sq. decimetre (sq. dm.) 
 100 sq. decimetres (sq. dm.) = 1 sq. metre{aq. m.) 
 
 For f Ordinary areas. — sq. metres, sq. decimetres, sq. centi- 
 Measuring "J metres, etc. 
 
 heasukembnt. 
 Abea. 
 
 PRIME UNIT. 
 
 " Are " (=Sq. Dekametre). 
 
 Table. 
 
 (Land.) 
 
 10 milliares (ma.) == 1 centia.."^ (ra.) 
 10 ce'itiares = 1 deciare (da.) 
 
 10 deciare =1 *'Are"(A.) 
 
 10 Ares =1 Dekare(Da.) 
 
 10 Dekares —1 Hectare (Ha.) 
 
 WHERK USED. 
 
 Farms, town- 
 ships, etc. 
 
 For 
 Measuring 
 
 measurfment. 
 Volume, 
 
 { 
 
 Land — Dekares, Hectares, etc. 
 
 PRIME UNIT. 
 
 Cubic Metre. 
 
 WHERE USED. 
 
 Bricks, blocks of 
 wood, stone, etc. 
 

 FIFTH CLASS. 
 
 165 
 
 Table. 
 
 (Ordinary Solids). 
 
 1000 cu. milliiMotres (cu. mm.) — 1 cu centimetro. 
 
 1000 cu. cotitiinetros — 1 cu. decimetre (cu. dra.) 
 
 1000 cu. decimetre.s = 1 Cu. Mi:tuk (Cu. i^F.) 
 
 For / C)rdiuary solida.- -Cub. Mecre.'i, cub. decimotrea, cub. 
 iMcMuring \ Centimetres, etc. 
 
 PRIME UNIT. WnKRK USED. 
 
 " Stere " (Cubic Metre). Wood, excavations, 
 
 MEASURKMKNT. 
 VOLUMK. 
 
 gravel, etc. 
 
 Table. 
 
 (Oreator Solids). 
 
 10 oentisteros (cs.) = 1 decistere (ds.) 
 10 decisterea = 1 Steue (S.) 
 
 10 Sterea = 1 Dekastere (Da.) 
 
 10 Dekasterea = 1 Hectoatere (Ha.) 
 
 10 Hectosterca =^ 1 Kilo.stere (Ka.) 
 
 For 
 
 Measuring 
 
 mbasure»ibkt, 
 Capacity. 
 
 PRIME UNIT. 
 
 " Litre " (cubic decimetre). 
 
 Table. 
 
 WHERE USKD. 
 
 Dry substances, aa 
 grain, fruit, vegeta- 
 bles, etc ; Liquids, 
 aa water, wine, eto. 
 
 60 
 
 B 
 
 S 
 
 10 centilitrea (cl.) = 1 decilitre (dl.) 
 10- decilitres — 1 1 Litre (L.) 
 
 10 Litres — 1 Dekalitre (Dl.) 
 
 10 Dekalitres — 1 Hectolitre (HL) 
 
 10 Hectolitres =- 1 Kilolitre (Kl) 
 
 = 1 stere. 
 
 Large quantities. — Dekalitres, Hectolitres, eto. 
 
 Moderate quantities.— Litre. 
 
 Small quantities. — decilitres, centilitres, etc. 
 
 measurement. prime unit. where used. 
 
 Weight (or Mass). "Gramme," (cub. centimetre of Tea, Sugar, 
 
 distilled water at 4° Centigrade). Hay, etc. 
 
 r 
 
 { Greater SolWs,»» woo,., eto, -Decastores.Hecto,tere,.eta \ 
 
 M 
 
166 
 
 KXfinCISEK IN AKlTHMSTia 
 
 Tabu. 
 
 10 milligrammes (Mg.) = 1 centigramme (eg.) 
 
 10 coutignunmos 
 
 10 decigriviuuies 
 
 10 Graiiimos 
 
 10 Dokiij^mmincs 
 
 10 Iloctognvinmos 
 
 10 Kilu^numiies 
 
 = I dccigmmmo (dg.) 
 — 1 Gkammb (O.) 
 = 1 Doki' ramme (Dg.) 
 = 1 Hootogrumme (Ilg.) 
 = 1 KilogruHimo (Kg.) 
 = 1 Myriugminmo (Mg.) 
 
 c 
 
 ti fLnrgo Quantities. — Tonneau (Ton.) or Millier (Mil.)=1000 Kg. 
 I I Quintal (Q) =100 Kg. 
 
 1;' j Moderate Quantities. — Kiiograniinea, Htjctogramines. 
 P [.Small Quuntitiua. — gramnioii, decigrammes, centigrammes, etc. 
 
 Since the Mectric System is a decimal system, moving the decimal 
 POINT to tlio rUjht MULTii'LKS by ten, and moving it to tlie left^ 
 DIVIDES by ten ; henco to do reduction deicending or ascendi)ig, we 
 simply move tlie decimal point to the H<jht or to the leftt as 
 required. 
 
 Equivalents. 
 
 1 Metre 
 1 centimetre 
 I Kilometre 
 1 Hectare 
 1 litre 
 1 store 
 
 1 Kilogramme 
 1 tonneau 
 
 ^Approximate). 
 
 = 39-37079 inches. 
 
 = '3937 + inches = f of an inch, nearly. 
 
 = 1093 033+ yards = | of a mile, nearly. 
 
 = 11900-3326 + 8q. yards = 2^ acres, nearly. 
 
 = 1-7607 + pints = 1 quart, nearly. 
 
 = 35 :{10+ cubic feet = ^ of a cord, nearly. 
 
 = 2 -2046 + lbs. = 2 J lbs., nearly. 
 
 = 2204 + lbs. ==: 2200 lbs., nearly. 
 
 tl 
 
 Coinage, Etc. 
 
 English Standard gold is f| pure. 
 English Standard silver is f^ pure. 
 Canadian Standard silver is f J pure. 
 American Standard gold or silver is ^ purs. 
 
 FoRMULiE IN Mensuration. 
 Area of a Circle=-^c. x ^d. = irT^, 
 Circumference of a Circle=- ir 4. 
 
rly. 
 
 ■ly. 
 
 FIFTH CLASS. 
 
 167 
 
 Area of a Triangle=^ base x the altitude or perpendioular 
 height, or ^/8(8-x)(8-y)(»-«). 
 
 ='K)- 
 
 Area of an Ellipse 
 
 Convex Surface of a Spliero=n'd'=o. x d.— 4 times the area of a 
 circle of the same diameter. 
 
 Volume of a Sphere— d^ x J tt =Convex Surface multiplied by ^ d. 
 
 Convex Surface of a Cone— icircumferonce of base x slant height. 
 
 Surface of a Cone— Convex Surface -»■ Area of Base. 
 
 Volume of a Cone=Area of Base x | Altitude, or Perpendicu- 
 lar Height. 
 
 Volume of a Pyramid of any number of sides=Are& of Base x ^ 
 Altitude (same as that uf a Cone). 
 
 Volume of Frustum of Cone — difference between Volume of 
 Complete Cone, and Volume of the Part Required to complete it. 
 
 N.B.,^at*c.— circumference ; d.=diameter ; ir— 3f ; r.— radius ; 
 >•"" i perimeter ; x. y. and z.^respectivti sides of any triangle ; a.= 
 major axis; b. •^minor axis. 
 
 il^ 
 
 I 
 
 
168 
 
 IXEHCIHEfl TN AinTIIMKTIO. 
 
 Exercise XXXIX. 
 
 1. A man incroaHed liis fjinn 20'/ in wize, and found that ho had 
 then 7H(> Hires. How many ucntu did h»( mid to iH 
 
 2. If th(! fraction § Iiavu It Huhtracted from each of itH turm8, by 
 how much )>ur cunt, in tho fraction incrcancd or diminished ? 
 
 3. If ^lL'..'«)4(;J is the interest on .<iH4.75 for .*{] yoarH, at what 
 rate per cent, per annum iy it h>:uie(l i 
 
 4. How mu'i» h ;lnios ^ 
 
 
 1 
 
 6. A chirk, w icei<v'<d ^JJ^o a year, had Ills salary raised 
 40%. What did ho recoiv*. . on / 
 
 6. A and B enter into partnership and invest capital in the 
 ratio (»f 2^ to JJ. After 7 ui(»nths A withdraws '^ of his capital and 
 B withdraws .^ of his. At the end of tho year they tind ihey have 
 gained ^8850. Find each man's gain. 
 
 7. A man in 5 days duf^ 100 busliels of potatoes for 15 per cent, 
 of them, and sold his share at 40 cents a ojishel. Find his daily 
 wages. 
 
 8. How m.my shares of .i?100 each can ho purchased with 3^210 
 cash, in the Northern Gas Company's stock at 105, brokerage being 
 
 9. Reduce $'221. 55i to £. s. d.. Sterling. 
 
 10. A merchant marks an article ^1.92, but throws ofri2^% for 
 cash. If his profit is still 40%, find the cost price of the article. 
 
 11. A dry article was exp(»se<l to damp air and having absorbed 
 10 ounces of water it then weighed 10 lbs. What per cent, of its 
 weight of water did it absorb ? 
 
 12. If I buy a 6 per cent. City Bond at 80, what is my rate of 
 income ? 
 
 13. By commercial discount of 8% a person would receive $G0.48 
 less than the nominal value of a note drawn payable rno year hence. 
 If true discount only were deducted from tho face value of the note, 
 what should the person receive for it ? 
 
 Exercise XL. 
 
 1. A and B together have $2700 ; but A spends | of his money, 
 and B spends ^ ( f his, after which they find that they, together, hav© 
 saved $000. How much money had each at first ? 
 
FIFTU CLASS. 
 
 169 
 
 ite of 
 
 loney, 
 k have 
 
 2. I rocoived a \*\ivso uf £177, 3 Hhillings, Sterling, h(»v much 
 ilid I riM'rivtt ill CuniKliiiM Ciirrmoy ? 
 
 [\. I rt'ri'ivi'd n 5" „ dividend «im K.ulway Stock, and iiiuiicdiatoly 
 invi'stiil \\\v nminy in tlio .hjuiio stuik at 7i">, after wliiili I found 
 tliut I licld •'ijdL'CXH) in tliu Haid btuuk. What was thu ani«>unt of my 
 divi<U)nd { 
 
 4. An av'«'nt hmr^rht a sot of fnrnituro, thu cataloj^uti pricro of 
 which WHS Jr'HO, sill) jffj t(» throo Hiifci-ssivu disi;(»iints of 2 »°/o, 10'/^, 
 and 5/ i>tl thi! eatalo'^iu- piico. lit) thon sold thu 8ut for )Bl»*J.U4 
 cash Kind his gain por inint. 
 
 6. Chani,'o (a) '«525 ; {!>} '875 ; and (c) 15)2 into uquivaleiit vulgur 
 fractions in their linwd tcniiH. 
 
 6. A bin, in a mill, is 20 ft. ion',', 1«» ft, wid' >i„ ' ^< ft docp, ami 
 it is filhid with wheat at .*>(> cents a hiishol. V ,ia the value of 
 the wheat I 
 
 7. A man jiaid A .', of his money, R I o' /', , n\ C ^ of it, and 
 liad lift )i<2.<)r). How much money hud \\v a^ iU < 
 
 8. A and B. two hoys, have ropes fast" I »■» the same stake. 
 A'« rope ! 14 ft. hcig and lis is .'].'» ft loi. ,. They both make a 
 circuit around the stake, keepin;^ their ropes tight. How many 
 yards does H go farther than A / 
 
 *.). (a) What time after i\ o'clock will (lie hands be opposite? 
 (/>) When will tho minute hand be 222 degrees aln;ad of the hour 
 hand { 
 
 10. What time after \ ii (('clock will tlie minute hand bo 9 niiuute- 
 apaces aliead of the hour hand ? 
 
 11. Ileduce (a) '()2.5 of a bushel to gallons, pecks, etc.; (6) 575 of 
 a week to days, hours, etc. 
 
 12. At what rate would )?t)50 produce $27'^ interest in G years V 
 
 13. A merchant sells an overcoat for $18 at 20^/^ advance on the 
 cost ; but the co.st price is 5 of the marked jirico. At this rate, 
 what would be the value of a case of three dozen overcoats at the 
 marked price ? 
 
 Exercise XLI. 
 
 1. Divide 52 lbs. of tea into three parcels, which shall be to one 
 another as the numbers ^, ^ and 1^. 
 
 2. The L.C.M. of two numbers is 1430 and their H.C.F. is 65 ; 
 find all the pairs of numbers which will fulfil tho conditions of the 
 (question. 
 
 
 I '1 
 
170 
 
 IZEBOrSBfl T?V ARITIIMBTia 
 
 y' 
 
 % 
 
 i4 
 
 1 ,|i 
 J 
 
 3. Simplify : 2f - 6 J of ^^ - 1| j + 58//,. 
 
 4. Tho .Hum of thn woi^litn of two hiu'Va of ^riiin in 410 lbs. and 
 thu dijjaencv. in 90 llm. Find thu ^vt•i^llt of each Murk. 
 
 D. (a) Ndiiiu thu two kinds of friictions and tliu Hub-diviHionH cf 
 t-aoli. 
 
 (6) Simplify : (D l-\-n \ {ii) U - I Ti i v"0 i of ^ ; 
 (iv)^ ; (v) 025 4- •138+ '20. 
 
 (c) Clttssifv fully HH HtuhMl in (a) Mh> various fniction.d oxpres- 
 Hion.s to;;(!tli«.tr Willi tliu tivo fractiuntd ixhuIlh olitainud. 
 
 (5. Whon liinil)t*r is |tl2.5() a tlimiHind Munaii' fi-ttt. and posts aro 
 worth !.'{ flints cacli, tinU tin- total cost of Imildin'^' a i loHcly Ixiuidt'd 
 uuard 7 if'^t high tor 21 rods aloii^ an fUil)ankniont, inch linnhur 
 bt'iMi,' us»'d, tho posts being set 4 fuut apart from contro to uuntre, 
 and labor and tithur oxpunsun buing i^7-'i5. 
 
 7. \N hat is tho lapaoity, in barrels, of tho snuftlcst tank that can 
 bo lillod ill an oxact nnmlior of mimitos l»_v f((cfi or hotli of two pipos, 
 eaoh of which rospectivtdy oinptios .»() and tJ.'J gaUouis of wator [»or 
 niinuto/ iJoth boing oponod, in what tinn' would tho tank li(( tillod? 
 
 H. Bought 75 shoop at )ii(2.()8 por lioad, and 45 others at .^2.20 
 por head. Sold tho wiiolo lot at .'::<.'1.25 por luail ; lind niy gain poi* 
 cent. 
 
 9, If a bag of silver containing }!i<l42 is made up of 25-coiit and 
 lO-cont pieces, thoro being 440 more lO-oeiit |>ii'Cos than 25 cent 
 pieces, how many aro thoro of each kind in tho liag ^ 
 
 10. If tho sum of 5 times tho larger and 7 times the smaller of 
 two numbers is 1442, and the <litForence between the nundjors is 
 70, what aro tho numbers ? 
 
 11. Find tho cash value of 50 shares of $10U each of mining stock 
 at H)0^, brokerage being J'Vo* 
 
 12. Divide $240 among A, B and C, so that A may have $140 
 more than.B, and twice as much as C. 
 
 13. Ice is 1KV7„ jw heavy as water, and lOM t(»ns were packed into 
 an ice-house 12 feet wide and 8 foot high. How miinv foot long 
 was it f 
 
and 
 cunt 
 
 ST. 
 
 r(jck 
 
 $«140 
 
 il into 
 li.n;^/ 
 
 l^imi CliAKl. 
 
 Exercise XLII. 
 
 171 
 
 I. TIki hiiiu (»f two niinihrrrt in .*ir>875, nn<l thoir difToronce it 
 uq'uil to <( of till) ({rcHt(>i' hui iIkt. N\ lint tiw tliu nuin^'irH / 
 
 'J. Till' intcrcMt on )!!ill()i) lot- on«) iliiv whh 2r> " nts ; find thtt 
 ruto pur cunt. |i*>i- untiiini ut wliiili it whm lutmrd. (N tut .'{I'm days.) 
 
 3. A cania^u diisf, 4 roil.s vvidu and having an ai'«>a of .'KifHi 
 mpiaiit rods, runs roiuid a circular graMtt plot, find tiiu dianiulur 
 uf tint plot. 
 
 4. Siiow that i-J-!l'«ixi| l\. 
 
 6. TIhnio Workman, A, H ami C, earning? tlio «amn daily wngon, 
 spend ri'HpuctiviJy :i, ^ i.:id ,^ <>f tlu-ir dady »)arnin.;H. I* I In; daily 
 wag«!H of a woilxinan liu ^!(. lo, what Huni of nionoy will they all 
 thr»)0 HAVu in a yt-ar'H time (5*_* wocks), no tiint' ht-inj; loHt i 
 
 0. Find thu nuinlHr which is hh much pur cunt, ahove .'10 an it i:4 
 per cunt, fft-lotv oO. What pur cunt. iH it / 
 
 7. An a^unt rucuivud !?.'10() for sullinj,' land at ^18.75 ui\ acru on 
 a connuiH.sion of 2h /^. Find thu nund)ur of acrus uoM. 
 
 8. Find the siniplu inturest on iBlii8r).44 fo.' 6 yuars at 5'/^ pur 
 annum. 
 
 9. A j)uhlic j^anlun in the form of a circle, contains 20;U) acrus. 
 It has ornamental trues planted II fuot apart around its circum- 
 ference. How many truuH aru thc^e? 
 
 10. A bought IVh note (drawing no interest), B allowinjj liim 207, 
 off thu face value. What per cent, did A realize on his investment? 
 
 11. If lemons cost 81 for 30, how many dozen must 1 handle for 
 $30 to gain 25'7o? 
 
 12. Simplify: ^x H-H of H + ^Jj. 
 
 13. A boy took 0000 steps in g'>ing a distance of SJJ miles. 
 Find the average length of his step, in feet and inches. 
 
 Exercise XLIII. 
 
 1. A's capital is to B's as 2;. 5, atid both loan their money for 
 one year at 8°/o. if the ditlenMico in the amount f)f interest received 
 is $24, find each man's capital. 
 
 2. A box, without a lid, is (V 5" lon^j;, 4' 2" wide, and .3' 3" deep 
 (extoDial measurement), (a) Ilow many square feet of inch lumber 
 does it curtain i (b) How many cubic feet and inches of material 
 are there in it ? 
 
 I 
 
 i 
 
 ■ 
 
 ! 
 
 11 
 
 'i 
 
 III 
 
 n 
 
172 
 
 f.XKnrtnr.n iw AhiTiiMrTir 
 
 t\. A i?if\n invpHtu i|4C7ft in tin- 4 piT mitH nr Oft, i\nr\ nt the onH 
 f»f the yi'ur lio ncIU imii ut MO, Hit<| inviNtM liulf tin* |iii»i'ih«U in tliu 
 IW |)(<i' i;u*itN ut Hi and tliu nrlii r liiilf ill tint l( \tvr wuIh ni MM. 
 Find till* i!liai)v;i< in Iiim yuarly iiiooniu. 
 
 •1. A f/ink II lilt lnnj< and 7 f«'t»f wido I'lmtftinH I.'IHL'I |iintH of 
 ^ati<r wlicii lilird til tlui tiip. (iivi>n tlmt a pint IidMh 28 87i'> luliic 
 inclu'N of wntor, how dci p is ilui tank / 
 
 6. lt(Mii{lit l)ittl«M- and Nuld I of it at a I^nm of L'O'/ . How niui'li 
 per cunt, must I now iidvaiK'i* my sullinu \nuv to ^ain 2r> / on tlio 
 wlioli) tranNiK^tion / 
 
 <i. A ran dii a pii'(n> nf wiifk in 7^ dayM wlirii It InlpN him 4^ 
 •hiyn, and H r.\i\ do tho woiU in 7 pi dayn whin A JH'IpM hnu lA davH. 
 How lori|{ would it tako A and It woikin;{ tiv^fthii to do the wmk I 
 
 7. If 'I Idock of toilut Hitap .'( inchiM lon^, "J inchi'H wido and H 
 im-hes thick wim^Iih *.) onticuH liiid iH wmih ^l.iio, what jh tho 
 valnu of a pyramidal <-aki' wIiohi- altitiidt* \h '24 inchuH and wIioho 
 basi) ia a uirclu thu diamt>ti-r of which \n It inchcM i 
 
 8. A luiB cloth m»irkcd at 8l.<»r» a yaid, which is lt>-J"/_, ahovo tho 
 coHt pricu. Find ilm «'i»Ht prii-c of 70 yaids nt that cloth. 
 
 1>. Simplify : 1 17 (ij 4- (5.\ - r'2')) x fT } +«• 
 
 10. Divide tho square of OL'o hy tlu) I'uhf of (Mil!. 
 
 11. From 12*6 take (;-227, ivnd to thu dilh-rcncc add fiH. 
 
 12. A .s(|uai'o plot, 40 yards to a Hide. Iwih 8 tlowcr hcds, each 
 18 ft. hy 10 ft., and one circidar portion 21 yani.s in diameter f^r a 
 fountain, tho roMt hoin^ j,'rav«dlcd. Find tho portion of the plot 
 gravelled, in ki|. yds., h<|. ft. and s<|. inches. 
 
 13. Express, explicitly, 4121 (a) in the denary scale, and (6) in 
 tho odenary sailo. 
 
 Exercise XLIV. 
 
 1. How many miles per hour does a train run, wlieii it traverses 
 821 yards 1 foot per minute ? 
 
 2. Divide loO into two such parts that 4 times (me part .shall lie 
 equal to 71 times the other. 
 
 3. If 8 per cent, of A's money cfiuahs 5J^"'/„ of B's, and botli 
 together have $5400, how much momy has li more than A / 
 
 4. Find the value of 
 
KUTii n.hHH 
 
 \::\ 
 
 civcli 
 
 plot 
 
 iTRoa 
 
 !l 
 
 llhu 
 both 
 
 ft. Fiti'l tho totnl coiif of 24A Hxt. of hnrt*v nr ^ contM a himhu), 
 8ft5 Um. «>f pt^iiHit Ht 70 cuiitM u btiHhul, hikI 1>17 IbN. oxn, of ryu nt 
 bU oi>nt!4 a liiiitliul. 
 
 A. A iliNuoiiiit of 20'^/^ uil tliu liNl pric*i« of a 840 tiiiuiil<iliii, utul 
 5**/^ oirtliikt ui^.iiii, in ui|iiivitlitiit to wliut iiiii^lu mt<t of WiHOMiiit / 
 
 7. A Rluttt ClNtoril (Witllollt A lltl) IH I fditt .'{ illi'llfM loii^, i fuut 
 Midi), Ullll *) ffUt U illl'llCH «l()l*p (olltsillu IIIUHMIIIlMlirllt). It iH 
 tilli.'il V\itll WiitiT, l< iml tiki) N\ri;l|t of till) I'iMtiTII UIhI tll«< lolitiiilli'il 
 
 uHtor, •{ivi'ii tliiit tlic Nliito itt 1^ tiiclii!M thick, uiul Hint nlutu wui;;hii 
 IW \)>H to l\w i!iihiu foot. 
 
 8. A ciiii ilo II job of work in ^ of u day. mu\ It in ;\ of a day. 
 If thoy both work to'^oHior to ooni|ilutu thu job, what in ouch iiiiui'rt 
 MJiaro of t^o.L'O paid for it / 
 
 U. Simplify : 
 
 (/») 4 : (MIH'J"), j^iviiiu the ri'Huit as a roptiatiii)^ dociinal. 
 
 10. Thu bano «)f an isoHonioH tri.in'^h) in *J0 ft'ot, and t»aoh of the 
 oijnal rti<h'H is L'O fm<t. What is tin) ahitn«h' of the trianylo ? 
 
 11. What is the valim of a Iioiino, if tlu) inHUiaiu'c prtMiiiuiii of 
 8*/o "" H "^ '•'* vabn>, iiiolntliiij^ ^l for the policy, amounts to l^Jif)? 
 
 12. If '2H lbs. of tea at 'J/ii bo luixt'd with 52 lbs. at :{/4 Storlinjj(, 
 how many dollais and cuiitN, Canadian monuy, would 72 Ib.s. of thu 
 niixturo bo worth '{ 
 
 in. How many planks H\\ feet lonir by 15 inuhus widu will be 
 required to tloor a building 50 foet x 3.'J foot/ 
 
 Exercise XLV. 
 
 1. Simplify : 
 
 2. At 2.") cents a bushol, a bin of oats, 08 feet lonjj, 8 foot wide, 
 nnd ,' feet doop, coHt.s $(510.00, How many lbs. of oats wore 
 reckon^ d to the cubic foot ? 
 
 M. .\ 'A;mk sidewalk IH feet wide and 2 incht>s thick is to ho 
 ))uilt round a i»|(»ck of land (i chains s(|iiare, tlu' walk to Ju' no part 
 of the block. \\ hat is the co.st to l>uild it, when huabor Ks $!20 m 
 thousand s([uaro feet? 
 
 \ The sum of two nund)crs is 25.1.^ and their flifi'jrence is 240*3, 
 Find till! (]uotieut arising from tho division of the Luger by 3 tiuiej 
 the smaller. 
 
 !l. 
 
 
 * ••■^' 
 
 4. 
 
174 
 
 tiXKHClSES tV ARtrnMKTtrt. 
 
 i\ 
 
 6. A broker charcfos ^"/^ for investing money, and receives $70 
 for a certain transjiction. Find the sum invested. 
 
 6. Which is the more pruHhibhi investment 5 per cent, bonds 
 at ^-Z'^/o disi'ount, or 8 per cent, bonds at 20"/^, prttmi\im? 
 
 \^hat would I gain on $1200 invested in the better concern? 
 
 7. How much must a merchant murk cloth which cost him 
 80 cents a yard, so that he may throw oil" 20 per cent, and still be 
 selling at cost ? 
 
 8. Bought a house and lot in a city for #7500 ; kept my pro- 
 perty for 5 years at an annual expense of $2i\5 ; sold out at a profit 
 of 20''/o ov my entire outlay. What was my selling price ? 
 
 9. Two upright posts, set 32 feet apart, stand respectively 
 33 ft. and 9 ft. above the suifaee of the ground. ^^'hat length 
 of rope, stretcluid tightly, would be recjuirecl to re.ich from the top 
 of one post to the top of the other ? 
 
 10. A commission merchant sold the following on 2^7o com- 
 mission : — 
 
 2800 lbs. wheat at IM) cents a bushel, 
 500 boxes cheese of 70 lbs. each at 8 cents a lb., 
 005 lbs. butter at '.O cents a lb., 
 90 bags of potatoes at 55 cents a b;ig, 
 35 busiiels timothy seed at $2.50 a bushel. 
 
 Find the amount of liis conunission. 
 
 11. A man spends 33.\% of his weekly wages, and saves $780 per 
 annum. What does he earn per week ? 
 
 12. Simplify : 
 
 13. A fruiter remitted to his agent S467.02 with which to buy 
 fruit at $2.27 a box, after deducting liis commission of 3 per cent- 
 How many boxes did the agent remit ? 
 
 Exercise XL VI. 
 
 1. A and B together have $7000, and twice A's money I's to 
 three times B's as 4; 9. How much money has each ? 
 
 2. Find the cost of flagging, with mar})le slabs, a ])lot of ground 
 20 yards long by 20 feet wide, the slabs being each 18 inches long 
 by 8 inches wide, and costing $30 a hundred. 
 
 3. A drover sold 200 cattle at $28 a head, gaining 40°/^ on ^ of 
 them, and losing the same per cent, on the others. Find his net 
 gain or loss on the entire drove. 
 
PIFTn CLASS. 
 
 176 
 
 per 
 
 s to 
 long 
 net 
 
 4. Wliat is the area, in square inches, of a circle whose diameter 
 is 3J yards ? 
 
 5. Bought 80 books for $300, nnd sold tliein at 84.20 each ; find 
 my gain per cent. 
 
 0. A can walk 4^ miles in oO minutes, and B can walk 3i miles 
 in 42 minutes 40 seconds. ITow many minutes' start should A give 
 B in 20 miles to beat him by filG yards? 
 
 7. A man received Jif878.75 for a debt on which a collector 
 levied 6°/o for his services. Find the amount of the debt. 
 
 8. Tiie cost of enclosing a rectangular farm with a fence at 75 
 cents a rod was 1^.'{75. Tho farm had 80 rods frontage and sold for 
 $3000. Find tho selling price jier acri'. 
 
 9. An agent sold a consignment of 7800 lbs. of butter at 25 
 cents a lb. on a commission (jf 4 percent. He paid $1!)!^ for freight 
 and storage, and invested the l)al;uice oi the proceeds in silk on a 
 commission of 5 percent Find tiie value of the silk remitted. 
 
 10. If 100 bushels of gr;iin oc -upy 128 cubic feet of space, and a 
 rectangular bin of grain lo'xS'xO' weigh i3h tons, what is the 
 weight of a bushel of that grain ? 
 
 11. If $120 be gained on .^584 in 125 days, what will bci the gain 
 on the same sum in 3()0 days at the same r.-ite ? 
 
 12. By selling goods at IfJsVo pi'olit a merchant clears $749 ; find 
 the amount of his sales. 
 
 13. I have an orchard 100 by 200 yards. The trees are set 20 
 feet apart and 20 feet from the fence which borders it. How 
 many trees are there in my orchard ? 
 
 Exercise XLVII. 
 
 1. A note the face valu^i of which is $."J20 is payable in 3 months 
 with interest at (1 per cent, per annum. It is discoinited at the 
 date thereof at 10°/^. What rate per cent per <inn\im does the dis- 
 counter realize on his money ? What ptiv cent, does he realize ? 
 
 2. What is the value of 
 
 |45h-9x5| 
 
 times 
 
 2i--16 
 
 I 93 
 
 times 35 ? 
 
 3. A and B together can mow a field in 3^ days, and A can mow 
 I of it in 6 days. In how many days can B mow f of it ? 
 
 4. A man having drawn 7^°/o of his money from the bank has 
 still a deposit of $10027 to his credit. What was his original 
 deposit ? 
 
 ! 
 
 
 I 
 
 I 
 
 M 
 
 It 
 
 i- r! 
 
II 
 
 h6 i:xi;ucKsKs in AKiTJiMirrir. 
 
 5. A sold a cRrn.'i<:;o to T5 mid r^aiucd 7^ per cent. B sold it to 
 C for 81 11.1)0, and tliorohy lest l-Vo- How much did the carriage 
 cost A / 
 
 (>. (a) Make out the following account neatly^ accurately, and in 
 commerr.vd form : — 
 
 James Ross liought from you to-day : 
 
 lOrJ 11)3. cheese 0^ 10,^ cts. a lb. 
 7} " rice (?>)24.\ " " 
 0^ " cornnKMl ("■ 10 cts. a lb. 
 •^l-'ff " prunes (" ,*ii?l fur 1*2 lbs. 
 (6) Ross paid you the cash and you threw off 10 Vg. 
 (c) Receipt the account as per data. 
 
 7. Find the anioiuit (»f a note mdde Ftiitruary 24th, 18JH, and 
 le(j(dlii due Marcli 10th, iS02, the face of which is $182.00 with 
 interest at C/q i)er annum. (Year^oOo days.) 
 
 8. A man insured 7000 barrels of app'es worth $2 a barrel for 
 ^ (.f their value at 2^°/o- -^^ ^^'^ occurring, 200 barrels were saved. 
 Find his loss. 
 
 9. A miller has 5(10 l)uslu'is of coin, 720 bushels of iieasu, and 
 815 ))ushels of rye to transjiort to his mills. What is tiie /t'((«^ num- 
 ber of the same-si/.ed sacks that will move the grain at one nutving 
 without mixing it 'i 
 
 10. A farnua- sold loads of oats, ouch weighing on the average 
 20()2r| lbs., at .'57'. cts. a bushel ; but the warehouse-man, by mis- 
 take, weighed the grain for rye, and gave the farmer a checpie for 
 the same at G3 cents a bushel. What did the farmer gain or lose 
 by the mistake? 
 
 11. Resolve 51480 and 3340200 into their prime factors, and 
 from inspection of tluse write, in prhut factors, — 
 
 (i) their L.C.M. and G. CM., 
 
 (ii) the quotient when the second number is divided by the 
 first, 
 
 (iii) the quotient when the product of both numbers is divided 
 by their L.C.M. 
 
 12. Simplify 
 
 •0 
 
 ■c, 
 
 •38 + -24 
 
 •0 + -(5 -16 - 15 
 
 13. Simplify 
 
 
 
 
 }• 
 
FIFTH CLASS. 
 
 17; 
 
 is- 
 ose 
 
 the 
 
 ed 
 
 Exerciee XLVIII. 
 
 1. A man's (3Xj»ensos are as folluwa : — Rent ^\ of iucoino, and 
 expenses of liviiii^ <>07„ of the rt'inaiiider. He Jinda that he will 
 then save ^oOO per aniiiini ; find his total income. 
 
 2. (a) If 51000 p..und8 of wheat cost ^787.50, fin<l the cost price 
 per bushel. 
 
 {!)) A mouldei" cast 84 iron discs, each 5(5 inches in diameter and 
 1^ of an inch thick. How miifii .should he ijet for tlieui at 5 cents a 
 lb., <,dven that 7 cid»ic inches of iron wi'IljIi .'> lbs. (J ounces? 
 
 3. A, li, C and D have together 1450 acres of land, and A's 
 land is to B's as 2:3. B's to C's as 2;.'}, and C's to D's as 9:10. 
 Find the size, in acres, of each man's farm. 
 
 4. A farmer sold, on tin' market, a load of oats at 28 cents a 
 b\ishel ; but the i^iviin-dtaler weighed it for barley and gave the 
 farmer a cheipie for it at 45 cents a bushel, by which the farmer was 
 ^1(..'>0 in pocket. How niany lbs. of grain had he on his waggon? 
 
 5. A music-dealer gave a discount of 8' 'I foi- cash, and a second 
 discount to teachers of L'O ' on all cash jjuiihiises. At what [)rice 
 was a book marked tor which a teacher paid J?4.(J0? 
 
 6. A and B entci' into partnership to cairy on a grocery business 
 for one year. A |>uts in .i^lOOO at the bi'ginning of the yeai', and at 
 the (Uid of () months S50J more. 11 puts in 82500 ut the beginning 
 oi the year, and withdraws $1000 at the end of the first three 
 months. At the close of the year, they find they have gained 
 |!1800. Of this, what is B's share more than A'a? 
 
 7 A retired merchant invests lioY, i>i his capital in the 5 per 
 cent, stock at 105, 20 of the re.uainder in 4 i)er cent, stock at 78, 
 and tlu! l),\lance in 'Ir, per cent, stock at 07^. His total yearly in- 
 come, thus derived, is $1575. Find his cash c;i,[)ital invested. 
 
 8. A connuission merchant sold (I00(> pounds of butter at 28 
 cents a |)ound. He remitted !jlG20, after ]taying freight $20, 
 storage $10, and deducting his commission. What rate per cent, 
 commission did he charge ? 
 
 9. Sold 140 shares railroad stock at 7-2% premium. What did I 
 receive, brokerage being |% ? 
 
 10. The sides of a rectangle are as 3:4, and its area is 972 square 
 yards ; find the length of the hiiKjad straight line which can be 
 drawn on its surface. 
 
 i 
 
 m 
 
 ill 
 
 I 
 
178 
 
 KXERC'ISES I\ AlllTQMBTIO. 
 
 11. A note is drawn up as follows : — 
 
 $1500,"o"a. Veh.schoyle, /une 1st, 1891. 
 
 Ono year after dato, T promise to pay Robert Endsleigh or 
 Order, tlio sum of fifteen hundred dollars, with interest at the rate 
 of four per cent, per annum. James Simcoe. 
 
 The fore<^oin<j; note was endorsed as follows : — 
 
 June Ith, 1802, ."^fjOl^.OO. 
 Deeeiiihcr 4th, 181)2, .^581.20. 
 June 4th, 18J).'}. ><2]0.00. 
 
 How much would lift the note on September 4th, 1894 ? 
 
 12. The length of a n-ctans^ular field, containing 13 acres, 80 
 square rods, is 2'i tinit'S its hi-eadth, and a bicyclist can ride the 
 length of a diagonal of the said field in 7«'i.l2.5 seconds. Find the 
 time it would take him to ride round the field at the same rate of 
 si)eed, 
 
 13. At what rate per cent, will $100 for 15 years amount to as 
 much as $250 for 3 years at 0% ? 
 
 Exercise XLIX. 
 
 1. A bill due 9 months lumce is discounted at 6% per annum 
 true discount and $40 is received for it. What is the face value of 
 the bill ? 
 
 2. A rect.'uigidar portion of ground, six times as long as it is 
 wide and of tlie l,ci(d [)nssible size wiiich could be plaidced with 
 planks 10, 12, or 14 feet in length and a tV>ot wide, is allotted by a 
 city for a ndlitacy pai'ade ground, {a) Find its size in acres, sq. 
 rods, etc.; aiid (h) tlie number of 14-ft. [)lanks necessary to plank it. 
 
 3. How much ready cash would buy stock at 8"^, paying an 
 annual dividend of 4 per cent., in order to realize an income of 
 $720 per annum ? 
 
 4. The weight of pure gold in a guinea is J^ffji of an ounce, and 
 ^ of the weight of a guinea is pure gold and the remainder an alloy 
 50 times less valuable. Find the value of ])ure gold per oz. 
 
 5. A grocer has teas at 45 cents a lb. and at 75 cents a lb., 
 respectively. He mixes tliem in ecpial quantities, and sells the mix- 
 ture at such a ]>rice that lie gains as much per cent, on one kind as 
 ^e Iw'ses per cent, on the other. What is his selinig price per lb.? 
 Wluio does he gain or lose per cent, at this selling price ? 
 
 G. \ man lost 5 per ' ent. hy selling 6500 bushels of wheat at 76 
 ■cencs a )ushe1 Find 'vhat total sum would have lost him nothing. 
 
riFTH CLASS. 
 
 U'J 
 
 7. If a merchant should sell a niece of cluth at $2.87j^ a yard, he 
 would gain $30.46 ; hut if he sliould sell it at $2.50 a yard, ho would 
 gain only $15.45. IIuw much would he ivcuive for his cloth at the 
 average of thostj prices ? 
 
 8. A and B, two teaohur.s in adjoining .secUons, each ongajro at 
 $400 per annum to ho paid (luartedy, with the further undorHtand- 
 ing that A is to gut an increase of $25 in his salary every three 
 mouths, while B is to gut an increase of SiOU every year. Find the 
 dijfereiice in tlioir earnings at the end of seven years, interest being 
 left out of the question. 
 
 9. After paying $12 for an overcoat, a man had $30 left. What 
 per cent, of his money did he spend ? 
 
 10. A speculator insured a cargo of 40000 bushels of corn for § of 
 its value at 1^%, and paid a i)runiium of $120. What was corn 
 valued at per busliel ? 
 
 11. A rectangular field contains (50 acres, and its length is J 20 
 rods. It is surrounded by a patii 6 ft. wide as far as the corners (»f 
 the field, and at the corners there are four S(iiiarus of which the 
 inner corner of each adjoins a respective corner of the field, the 
 path and the squares containing 4700 sciuare yards, 4 square feet. 
 Find the length of a side of one of the square corners. 
 
 12. Sold 50 geese and turkeys for $49, the geese at 80 cents and 
 the turkeys at $1.10 each. How many turkeys did I sell? 
 
 13. (a) If -257 of a farm cost $9280, wliat is the value of J ^ of it ? 
 
 (6) How many yards of satin | of a yard wide will be required 
 to line 22^ yards of velvet ^ a yard wide ? 
 
 i n 
 
 ifli 
 
 * 
 
 it. 
 
 an 
 of 
 
 lix- 
 
 as 
 b.? 
 
 76 
 U2. 
 
 Exercise L. 
 
 1. Find th« result of the series ; — 
 
 111111 
 
 + + +- 
 
 8 (5)* (5)'^ (5)* (.'i)* ([>)» ( 
 
 1 1 
 
 + . 
 
 (5)- (5)9 
 
 2. The numerators of two fractions ; .• 5 and 11, and ^ of the 
 sum of the fractions is equal to | of j^. m it are the fractions ? 
 
 3. The product of two numl)ers is 5103, and their G.C.M. is 9 ; 
 find their L. CM. 
 
 4. A farmer took a load of barley to tiie market where he sold it 
 at 60 cents a bushel; but on delivering it the warehouse-man 
 weighed it for oats and gave him a chucjue for it at 35 cents a bushel, 
 by which the farmer lo;3t $(3. What was tu> weight of his load in 
 lb3.'< 
 
 I* 
 
 1(1 
 
 \:S I 
 
 I' 
 
ISO 
 
 KXEHCISKS IN' ARITMMKTK', 
 
 ."). I. invest a cfrtdiii sum in Mmj four per cents at 80, and an equal 
 8um in the five fior cents (it '.)0. At tlie en<l of the yo.ir I rocoivo 
 my (lividi-nds ; ami uacli kiini »>f .stock liaviny risun 10% in value, I 
 ■•^ell out for cvihIi, roaliziu'^ ii ;^'uin of $1220. Find my total cash 
 investnitiit. 
 
 <}. A fruitor sold apples at 5 ct;nfs a gallon, and -.'ained <I0 per 
 uunt. At tliis rate, find the cf)Ht price? of apples per liushel. 
 
 7. What is the ^reato.st distance between any two points on tho 
 floor (»f a room 3(5 feet lont' hy 27 feet wide ? 
 
 8. If I buy ft [)er cent. Imperial Rank Stock on which tliere i.s a 
 (piaittnly dividend of i^V20, wluit does tiie stock cost me at 137^ '^ 
 
 '.>. I invest in the 4^ per cents at 75 ; what per cent, do I realizo 
 on my investment ? 
 
 10. Simplify : - 
 
 Of 
 
 of 7J 
 
 li^ 
 
 « 7 _ •{ .5 
 "2 t ''12 
 
 1^-i 
 
 +- 
 
 [^t of 4g ] 
 
 11. A can mow ^ of a field in three days, and B can mow ^ of the 
 field in the same time. Tn what time woidd ))oth working to; ether 
 
 mow "53 01 tho field ? 
 
 12. Jf jl of the cost price of an art;i' 'o is ecpial to the gain and 25 
 ])(;r cent, of 'he selling price, find the gain percent, at which the 
 article is sold. 
 
 13. The extreme point of the minute hand of a tov/or clock moves 
 5^ inches in 5 minutes. Find tlic Icngtli of the hand, L'iven that it 
 projects 1^ inches beyond the central pivot around which it moves. 
 
 I ■' 
 
 Exercise LI. 
 
 1. A wood-dealer buys wood at S3. 00 a cord, ^""ow, at what 
 price per cord must he sell it, in order to realize a profit of 15%. and 
 alh)W 10 per cent of Ills saL'S as worthless ? 
 
 2 If 90 gallons brandy, 15 gallons rye whiskey and 5 gallons 
 cider are mi.xed together, what per c(3nt. of the u)i\tuni is each 'i 
 
 3. A owes B !i?2r),30.88 tn be paid ui three eqnai payments in one 
 ye.ar, one and one-l!?ilf years, and two years, respectively, without 
 interest. Wliat ready cash payment '.should A accept, money being 
 ■worth 8 per cent, per aiinum ? 
 
 4. What principal will amount to $455.05 in 7f years at 47^ box* 
 annum, simple interest ? 
 
FIFTH CLASS. 
 
 181 
 
 6. Find thocost of ctiu^ing u dniiii 48 rods l«»ng, 3 foet doup, iij; 
 feet wide at the top, aucl 2^ feot wido at the b(>tt«»»i, at 4 cents a 
 cubic y.ir<l. 
 
 (>. At 30 coiits H Hiiuari- font, wliiit in tliu valuu '»t' a triuii>(itlar 
 jji»}(3y of Htoiif wlmst' haso is 1) fuft and vvlioHt- jierp'mlicular heiglit 
 18 7 feet '^ 
 
 7. A gontloiaaii insured a terrace of 7 houses for I of theif yaluj^ 
 at Ih^/^y payin'j; i preiuiinu of ^\47 Find the v;due <;f the ivthua. 
 
 8. What, nuist Ik- ' he f.ice <if a note fur 7''i days, which disc//fWitA<l 
 at th(} bank ul <"» / v\ill juMcUice J:5tW8 casli ? 
 
 l>. A drover luxi-ht. I,", fat eattle at *:{5.0i». ^'.',7.()i). $'47 oCf. 
 
 jp:iH.(X). }<ii).(Hi ,^10. .c' ^iU)ii $42.00, «;t2.7r), #4:125, •45.00. 
 
 ^4»j,00, .^52.00 por head, respectively. Wliaf would 60 such cattle 
 cost at the iiveruge price ? 
 
 10. If si.x. jiiou can do as nuich work as 20 boys in a given time, 
 )iow umch shr»{)id ,1 bc^v reeiive a day, if a rn.an's d.iily vii</^Qy, 
 art^ S2.40 ' 
 
 11. 'I'he ilidecenee lyetwt^en i^ of a fraction and | of the same frac- 
 tion is ,;,„ , ti;id tlu! fraerion. 
 
 12. A furnisiu;r .sold a suit of cl. i; ;s for ^.*)2 and lost thereby 
 20'^/^, ffe then sohl anoHu.-r suit for !?42 md j^aiiied as uiuch per 
 »'eiit. us lie lo.st (pU the lirst. Wlutt did boi li .suits eo.st hiui i VV'h.it 
 AVas liis enl.ir'J Jijuiii or loss ])el' '•eiil, oil tile .nab' of tlu' suits? 
 
 l.'l. A mail dTen 14'^;, ot his tb po.sit fi-oni the l)ank, and spent 
 !?70, whieli was lO'/,-, of wliat he drew out. Hov much money had 
 ho in the bank ? 
 
 Exercise LII. 
 
 1. A miller jiaid .¥21.50 U>v iivniu for choppintr ; ^ of it was 
 barley at 40 cetus a bu.diel, I of it was rye ;ir (iO ei nts a bushel, and 
 the rest corn at 50 cents a bushel. How niai+^y bushels in all did he 
 get, and how many bushels of each kind of mi\ 
 
 2. Find the avoraijie of 10 lbs. 1<» o/.s., 14 Jbs. 8 ozs , 15 lbs. 
 7 o/s. , 11 lbs. 4 ozs., a)td .'5 lbs. 2 ozs. 
 
 o. Two plac»^s on the globe, due eftst and west of e-aeh other-, 
 are 125 de^re'ds of longitude apart. \V]i,it is th*- ditie-rence in time 
 of the two [)1 ices ? 
 
 4. A nic'chant gained 20*^/0 by selling cloth at 00 cents a yard ; 
 find his gain on the sale of 1000 yard- of the <ame cloth at 75 cents 
 a yard. 
 
 
182 
 
 EXKRGISKS IM ARIIIIMKTlU. 
 
 6 If 8 houm constitute u diiy'H Mrurk, and 20 men or 36 boyi 
 cmi do a piece of work in 5 duys. how lonj< will it take 8 mon and 
 6 hoys working toj^uthor to do it '( 
 
 0. A Htoru (ind iU contoiits to^otliur are vnliiml ul $700U, and the 
 contciitH aru worth l^ tiinus liH much uh thu Htoru. Find the value 
 of ouch. 
 
 7. Find tho .siinplo interest, on i!i<438 from Jan. J 0th till April 
 6th, 181)4, at 5 per cent, [lor annum (civil yiar). 
 
 8. A nuTchant hou^'ht a rert lin numlier of pairs of fthoes at G2J 
 centH a pair, firirt- hh many ) airs of lioot.s at 75 fciifs a pair, and 
 thiri: times ;is many pairs of slippers at 25 cents a pjiir, paying for 
 ♦"ho lot ^H 1. How many pairs of each tlid he buy i 
 
 1). A tank is 22 ft. l'>n^ at the top, 20 ft. lon;^ at the bottom, 5 ft. 
 wide and ft. deep, inside measurement. How uuiny barrolH of 
 water will it h(»ld 'I 
 
 10. It takes 70 yards of 27-in(;h car|teting to cover the floor of a 
 hall 45 ft. loiij,' ; how many fet;t and inches wide is the hall? 
 
 11. A hole 'A\ inches in diameter is bored lenj^thwise throu;4h 576 
 feet oi pump-lo^. How many cubic ieut and inches )f material did 
 the auger remove ? 
 
 12. Find the marked price of a bale of i21K) yards of linen that 
 will leave a net cash price of 34 cents a yard, after two successive 
 discounts of 20°/o and 157o have been made. 
 
 l.'i. Find the equated time for tho payment of the following 
 accoinit : — 
 
 Dr. 
 
 Geouor Leeds. 
 
 Or. 
 
 fi m 
 
 1894 
 
 
 
 
 
 ' 1894 
 
 
 
 
 
 March 
 
 1 
 
 To Mdse. . . 
 
 80 
 
 00 
 
 March 
 
 15 
 
 By Cash. . . . 
 
 100 
 
 00 
 
 •^■i 
 
 7 
 
 (t (( 
 
 37 
 
 00 
 
 i i 
 
 29 
 
 (4 .( 
 
 10 
 
 00 
 
 April 
 
 6 
 
 (t it 
 
 50 
 
 00 
 
 
 
 
 
 
 May 
 
 4 
 
 4 t t • 
 
 30 
 
 00 
 
 1 
 
 1 
 
 
 
 
 
ANS\VERS. 
 
 PART II. 
 
 FOURTH AND FIFTH CLASSES. 
 
FOURTH CLASa 
 
 Exercise I, 
 
 1. (00; B$nOO; C $300. 
 
 2. 15 iniinitoa. 
 
 3. 6/, days, 
 
 4. 53 \ per cent 
 
 5. 31 Iba. 
 U $140. 
 
 7. 91.>5.62. 
 
 8. $186,000, 00. 
 
 9. 70 do/un. 
 
 10. 8(53. 
 
 11. ^ of an ounce. 
 
 12. A'o. 
 
 13. 460timoii. 
 
 Exeroise II* 
 
 1. $U750. 
 
 2. Product 518 acren, 16 rods, 3 ft. , 48 inches. Quotient 67 
 (icres, no r.Kls, 20 yds.. 1 ft., 126.^ i i id ich =^301090029 J inch wk 
 
 3. (a) 50 milfs ; (b) 31GS000 inches. 
 
 4. 207 rods, 2 yanls, 1 t. 10 inchi-s. 
 
 5. $385.'. 10. $80. 
 
 6. 2 inches. 11. $7G8. 
 
 7. $1 .05. 12. $29.(50. 
 
 8. 13. (a) $13.76 ; (6)99 times. 
 
 9. 25 per cent. 
 
 1. 660 yds. 
 
 2. 6 years, 
 
 3. $20. 
 
 '. 38 bushels 24 lbs. 
 5. $6G6 gain. 
 
 Exercise III. 
 
 6. (a) 18H ; (h) 9^. 
 
 7. 10300. 
 
 8. $.72 a owt 
 
 9. 55 days. 
 10. $2.92. 
 
 11. 31 miles, 219 rods, 4 yds., 1 f t , 3 inches. 
 
 12. 27,^, ™Jn- past VI. 
 
 13. (a) $64801088; (6) {^? }^«;; ^ ^^;} ; (c) $189.61. 
 
 [39J 
 
 l( 
 
 ■} 
 
 m 
 
 II 
 

 >.V^< 
 
 IMAGE EVALUATION 
 TEST TARGET (MT-3) 
 
 y 
 
 ^ 
 
 
 /L 
 
 
 ^ 
 
 1.0 
 
 I.I 
 
 1.25 
 
 "Si- 
 
 H; M£ 112.0 
 
 u 
 •- I- 
 
 IU& 
 
 1.4 
 
 ^ 
 
 
 
 7 
 
 /^ 
 
 Photographic 
 
 Sciences 
 Corporation 
 
 \ 
 
 iV 
 
 •s? 
 
 r^ 
 
 ^9> 
 
 V 
 
 33 WEST MAIN STREET 
 
 WEBSTER, N.Y. 14580 
 
 (716) P72-4503 
 
 
 ^ 
 
 C^ 
 
 ^^ 
 

 f 
 
 P^ 
 
 f 
 
 '■\ 
 
 
40 
 
 ANSWRBft. 
 
 1. 1 mile. 
 
 2. 80 roda. 
 a 19.60. 
 
 i, $65.60 gain. 
 d. 49 days. 
 
 6. 25 gallons. 
 
 7. 16.84. 
 
 BzerolBe IV. 
 
 8. H.O.P. 3 inches ; L.O.M. 
 
 166060. 
 0. 26 per oent. 
 
 10. 961200. 
 
 11. $620. 
 
 12. 176 feet 
 
 13. 7^ per oent. 
 
 Bzeroise V. 
 
 1. 4 lbs. 4. 46 gaUona. 
 
 2. 330 yds. 6. 4^ per cent. 
 
 3. 78| cents. 6. $192. 
 
 7. (a) 2562 cub. feet, 1088 cub. inches ; (6) 1120 sq. feet, 96 
 sq. inches. 
 
 8b 60 per cent. 
 
 9. A's $400 ; B's $700 ; O's $36a 
 
 10. 40 tons, 600 lbs. 
 
 11. 112 days. 
 
 12. 226 cords. 
 
 IS. (a) $240 ; (6) $902.40 ; (e) $96.10. 
 
 Exercise VI. 
 
 1. 23^ rain, past 6 o'clock. 
 
 2. 11. 24 o'clock, or 24 min. past 11 o'clock. 
 
 3. 16^ min. 
 
 4. (a) 21^ min. past 7 o'clock ; (6) 21^ min. to 8 o'clock ; 
 (c) 5^ min. to 8 o'clock. 
 
 6. 9^ min. to 12 o'clock. 
 
 6. 48 min. past 11 o'clock, or 12 min. to 12 o'clock. 
 
 7. 4.43/y o'clock p.m. 
 
 8. 6^ min. to 11 o'clock. 
 
 9. 24 min. 
 
 10. 43/x min. after III. 
 
 11. 18 1^8 °^^* past 4 o'clock. 
 
 12. 4 min. 
 
 13 (a) In 6 min. 12 seconds ; (6) in 16 A min.; (c) in 24 mia; 
 (d)in 32A min.; (e) 49^^ min.; (/) in 1 hour (at one o'clock): 
 (g) in 66^ minutes. 
 
ANSWERS. 
 
 Bxeroise VII. 
 
 41 
 
 1. 110. 
 
 2. (a) $4.80 ; (6) $1.00. 
 
 3. $940. 
 
 6. 8 bushels. 
 
 7. 3 acres, 106 sq. rods, 22 sq. 
 
 yds., 7 sq. ft., 72 sq. inches. 
 
 8. 79. 
 
 9. 14 days. 
 
 10. CDLIVCDXV. 
 
 11. 1000. 
 
 12. $40. 
 
 13. (a) $823.44 ; (b) $40.30. 
 
 Bxeroise VIII. 
 
 1. £2, ISsh., 4d. 
 
 2. 12 minutes to 10 o'clock, or 48 minutes past 9 o'clock. 
 
 3. 5750 pieces. jq^ $2294 
 
 4. (a) 22 feet, 6 inches ; (b) 112. 11.* 100 per cent. gain. 
 I- *2'- 12. 4320 times. 
 
 6- 385 tons. 13. (a) $85 ; r6) $1, 
 
 7. 180 bushels. 1050 g^^^ 
 
 9 Lf^''^'^' ^'^ 1008 second. 
 
 ^' *^""- 1 1200 third. 
 
 Exercise IX. 
 
 1. 320 loads. 
 
 2. 45 bushels pease. 
 
 3. $500. 
 
 4. $4.00. 
 6. $3600. 
 
 6. A $40, B $240, $360. 
 
 7. $25,620. 
 
 8. $73.50. 
 
 9. $1.75. 
 
 10. $100. 
 
 11. 35 per cent. 
 
 12. J. 
 
 13. 12^ per cent. 
 
 Exercise X. 
 
 1. 28x0x17; 2*x62x7; 22x5x3x7*. 
 
 2. 22x3«x5; 22x3x7x71; 22x32x68. 
 
 3. 2*x3x52x7; 2*x239; 22x3x5x23. 
 
 4. 2*x52xll; 2»x33 ; 23x33x62. 
 6. 2»x6x 7; 2^x5; 2x33x11x13. 
 
 6. 28x3x5; 23x32x52; 22x5*. 
 
 7. 33x5x7x11x13; 2x3x7x11x19; 2«x52x7xU. 
 
 8. 2»x6; 2»x3«x52; 22x3*x62. 
 
 H 
 
 i 
 
42 
 
 ANSWKRS. 
 
 9. 2« X 3 X 5' X 11 ; 2' x 6« x 13 ; 2« x 3 x 5* x 13. 
 
 10. 2«x3«x52; 2*x52xl3;2>x3x5*. 
 
 11. 2x6^x23; 23x3x5x47 ; 2''x5x7xl3. 
 
 12. 22x62x3x7 ; 22x3x6^x29 ; 22x6»x7. 
 
 13. 22x6x67; 2x3* x6-; 7x29=*. 
 
 Exeroise XI. 
 
 r » 
 
 Hi 
 
 I 
 
 ii 
 
 I. 11692. 
 
 
 8. 5040. 
 
 
 2. 7436429. 
 
 
 9. 6300. 
 
 
 3. 720720. 
 
 
 10. 1673100525. 
 
 4. 672. 
 
 
 11. 10810800. 
 
 6. 180. 
 
 
 12. 3255840. 
 
 6. 504. 
 
 
 13. 565081020. 
 
 7. 1630. 
 
 
 
 
 
 Exeroise XII. 
 
 
 L 610510. 
 
 
 8. 28728. 
 
 
 2. 6040. 
 
 
 9. 3300. 
 
 « 
 
 3. 25200 
 
 
 10. 378000. 
 
 4. 8400. 
 
 
 11. 864. 
 
 
 6. 2620. 
 
 
 12. 1511640. 
 
 6. 6019589575. 
 
 
 13. (a) 3617800 ; (i 
 
 7. 277200. 
 
 
 
 
 
 Exeroise XIII. 
 
 
 1. 477. 
 
 6. 89. 
 
 
 10. 39. 
 
 2. 788. 
 
 7. 13. 
 
 
 11. 267. 
 
 3. 192. 
 
 8. 3. 
 
 
 12. 4;i. 
 
 4. 47. 
 
 9. 3224. 
 
 
 13. 837. 
 
 6. 1 (Prime to each 
 
 
 
 
 other.) 
 
 
 
 
 
 Exeroise XIV. 
 
 
 1. 225. 
 
 6. 7. 
 
 
 10. 492. 
 
 2. 267. 
 
 7. 41. 
 
 
 11. 21. 
 
 3. 29. 
 
 8. 186. 
 
 
 12. 97. 
 
 4. 131. 
 
 9. 37. 
 
 
 13. 99. 
 
 (. 4. 
 
 
 
 
ANUWEKS. 
 
 43 
 
 I. 
 
 2. 
 3. 
 4. 
 5. 
 
 6. 
 
 7 
 
 1. 
 2. 
 3. 
 4. 
 6. 
 6. 
 
 1. 
 2. 
 3. 
 4. 
 5. 
 6. 
 7. 
 
 Exeroise XV. 
 ^28320. 8. 2327926GI. 
 
 32340-1617 = 20. 9. «0-A = 676. 
 
 1680-108== 10. 10. 184J. 
 
 690760-147=4080. 11. l|. ' 
 
 720720-1001=720. 12 9 
 
 2227680-.4641 = 480. isl (a) ^ ; (6) G.O.M. 3 ; L.O.M. 
 
 128x2304 = 294912. 12 ; (c) (JO centa. 
 
 Exeroise XVI. 
 
 13^. 
 
 8tVi. 
 
 14J. 
 (a)3f;(6)2g«;(c)2^,U. 
 
 8. 6Jf5 and 5|f 
 
 9. 7iV2 and 4^1. 
 
 10- («) 5/i ; (6) 4f y^S. 
 
 11- (a) 1^ ; (6) 'm. 
 
 12. 3. 
 
 13. (a)63|f|§; (6)23 sq. yds. 5 
 sq. ft. 30 sq. inches. 
 
 1, 
 2. 
 3. 
 4. 
 
 L 
 2. 
 3. 
 4. 
 5. 
 6. 
 7. 
 
 Exercise XVII. 
 
 (a) 11»^ ; (6) 100. 8. (a) 16 ; (6) 1^. 
 
 ^^ 9. f ^ and if. 
 
 f- 10. («) 8,V.«5 ; (6) IWJ. 
 
 *• 11. 5 ; 144 ; 1^^. 
 
 l^t- 12. |. 
 
 ^^' 13. (a) 3i ; (6) jC. 
 
 Exercise XVIII. 
 
 6- 6. 8. 1. 
 
 2- 2. 9. i 
 
 7. 1. 10. ej. 
 
 8. 
 2. 
 
 11. *. 
 
 12. 2. 
 
 13. m- 
 
 32 vests. 
 32. 
 
 93J yds. 
 $3135. 
 
 1^ hours. 
 
 Exercise XXX. 
 
 8. 7^^ acres. 
 
 9. 13§ lbs., or 13 lbs., 10 oza 
 
 10. ^• 
 
 11. iHs- 
 
 12. House, $2100. Lot, $300. 
 13. (a) 1089. 
 
 (6) 2 quarts, 1 pint. 
 
 ifi 
 
 i 
 
 II 
 
 
44 
 
 ANIWBB8. 
 
 Bxeroiae XX. 
 
 1. 2|. 16 
 
 2. Sum = lf§ ; Quotient 7. 6- — • 
 
 3+4 ^h 
 
 3. I, , and I 7. 70/^A. 
 
 4 + 6 8. 3108. 
 
 4. (o)L.O.M.382109;(6)jf^jfn. 9. 34iV2. 
 
 , 3 10. (a) 4 ; (6) |480. 
 
 kT* 11- 1- 
 
 12. St. 
 E B 
 
 13 
 
 /(a) aV ; 
 
 (c) 
 
 G 
 
 iil;i « ^ i 
 
 IH i 
 
 rAODB^rone whole 
 
 rectangle. 
 
 A C F E=J of the 
 whole. 
 
 G C F H=i of § of 
 the whole ; = J or 
 I of the whole 
 rectangle, etc. 
 
 (d) A ao.=19 sq. rods, 6 sq. yds., 64.8 sq. inches ; (e) 1. 
 
 Exercise XXI. 
 
 1. 28656 ounces. 
 
 2. 13^ dozen. 
 
 3. 12 acres, 86 sq. rods. 
 
 4. $1.66. 
 A 12 days. 
 B 6 days. 
 
 6. 3 feet 
 
 { 
 
 7. 16 miles. 
 
 8. 6880G00 sq. inches. 
 
 9. $4791.12. 
 
 10. 142992 cubic inches. 
 
 11. 26 per cent. 
 
 12. ^. 
 
 13. 6240. 
 
 Exercise XXII. 
 
 1. 1900. 
 
 2. 11640. 
 
 3. $3430. 
 
 4. $6. 
 
 6. $34.28f. 
 
 6. $1000. 
 
 7. $8ioa 
 
 8. $311.11^. 
 
 9. mo. 
 
 10. $2.50 ; 3^5 cents. 
 
 11. 9000 sq. feet. 
 
 12. 1800. 
 
 13. (o) $49; (6) 1^ ; l^x $660.00 
 
 = $072.00. 
 
AN8WEI18. 
 
 45 
 
 whole 
 
 )f tht) 
 
 f f of 
 =Jor 
 whole 
 tc. 
 
 1. 
 
 60.00 
 
 Exercise XXIII. 
 
 1. lOJdays. 
 
 2. $3. 
 
 a $110.34. 
 
 4. 037. 
 
 5 «10. 
 
 6. $1057.50. 
 
 7. The latter, by f 10. 
 
 8. 607. 
 
 9. 21,^ minute*. 
 
 10. 819.78. 
 
 11. 350 bush els. 
 
 12. 1 ton, 1125 lbs. 
 
 13. (a) $80.04 ; (6) 3 days. 
 
 Erarcise XXIV. 
 
 1. ^. 
 
 2. A $120, B $105. 
 
 8. C| gallons, 
 
 9. 64 men. 
 
 3. 84000, and 12| per cent. loss. 10. 70400 chains. 
 
 4. $222. 
 
 5. A 10 years, B 24 years. 
 
 6. A $00, B $SU, C $90, D 205, 
 
 Hud £ $180. 
 
 7. 10 miles. 
 
 11. 27 cub. feet. 
 
 12. 4 lbs. green and 10 lbs. 
 
 black. 
 
 13. 587 lbs., 8 0Z3. 
 
 Exercise XXV. 
 
 1. $900. 
 
 2. 120 hats. 
 
 3. $87.50. 
 
 4. 40 per cent. 
 
 8. $nf).00. 
 
 9. $200. 
 
 10. $397.50. 
 
 11. 40 per cent. 
 
 5. A $22.50 ; B $15.00 ; 10.00. 12. $8.00. 
 
 6. («) ^ ; (i) ^. 13. $90.8085 an acre. 
 
 7. $12.00. " 
 
 Exercise XXVI. 
 
 1. (a) 5 hours ; (6) 5 miles. 
 
 2. 200 yards. 
 
 3. T*g-. 
 
 4. 140 lbs. 
 6. $00. 
 
 6. 200. 
 
 7. 105 acres, 128 sq. rods. 
 
 8. 15 gallons. 
 
 9. $42 safe, $147 contents. 
 
 10. 12 feet. 
 
 11. $150, $200 and $250 for A, B 
 
 and C, respectively, 
 
 12. $750. 
 
 13. 35. 
 
 t 
 
■; 
 
 ^ 
 
 V, 
 
 ■ifl 
 
 46 
 
 NNHWKIia. 
 
 Exorcise XXVII 
 
 1. 8.30 o'clock, or 24 mimit,"H to 9 o'clock. 
 
 2. 10 rods. 
 
 3. 1280 ju; res. 
 
 4. 22^.1. jHT 11). 
 
 6. .'?H W.irnils, 127 Uts. ; iiid 25 Ib.s. in a hug. 
 G. $152.UO. 
 
 7. $0. 
 
 8. 1 ftcro, 38 H(|. rod.s, 29 Btj. yds., o sq. foot, 1)0 8q. iuchoa. 
 
 0. |iU2. 
 
 10. 9.41 ,7;^ o'clock. 
 
 11. 8 days. 
 
 12. 143] j por cunt. 
 
 13. (a) 87318 bushols ; (6) 351 times ; (c) 8120. 
 
 1. $!2IO.fl3. 
 
 2. $4.50. 
 
 3. 82252.25. 
 
 4. 602 carats. 
 
 5. $14000. 
 
 6. 5 dozen. 
 
 7. 1000 papers. 
 
 Exercise XXVIj.1. 
 
 8. 103(J acres, 127 sq. ruds, 30 
 sq. ydi^., 2 sq. foot, 30 sq. in. 
 0. 4 duzon. 
 
 10. TfYff. 
 
 11. 12 o'clock, noon. 
 
 12. 405, 300 and 324, respectively. 
 
 13. 82,305,800, an acre. 
 
 1. 280 sheep. 
 
 2. $900. 
 
 3. $7.30 an acre. 
 
 4. M a cwt. 
 
 Exercise XXIX. 
 
 8. 27390 feet. 
 
 9. 109 foet. 
 
 10. (o) J ; (6) 25. 
 
 11. $37800. 
 
 5. 1400 fivo-cont pieces ; $74. 12. $42834.00. 
 
 6. The first, by 703 lbs. 13. 1 foot, inches. 
 
 7. $71.28. 
 
 - Exercise XXX. 
 
 1. 1713G times. 
 
 2. ((t) (2x2x3x3x6), (2x3x3x5x7), (2x3x5x6x7x7). 
 (h) I. G. C. M.=: (2 X 3 X Hi the (jrentest solection of common factors 
 of those numbers - 30. II. L. C. M. = (2=^ x 3^ x 5-' x 7 -) the 
 smallest selection of factois, including the factors of each given 
 number = 44100. 
 
ANBWKRa. 
 
 47 
 
 7). 
 iors 
 the 
 ven 
 
 X ((I) (H X 5 X 7 X 13) uiid (2 X fi X 5 X 7 X 13). (/>) (i.) 0. 0. M. in 
 o.|ii!il t«) (^{"i X 7 X 13) = 45'> ; (ii ) L. r*. ^^ i-* rquul to (2 x 5 x 5 x 7 x 
 13x3) -- 13«;:>0. ((•) (I.) Fr.im (/*) (i.) iiii.l (ti.) wo hiivo <;. (' M. x 
 L. ('. M. — (."> X 7 X 13) X (2 X 5 x .» x 7 x 13 x 3) = (;i x a x 7 x 13 x 
 2x5x5x7x 13) (ill tho fuoiors tif \:'A\it aixl ITmO ; (ii.) fiDiu (c) (f.) 
 wo sou tliiit (». 0. M in oompM.si-jl of tlui factors «)f IIUm jiIkI 4r)rtO 
 ioJoiiUmI hy ]j C. INI. iviicl cjrc rrr.sd : (III ) (i. C. M. ftiid L. ('. M. uro 
 iiiJiilo ii[» of all tlio factors of 13(;r) ami 4.">.'ti) [<•. (i )J; thtTt'ttirc < J.(', .M. 
 X L. C .M.= proiluct of the two nmulu-rs (liociuso (J.C.M. aiid 
 L.C.M. — a// //(»•/(((/(;>•:< of tilt' ^iviu nuniliurs) ; (iv.) siiuo («.(!. .M. 
 X Ii, C M. of tho two miniht'rs product of iiiiiiibtMs ; thortforo 
 tiioir product -j- ono of tho niinihers -= thu (»tlu!r miiui)or, iviid 
 cice versa ; ^v.) Kiiico j)r<iduct of tho two iiuinl)er8 =-; (». C. M. x 
 L. C. M ; thoroforo tlioir product -r 0. C. M. ^-^ L. C. M. nnd 
 vice vcrad. 
 
 4. 180. 
 
 5. (Thoory). 
 
 0. 740. 
 
 7. Tlui Kinallosb miinhcr wo could have for ono is 240 ; tlioro- 
 foro, 240 and 2o.sO, or 72'? (tliiid uudtii.lo) and 1»G0, etc. (N.B. ull 
 tho multiples of 240 will uvt do, howevei). 
 
 8. L. C. JNI. 40 ; QuoL., 525. 
 1). II. C. F.,5; L. CM,, 30. 
 
 10. (tt) II. C. r., lij ; L. C. iM., f ; (^) 1 and 81 times, respect- 
 ively. 
 
 11. 243,700,050. 
 
 12. L. C. M., 00, and II. C. F., yj^. 
 
 13. 272. 
 
 Exercise XXXI. 
 
 1. 312 bushels. 
 
 2. 4. 
 
 3. 25 of each. 
 
 4. (a) Tho latter kind by ^'^ of a cent, per inch. (6) 40 sticks of 
 the 7-iuch kind. 
 
 5. 410 and G15. 
 C. 4840 times. 
 
 7. 21 lbs., 0} ounces, (21 j^^ lbs). 
 
 8. G50 lbs. at 4, G and 8 cent.s, respectively, and 15G0 lbs. at 16 
 cents. 
 
 9. 5]S%. 12. 8240. 
 
 10. 89(5.24. 13. (a) 514 bushels. 16 lbs. ; 
 
 11. $20 cost. (t) 9000 ; (c) $18.48. 
 
 Ii. 
 
 I 
 
48 
 
 1. 11^ centa. 
 
 2. 3^ ozs. 
 
 3. A «$78.32. B (121 04. 
 
 4. 3 : Ui. 
 
 5. «4, 150,000. 
 
 ti. 410 gq. ft.,90Hq. iiiciujH. 
 
 7. 1240. 
 
 ANHWKUH. 
 
 Exeroine XXXII. 
 8. 7 t'onti. 
 
 9 f> iliiys. 
 
 10. $U\VA.20. 
 
 11. i'Hi, iStorling. 
 
 12. mn. 
 
 13. (a)50cuntii (b)L.U.M.,90 ; 
 73 tim«ti. 
 
 Exeroise XXXIII. 
 1. A $4.60. D 92.00. 91.80. 9. 357, the ^'niifor ; and 136, tha 
 
 2. 200. 
 
 3. 95,700. 
 
 4. 20 per cent. 
 
 5. 1|3. 
 
 6. 210. 
 
 7. 22. 
 
 8. 6G7, L.O.M. 
 
 1. 92. 
 
 2. November 19th, 1888. 
 
 3. 40 per cent. 
 
 4. 9200. 
 
 5. First cost, 94 ; second 
 
 cost, 92. 
 
 6. 9131.25. 
 
 less. 
 
 10. 100 lbs. of tlie dearer, and 
 
 120 of the oheapur. 
 
 11. 70 cents. 
 
 12. 2f per cent. 
 
 13 (a) 87000 cost, 98U0O iisking 
 price, lii<7500 selling price ; 
 (6) 932.00. 
 
 Exercise XXXIV. 
 
 7. 200 buHheli. 
 
 8. 4 per cent. 
 
 9. C6§ per cent. 
 
 10. 96876. 
 
 11. (a) 57} J; (6) 35 J. 
 
 12. 9 years. 
 
 13. (a) 16 feet; (&) 36 years. 
 
 Exercise XXXV. 
 
 1. 3^ years. 8. 94800. 
 
 2. 4 per cent. 9. 954. 
 
 3. 91800. 10. 9504. 
 
 4. 112 barrels, and 500 boxes. 11. 4 time?. 
 
 6. 20, 80 and ICO. 12. GiB; :2:3 (or 120 lbs. green 
 
 6. 610 cords, 60 cubic feet. and 180 lbs. black). 
 
 7. 5166 acres, 119 sq. rods, Osq. 13. (a) 336 ; (6) 92.36. 
 
 yds., 2 sq. ft., 36 sq. in. 
 
Asnwr.RH. 
 
 41 
 
 Exercise 
 
 1. 9607-60 Amount (principal 
 
 ami interuHt). 
 
 2. 6 pur cunt. 
 
 3. 12^ yeiwn. 
 
 4. The luttur by i|5440. 
 B. i 
 
 0. 84. no. 
 
 7. $33.76. 
 
 XXXVI. 
 
 8. 5686 miloH, l(t60 ynrdn. 
 9 10 tons, 1800 ll>s. 
 
 10. ISucruM, 157 h(|. rods, i:(U 
 
 H({. yde., 6 mj. fuet. 
 
 11. $ir>.m 
 
 12. I'flO. 
 
 13. 3170 iniloH, 80 rods. 
 
 1. 4 per cent. 
 
 2. 25 per cent. 
 
 3. 3000 men. 
 
 4. 857.00. 
 
 6. 2040 times. 
 
 6. *tO coiits. 
 
 7. 90 dfiys. 
 
 8. $1760. 
 
 Exercise XXXVTI. 
 
 9. 20 lbs. at 40, 50 and 76 cents, 
 roHpoctivcly, and 9 lbs. ut 80 
 cuntft. 
 
 10. 385} per cunt. 
 
 11. 813:{33J^. 
 
 12. $92. 
 
 13. 104 yds. at $1.80 = $18720 
 
 (practically); 26%. 
 
 Exercise XXXVIII. 
 
 1. $1880. 
 
 2. $327.00. 
 
 3. 9}j| diiy.s. 
 
 4. 3 min. [icr hour. 
 r». 00 ij;all<»ns. 
 
 0. 3l,6.']0,000 seconds. 
 
 7. $180.00. 
 
 8. 4 montlis. 
 
 9. (a) Side moasuromont, 32 sq. 
 ft. to a cord, (h) In tiers 
 lengthwi.so of the pile. 
 
 10. $271.26. 
 
 11. 8 lbs. at 50 cents, 6 lbs. at 
 
 70 cents. 
 
 12. 18 gallons. 
 
 13. (a) $10 ; (6) 30 cents. 
 
 
 1. 4 hrs., 35 min. 
 
 2. 150 por cent. 
 
 3. 20. 
 
 4. 420 sq. inches. 
 
 5. 02 i'y per cent. 
 0. $24.80. 
 
 7. i 
 
 Exercise XXXIX. 
 
 8. 07n2 ; 1079, sum. 
 
 9. $8. 
 
 10. $4.20. 
 
 11. $75. 
 
 12. $22.60. 
 
 13. (a) 70 tons ; (b) $384 
 
 
50 
 
 I 
 
 ANSWKIW. 
 
 Excrcitte XL. 
 
 1. ♦5B1V 
 
 2. FiiKt, 70; iocond, 140 ; 
 
 thiril, CO. 
 
 3 171.16. 
 
 4. I')1,h;»||. 
 
 i\. Mil. 
 
 7. 00 Iba. 
 
 8. A, 80.00; n, $|..10 ; C, m.Wtl 
 
 I), 8rj.<;(). 
 
 0. 1)1 » (Ivuh; 80 to Hi. 
 
 10. 81 1:;2.:}2. 
 
 11. e.m.uO. 
 
 12. IIX 
 
 13. («) in coi»t«; (6) A, $350; U, 
 
 650 ; 0, 6250. 
 
 Exorclso XLI. 
 
 1. 87000. 
 
 8. 
 
 •J 
 
 2. ('0 if'.^b) 8?;('^) i. 
 
 0. 
 
 4 per cont. 
 
 .^ 8 1< '75.20. 
 
 10. 
 
 107 c.ii t-loadg. 
 
 4. i) iiiiloH. 
 
 11. 
 
 5200. 
 
 5. 8175.50. 
 
 12. 
 
 fiO per cont. 
 
 0. I of ;m inch to tho mile. 
 
 13. 
 
 6 p. III. 
 
 7* 00 conts. 
 
 
 
 Exorciso XLII. 
 
 1. (a) 10 minutes ; (6) 3 miloH. 8. 3;V\ per cent. 
 
 2. 4:}2(laya. 0. 81U50. 
 
 3. $X]3. 10. 82 10. 
 
 4. 12 (liiys. 11. 1(5 (liys. 
 
 5. 81410. 12. l\ por cont. gain. 
 C. 24702 ton.s, 1678 lbs. , 2 ozs. 13. 5 pur cont. 
 
 7. 2 games. 
 
 Exercise XLIII. 
 1. (a) 80 cents ; (b) 3 J per cont. 8. 2 lbs. 8 ozs. 
 
 2. 
 
 2000 gallons 
 
 1. 
 
 
 
 0. 
 
 12 per cent. 
 
 
 
 3. 
 
 48 tons. 
 
 
 
 
 10. 
 
 15 cents a cloz. 
 
 , before ; 
 
 12 
 
 4. 
 
 8150.00. 
 
 
 
 
 
 cents a duz., 
 
 after. 
 
 
 5. 
 
 6 per cent. 
 
 
 
 
 11. 
 
 8244.48. 
 
 
 
 6. 
 
 827.50. 
 
 
 
 
 12. 
 
 20. 
 
 
 
 7. 
 
 A. $40 ; B, 
 
 8120; 
 
 0, 
 
 8180. 
 
 13. 
 
 884. 
 
 
 
ANMWKKH. 
 
 b\ 
 
 ; 12 
 
 1. fi.ia. 
 
 Exflroleo XLIV. 
 8, 8<J.li.'. 
 
 2 il 0. ^U'so. 
 
 3. 7 y«' n'«. 10. ^a.i.HU. 
 
 4. A, ^Hi ; h. i8')0 i 0, iiioa II. NoNuul.cr lUlli, 1888. 
 
 12. H llnlll'H. 
 
 13. C(4.UU loM. 
 
 0. 4'.) hoys. 
 
 0. 4J0. 
 
 ExurciBu XLV. 
 
 1. 07.17.10. 8. 'J4 milon. 
 
 2. 8t:U].48. 0. 8U.(i(). 
 
 3. 20. 10. 8*) 1 7. 11. 
 
 4. 81(5.30. II. $'i"j(M).()0. 
 
 5. L'O iliiys, 12 hrs. , 18 tniiiutes. I'J. 21 milus an hour, 
 0. 50 purciiiib. 1:J. lOH'.MM). 
 
 7. 2251 ciihIvh, and .')!( pintN loft. 
 
 Exorcise XLVI. 
 
 1. 
 
 435. 
 
 B. smijo. 
 
 9. 8125 and !?280. 
 
 2. 
 
 1120. 
 
 6. J no. 
 
 10. i|] of a 8«i. inch. 
 
 3. 
 
 40 c<>nt8. 
 
 7. n2. 
 
 11. 8«il88.80. 
 
 4. 
 
 210.5. 
 
 8. 112. 
 
 12. 7:5. 
 
 Hi. (fi) turkoy.s, 3 ducks, 2 gcoRo and 2 chickens ; (b) £10 
 Ush. lid. 
 
 Exerciso XLVII. 
 
 1 . 7 J 5'. 
 
 2. Yes ; bocftuso it i.s tlio nio.'vsmo of ii ([uantity. 
 
 3. Due Doc. l^th, 1891, hut must bo paid on tliu IGth Doo. (3 
 days' grace) ; 8C54 will redceni it. 
 
 4 81.55. 
 
 6. 6. 
 
 6. A, 85G0.00 ; B, 8784.00 ; C, 811 20. 00. 
 
 7. $180.00. 
 
 8. 132. 
 
 9. 42. 
 
 10. 81287.45. 
 
 11. 8420. 
 
 12. 25 per cent. 
 
 13. (a) 840 ; (6) 1 ft. 4 in. 
 
 .4 
 
 i 
 
1 1 ^' 
 
 (i 
 
 I .' 
 
 If 'H 
 
 ■ ■ n 
 
 'i ii 
 '■■ ii 
 
 62 
 
 ▲NSWEKS. 
 
 Exercise XLVIII. 
 
 1. $140000.00. 
 
 2. A $14.00 ; B $70.00 ; 
 
 $28.00. 
 
 3. 13 sq. fcot, 153 sq. inches. 
 
 4. A 
 
 /20,Yf gallons of wine. \ 
 \ 'JiY-r g'^^'ons of water./ 
 
 7. Sum $800.00 ; 
 
 Shores 
 
 8. 4. 
 
 9. 33.33^ less. 
 
 
 3/ ^iYt gi^ll""sof wine. 1 10. 73^ cents. 
 \i0^^f gallons of water. / n. is Iba., 12 ozs. 
 
 
 5. 
 
 ^»0. 12. ^90. 
 
 6. 
 
 $30.00. 13. (a) 504 rails ; (6) 515 yds. 
 
 
 Exercise XLIX. 
 
 1. 
 
 $122.88. 8. 81. 
 
 2. 
 
 115 yards. 9. Cfi trees. 
 
 3. 
 
 12 horses ; 108 sheep. 10. 13^ % gain. 
 
 4. 
 
 100 gallons. 11. 135 ounces. 
 
 5. 
 
 8 per cent 12. 660 times. 
 
 6. 
 
 700. ,« /201bs. ateOcenta. 
 2^j. "^'^" \30 " "70 " 
 
 7. 
 
 
 Exercise L. 
 
 1. 
 
 $11,900.00. 8. 32 dozen. 
 
 2. 
 
 80. 9. 37 f per cent. 
 
 3. 
 
 7,115,505. 10. 7 X 907 ; 22 X 3" X 5»{ 
 
 4. 
 
 $183. 28x52. 
 
 6. 
 
 $U5.71. ^"^ \32^V " 
 
 6. 
 
 7. 
 
 8^1jerceut. 13. $246.31f 
 
 
 Exercise LI. 
 
 1. 
 
 A, $30 ; B, $48 ; C, $40. 9. Both (a) and (6) Theory ; (c) 
 
 2. 
 
 i5^1«. (I.) U ; (" ) 62 ; (d) (I.) 
 
 3. 
 
 m 9091; (II.) 61 ac, 96 rods. 
 
 4 
 
 Clay, 60 feet; sand, 12 feet; 26 yds., 6 ft. 108 in. 
 
 
 rock, 18 feet. 10. $103,000. 
 
 5. 
 
 13 days. 11. $72. 
 
 6. 
 
 28. 12. A, *615 ; B, $1026. 
 
 7. 
 
 6040. 13. 40 cents. 
 
 8. 
 
 6 days. 
 
ANSWERS. 
 
 M 
 
 Exeroise LII. 
 
 1. 660 acres. 8. 027046. 
 
 2. 60 per cent. 9. $100. 
 
 3- 2. 10. 2880 times. 
 
 *• 5 lbs. 11. Lose, $1400. 
 
 6. -$60. (He is $60 in debt.) 12. 25 ft. 6 in. long ; 17 ft. in. 
 
 6. (a) 71 ; (6) 1,244.880. wide. 
 
 7. A, CO days ; B, 180 days. 13. (c) $91.26 ; (6) 28 cents. 
 
 1. $1 26. 
 
 2. $200. 
 
 3. $649.97igf. 
 
 4. $6864. 
 
 5. 5;\ cents. 
 
 6. $677.60. 
 
 7. $28.75. 
 
 Exercise LIII. 
 
 8. $44.00. 
 
 9. $764.00. 
 
 10. $32. 
 
 11. 242. 
 
 12. $497.61. 
 
 13. 114. 
 
 i. 
 
 Exercise LIV. 
 
 1. $80 per annum. 
 
 2. $8500.00. 
 
 3. (a) h ; (^) A'.. 
 
 4. 17 days. 
 
 5. 40 days. 
 
 6. $192. 
 
 7. A, $480 ; B, $360. 
 
 o. $3. 
 
 9. H. 
 
 10. $170-555264. 
 
 11. 40 barrels. 
 
 13. (a) $189.00; (6) $75.60 
 
 'li 
 
 Exercise LV. 
 
 1. A, $242.10; B, $121.05. 
 
 2. The ninth = 9 x 450= 4050. 
 
 3. 7^ per cent. 
 
 4. 28000. 
 
 5. 1048 yds. 
 
 6. $560. 
 
 7. $400, first ; $350, second. 
 
 8. 225 bushels. 
 
 9. 2 tons, 913 f^ lbs. 
 
 10. L.C.M. 40320; H.C.F. 133. 
 
 11. $15.48. 
 
 12. 456 bushels. 
 
 13. (a) $12.75; (&) 16 acres. 
 
54 
 
 A.NSVVEUS. 
 
 1. 18 times. 
 
 2. 43 tons, 400 lbs. 
 
 3. 704 bushels. 
 
 4. $2154.27. 
 6. 2 tons. 
 
 6. $54.45. 
 
 7. A : B : : 45 : 32. 
 
 Bxeroise LVL 
 
 8. $4375. 
 0. $1.05. 
 10. 5. 
 
 u. $a.mo3|. 
 
 12. $121.21 J. 
 
 13. $7.00L'ain. 
 
 Exercise LVII, 
 
 1. 45 sheep. 
 
 2. $320.00. 
 
 3. 4 per cent. 
 
 4. $903.90. 
 6. $192.50. 
 
 6. 1^. 
 
 7. $81.60. 
 
 553.55. 
 
 8. $8.00. 
 
 9. 23 H.C.F.; and 211 L.C.M. 
 
 10. $19.80 + .i!33.75 = 
 
 11. IJ of cost. 
 
 12. $9405. 
 
 13. (a) $34.66 ; (6) $18. 
 
 Exercise LVIII. 
 
 1. h 
 
 2. $20.00. 
 
 3. (a) U : (&) If ; (c) 1. 
 
 4. 28|%. 
 
 5. 117,612 tons. 
 
 6. 2 tons, 56 lbs. 
 
 7. $84.00. 
 
 8. $4.80 (80 cents each). 
 
 9. $31,500.00. 
 
 11. 3^. 
 
 12. 20 miles. 
 
 13. $1000. 
 
 Exercise LIX, 
 
 1. $30.00. 
 
 2. The former ; $6.00 saved. 
 
 3. 2^ L.C.M. 
 
 4. 35 (lay.s. 
 
 5. $21.07. 
 
 6. 10 years ; f> per cent. 
 
 7. 4 per cent. 
 
 8. $30,000. 
 
 9. $532. (Quintal =lcwt-.) 
 
 10. $13.80. 
 
 11. $350.00. 
 
 12. 3 days. 
 
 13. 60. 
 
 m 
 
ans\vi:h8. 
 
 bb 
 
 
 Exercise IjX. 
 
 
 1. ^17.01. 
 
 
 7. ^^j of a ton. 
 
 ■• 
 
 /First, 170 bushels. 
 
 8. G,l!)H,O8O,O0S,401,003,412,80O. 
 
 i ■■ 
 
 2. . Socoiul, 170 
 
 
 9. A, .-J.'JlI.OO ; B, SIJO.OO. 
 10. 870 bbla. 
 
 'It 
 
 3. 1,V 
 
 
 11. 4 acres. 
 
 
 4. 81.00. 
 
 
 12. IfrSi 
 
 5. 107 rr. 
 
 
 13. SJ80. 
 
 
 6. A, yOO ; B, 300. 
 
 
 
 1 
 
 Exercise LXI. 
 
 1. $34.40. 
 
 2. 7,V ; $2400.00. 
 
 3. 32 (biys. 
 
 4. A, 450 ; B, 400. 
 
 5. $125. 
 
 6. 1 ton, 025 lbs. 
 
 7. $38.70. 
 
 8. $240. 
 
 9. $1400. 
 
 10. I 
 
 11. $10. 
 
 12. 80 dozen. 
 
 13. (a) Gains 10 per cent.; 
 {b) 27 tiiuea. 
 
 Exercise LXII. 
 
 1. $270,000.00. 8. 408 yards. 
 
 2. A, 8480 ; B, $100 j C, $040. 9. 8%. 
 
 3. $24.00. 10. B, $1.02 ; G, $2.04. 
 
 4. $73.00. 11. 45 gallons. 
 
 5. 243. 12. $87.50. 
 
 6. $153.00. 13. 1, 4, 3 and 2 lbs. resp., (or 1 
 
 7. $27|375. lb. of each, for another set.) 
 
 Exercise LXIII. 
 
 1. 13^. 
 
 2. 8L tons. 
 
 3. $1300. 
 
 4. 20 per cent. 
 
 6. $10.40 a head. 
 
 6. 00 miles. 
 
 7. $300. 
 
 8. 1 day. 
 
 9. 117,023. 
 
 10. $1304. 
 
 11. 8. 
 
 12. 5.20 p.m. 
 
 13. (a) 110 sq. inches ; (6) 1320 
 sq. inches ; (c) 2354 sq. incliea. 
 
I 
 
 : 1 
 
 Ij ; 
 
 6e 
 
 ANSWERS. 
 
 Exercise LXiV. 
 
 1. 164 Bq. inches. 
 
 2. 10 feot, 6 inches. 
 8. 56 yards. 
 
 4. 1886 sq. yards, 4 sq. feet, 72 sq. inches. 
 
 6. 8 acres, 23 rods, 8 yards, 2 feet, .3(5 inches. 
 
 6. 7r(802 - C0») 8(1 inches = 3f (140 x 20) sq. inches = 6 sq. yds., 
 7 sq. feet, 16 sq. inches. 
 
 7. 1078 cubic inches. 
 
 8. 605.14 ... + . . . sq. inches. 
 
 9. 891 cubic inches. 
 
 10. 20 inches. 
 
 11. 42 rods. 
 
 12. 20 inches. 
 
 13. (a) 9 feet, 4 inches ; (6) 44 sq. rods, 6 sq. yards, 6 sq. feet, 
 72 sq. uichos. 
 
 Exercise LXV. 
 
 8. 50Jg days. 
 
 9. 303 dozen and 4, chairs. 
 
 10. He would neither gain nor 
 
 lose. 
 
 11. $120. 
 
 12. m. ^Vm i^ ; lA. 
 
 13. 10 years. 
 
 1. 
 
 2. $1201.40. 
 
 3. $105.12. 
 
 4. 8 : 5 respectively. 
 6. $230. 
 
 6. (a) of, first ; -r, second 
 
 X , third ; (h) 3iV5. 
 
 7. (a) i«A. (b) iif . (c) ih 
 
 Exercise LXVI. 
 
 1. (a) 9i; (6)9J. 8. $2707.20. 
 
 2. $0.00"! 9. $133.20. 
 
 3. Either directly North or 10. 1st, 205 ; 2nd, 328 ; 3rd, 4th, 
 South. 5th, etc. ... to lltli, 123 each. 
 
 4. $121.70. 11. $100.70. 
 
 5. 7800 miles. 12. $390. 
 
 6. 9 acres, 52 rods, 24 yards, 13. (a) 8^ ; (b) 48 cents, tea ; 40 
 3 feet 21 g inches. cents, coffee. 
 
 7. 21,315 lbs. 
 
ANBWSB8. 
 
 57 
 
 Exercise LXVII. 
 
 t. 1. 
 
 2. 91.26. 
 
 3. 9j'y lbs. 
 
 4. 46 sheep. 
 
 6. 733 yds., 1 ft. 
 
 6. 4^ hours. 
 
 7. 1 pint. 
 
 8. At A '8 comer; once. (But A 
 
 will have reached his corner 
 the second time'. 
 
 9. Horse, ^240 ; carriage, $400. 
 
 10. $560. 
 
 11. 030. 
 
 12. 20 per cent. 
 
 13. 9^ inches. 
 
 Exercise LXVIII. 
 
 1. (a) Book-work; 3341520 ; (6) 37 ; 3rd, 4th, 5th, 0th, 7th, 
 8th, and 9th. 
 
 2. (a) Book-work ; (6) $14.37^ ; (c) 25 per cent. 
 
 3. (a) Book -work ; (6) 150 barrels. 
 
 4. 75 cents. 
 
 5. July 13th, 1890. 
 
 6. 2 days. 
 
 7. 7. 
 
 8. Book- work; 375-70446355. 
 
 9. (a) $32 ; (b) 104 days. 
 
 10. 046.71. 
 
 11. 11 dozen. 
 
 12. 67. 
 
 13. $60, A's share ; $50, B's share and $36, C's share. 
 
 Exercise LXIX. 
 
 1. 6 days. 
 
 2. 4 hrs., 22 min., 30 sec. 
 
 3. $4.50. 
 
 4. 13 miles. 
 
 5. 4 lbs. 
 
 6. 26^ per cent. 
 
 7. ^ of an acre. 
 
 8. 13 lbs., 8 028 
 
 9. $43,200. 
 
 10. (a) 2,505,600 
 (6)7 times, 
 
 11. A, $70 ; B, 
 
 12. 664 lbs. 
 
 13. $16,044. 
 
 sec 8. J 
 
58 
 
 AN8WKK8. 
 
 Exercise LXX. 
 
 1. 80 yiirdfl, 
 
 2. 45 acres. 
 
 3. (»3 cunts. 
 
 4. 82400. 
 
 5. .«(:M)42. 
 
 6. .^(iO. 
 
 9. 1st, .Sr.OO; 2ii(l,$l'J00; .'Jrcl, 
 .":<()()() ; Ifh, JjliTOO. 
 
 1.0. .siivj.h:).;. 
 
 11. 147 Hi{. rods, sq. yds., 8 aq. 
 
 ft., no sq. in. 
 
 12. 70 times. 
 
 7. A, $100; B, !iiil50; C, §250. lo. ^bU.Gl). 
 
 8. $13500. 
 
 Exorcise LXXI. 
 
 1. 28 per cent. 
 
 2. 50 lbs. and 37 J lbs. 
 
 3. 1221. 
 
 4. $002.40. 
 
 5. 300. 
 
 G. 80 per cent. 
 
 8. 244 iicrcH, 88 rods, 22 s(|. yards, 
 
 7 'Scj. foot, 72 8(1. iiiolies. 
 
 9. A J?t ; B S87.50, and §2G2.50. 
 
 10. (a) 810 ; (b) £3, 33, 3d. 
 
 11. $18.'J0. 
 
 12. 37. 
 
 7. $40.30 gain. 
 
 13. (a) 28512 ; (h) (i.) By the ' local value* of a digit i.s meant its 
 \^aluo according to (he /)o>s//io/t it or.cnpii'.i in oiir scale (dec;im;il scale) 
 of NOTATION, (ii.) First its null or iutriiuiic value as tJu; number 7 
 (7 time.s the unit) ; and second, its ^hxud value' in the tkns' place 
 
 (7 tens, or 70 times the unit), (iii.) 6xLiC LXXXIGMXXI V. 
 
 II M 
 
 Exercise LXXII. 
 
 1. (a) Book-work ; (6) 247 ; (c) 442857. 
 
 2. (a) Tlieonj : Fiuite, Pure Rcpotend, Mixed Repetond, respect- 
 ively. (If the denomiiiatiii- of a fraction c(jntains no other factors 
 than 2 or 5, the decimal Ia finite ; if the denominitor contains neither 
 of the fti-tnrs 2 or 5 it is a pxre repjtouil ; bur if it contains either 
 of the fa-tors 2 or 5 it is a mixed repijtund.) (l)) (r.) ^Vj ; (ii.) /j- ; 
 
 ^171 \ 22 7 8 
 
 3. i 
 
 4. $610. 
 
 5. $10. 
 
 6. '078125. 
 
 7. $675. 
 a H.O.F., 41 ; L.O.M., 34,440. 
 
 9. LIXCCXXIV. 
 
 10. $384. 
 
 11. $41.25. 
 
 12. 101 barrels. 
 
 13. 1036 acres, 128 sq. rods. 
 
ANBWBK8. 
 
 09 
 
 Exercise LXXIII. 
 
 1. 72 gals. 
 
 2. 37i%. 
 
 3. Tho latter, by $1 on $100. 
 
 4. $17.81. 
 
 6. 10 hra., 48 inin., »i.m. 
 6. Lun;,'th, 27 ffc.; broiidth, 
 18ffc.; height, 13 ft. 
 
 7. $1.07. 
 8 $240.67. 
 
 «. if. 
 
 10. 3 sli. St'g. 
 
 11. 2 niilus. 
 
 12. 7 ft. 
 
 13. 1100. 
 
 Exercise LXXTV. 
 
 1. $72. 
 
 2. Total, 14215. 
 
 3. 2 ozs., 13 d\v 8., 4 grs. 
 
 4. $i:U3. 
 6. C0%. 
 
 C. (a)303G; (6) 81.(ir5rnrackot8) u. ^^. 
 7. A, 54 ; B, 3G; C, GO sheep; 12. $22.16, 
 $5 per head. 13. $5.10. 
 
 8. A, $10 ; B, $8 ; 0, $22 ; $2 
 
 ft (lay. 
 
 9. 15 045. 
 
 10. 71 uc., 98 sq. rods, 29 8q.y(l8., 
 1 sq. ft, 54 sq. in. 
 
 II 
 
 Exercise LXXV. 
 
 1. $604.80. 
 
 2. A, 123 lbs., 6 ozs. ; B, 1G4 lbs., 8 ozs. 
 
 3. 54 yards ; $2 left. 
 
 4. $23.04. 
 6. $2G4G. 
 
 6. $19.08 gain. 
 
 7. 28 lioura. 
 
 8. 27 acres, 20 sq. rods, 15 sq. yards. 
 
 9. 54 minutes. 
 
 10. 15 miles. 
 
 11. 42 acres, 108 rods, 7 yards, 81 inches. 
 
 ;4i+(^ of T"n)+aof ,",)■ 
 
 13. 23G250. 
 
 83J 
 
 
60 
 
 ANRWBKS. 
 
 1. 216 yds., 2 ft. 
 
 2. 16 days. 
 
 3. 60 per cunt, 
 
 4. 240 11)8. 
 
 5. 5 per cent. 
 
 6. 13 cents. 
 
 7. $43.20. 
 
 Exercise LXXVI. 
 
 8. 24 days. 
 
 9. 9 cents. 
 
 10. 30 lbs. 
 
 11. $967 50. 
 
 12. 4(jr%. 
 
 13. 3 cents. 
 
 1. 25 cents, 
 
 2. $3872. 
 
 Exercise LXXVII. 
 
 7 J 75 hours. 
 8. 45 minutes. 
 
 3. 32 bbls. at $4.50 ; 113 bbls. 9. A, $1H() ; B, $100 ; C, $280. 
 
 at $5.00. 10. l«ii i)ercin^ 
 
 4. A, $90 ; B, $70 ; C, $040. 11. Tom, .*o.91 ; «nd Bob, $3.44. 
 
 5. 99. 12. *55.12gHin. 
 
 6. 3 diiks. 13. 41 acres, 120 rods, 19 yards. 
 
 
 Exercise 
 
 LXXVIII. 
 
 
 1. $43.20. 
 
 
 7. 33. 
 
 
 2. 9 -4 1,^5 p.m. 
 
 
 8. $360. 
 
 
 3. Each man $15 ; each woman 
 $6 ; each child $1. 
 
 9 $50. 
 10. A must pay B $0.50. 
 
 
 4. $81. 
 
 
 11. 48G lbs. 10§ ounces. 
 
 
 5. $95. 
 
 
 12. 07. 
 
 
 6. 23 lbs. 
 
 
 13. 492 bushels ; i*. 
 
 
 
 Exercise 
 
 LXXIX. 
 
 
 •1. $28. 
 
 2. $48.64. 
 
 3. 20. 
 
 4. 1522 yards. 
 6. $6000. 
 
 6. 13 miles. 
 13. (a) $9210 ; 
 
 ) (1), H.C.F. 89fj 
 
 (-16128 1^ 
 .81536 9] 
 
 7. 30 cents. 
 
 8. 5 per cent. 
 
 9. $7.20. 
 
 10. Note {face value), $584, 
 
 11. $112. 
 
 12. $73. 
 
 $ 16128 2304 288 
 
 18 
 
 [ 81536 11048 1466 
 
 91 
 
 9 
 
 (3) - X — 1 
 <JL 9) 
 
 2 
 ^ 18 
 
 'h~91 
 
 •a- 
 
 1 
 
 
i\ 
 
 AN8WKUtl. 
 
 61 
 
 18 
 91 ' 
 
 Bxercise LXXX. 
 
 1. 2 qimrts, 1 pint,. 
 
 2. Thu mnlllplier •- 1^ ; 
 
 31!) 
 
 3. of a lb. troy. 
 
 li X 3500 = $072, the atnount. 
 
 7032 
 4. 20 per cent. 
 6. 40. 
 
 6. 18 tons. 
 
 7. $700. 
 
 8. lOdoz. 
 
 9. (a) 'I'ho Jj.C.M.. oi fujo iinmhers cnw^iHta of the HniiilJp.Ht selection 
 of f<v'ti)rs which contdins tho fivctorH «»f o.icli givoii niiinhcr ; iiiid the 
 Il.C.F. of two nit mini's eoiisi.sts of tho (ji'entent udectinti of /tutors 
 common to both immliors. Tlio M.C. F. is c»>iiip()so<l of till Ihc factora 
 rejirfyd by tho L.C M. and vice rer.vi ; thoroforo, thu fdctont of tlie 
 H.CF. and L.C. M. compriso <il.l the I'm' tors of the tiro numbers; 
 and conso(iuently, tlie U O.F. inubii)lie(l by tliu L.(J. iM. is ccm-d to 
 tho proilnet of tho tujo nnmbers, c.f/. ;- Qiiustion ') (//). Il.C.F. and 
 L CM. of 2340 and 252(», which ve.vAi'cd into their prime factors = 
 /2:U0^2x2x:{x3x5xl3. i ^r ^, , « ; ,• / 
 
 factors, common to tht!SL3 nmnlters, is 2x2x3x3x5 = 180, tho 
 
 H.CF. ; and the snutUrst Hcleetion of ftirtors which contains the 
 
 factors of eacli of tho i,dven nunibors, is (2 x 2 x 3 x 3 x 5 x 13) x (2 x 7) 
 
 = 327<>0, the L.C.M. ; but tho.so are all the factors of tliose two 
 
 numbers; therefore the H.CF. x L.C.M. of anij tir , nuuibirs is the 
 
 , ^ . ^, . , H.CF. X L.C.M. of <ni(/ <u'o No's. 
 
 product of the two numbers ; • 
 
 ; the other No. (c) 
 
 31 X 28520 
 
 = 1240. {d) 
 
 One of tho No's. 
 38700 
 := 120. 
 
 H.CF. =^ 
 
 323 
 168230800 X f = 
 
 713 
 10. L. CM. = 158230800 ; 
 35102400. 
 
 U. ''t.) 15.30; (II.) $4.80. 
 
 12. A, $90 ; B, $00 ; 0, $50. 
 
 13. (a) A, $100 ; B, $lftO ; 0, $180. (6) A, $30 ; B, $20 ; C, 
 $16. 
 
 Exercise LXXXI. 
 
 1. $7200. 
 
 4. 3 cents a pint. 
 
 2. 16 days ; \ of the work. 5. 10 psr cent. 
 
 3. 10 per cent. 
 
 6. 70x56 rods. 
 
 ^! 
 
 
62 
 
 ANSWKM. 
 
 M 
 
 I 
 
 if 
 
 7. In brnrk«ti= -{ 4| + (| of JJ) >• 4- ^ (| of |)+2A )•-•(*'< 
 
 d'n + l/o))- --= + ix =18. 
 
 7 fofjil 2A la'i, 7 
 
 8. 20 at $3.00; 13 at «0.r.O. 
 ». llOfonii. 
 
 10. I.iii^tli, (>4 ft. ; bromlth, 48 ft. ; hoight, 6 ft. 4 in. 
 
 11. 12(luyH. 
 
 12. 00 galloiw. 
 
 13. 910.60. 
 
 Exercise LXXXII. 
 
 1. A, 20 (lays ; B, 27i duya. 
 
 2. 30. 
 
 3. 26 times. 
 
 4. 980. 
 
 6. 4 pur cunt. Ioha. 
 (i. $1.20. 
 
 7. A, $180 ; B, $240. 
 
 8. $M()24. 
 
 9. 15 days. 
 
 10. $429. 
 
 11. $9000. 
 
 12. 373. or. not. 
 
 13. I of an inch. 
 
 Exercise LXXXIII. 
 
 1. Of all fhe fadorsol tlio two niniiljcrs ; hencoL.O.M. x II.C. F. 
 =J'rodnct of tho two nuniliurs ; 170,0130. 
 
 2. In tho sinipUi rulus the unit is uniform; in thu compound 
 
 _ , r Product "1 
 rules it vanes ; V [ q^ ». . ^. J = sumllor numbur— 0,081 ; and 
 
 V (Product X Quotient) = large number = 1,800,807 ; 1 tb., 2 ozs., 
 12 dwts., 10 grs. 
 
 3. Same ditlorence as between simple and compound rules ; in 
 decimal fractions the unit is uniform (decimxil iCiiU)^ and in vulvar 
 
 fractions the unit varies ; 2 ; 1300669C15. 
 
 4. (6 strii)s=2 double rolls) $245. 
 
 5. $1426. 
 
 6. $22.50. 
 
 7. $5000. 
 
 8. 250 gallons. 
 
 9. A, ISO; B, $90; C, $100. 
 
 10. 15 ozs. 
 
 11. 2. 
 
 12. 3 horsesas2 oxen. 
 
 13. $ia 
 
 i* 
 
ANflWlKt. 
 
 63 
 
 Exercise LXXXIV. 
 
 1. i 
 
 2. $42. 
 
 3. f 
 
 6 14 11)8. tua; 30 lbs. oollue. 
 
 0. 8(;:j.75. 
 7. £05. 
 
 8. 0.37500. 
 
 9. A, «tO; B, «00; 0, 9(). 
 
 10. 33. 
 
 11. $1.50. 
 
 12. $504. 
 
 13. 13004, 
 
 Exercise LXXXV. 
 
 1. £24 Os. 2d. 
 
 2. Wljeut, 40 bushols ; barloy, 
 
 00 busliuls. 
 
 3. $100. 
 
 4. 30 rods. 
 6. 00 coiits. 
 
 0. A, $00 ; B, $75 ; 0, $90. 
 
 7. $122.20. 
 
 8. 6 ft. 
 
 0. $50.40. 
 
 10. ,k. 
 
 11. $45. 
 
 12. $7188. 
 
 13. $310.10. 
 
 
 Exercise LXXXVI. 
 
 1. lOdayi. 
 
 2. $531. 
 
 3. 8 (lays. 
 
 4. $8.89. 
 
 5. 8 miles, 80 rods. 
 0. 6. 
 
 7. $79. 
 
 8. $90. 
 
 9. Each eqtials— 04 sq.rods, 9 8q. 
 
 yds., 5aq. ft. 
 
 10. 9 hours. 
 
 11. 300. 
 
 12. 82?!}J. 
 
 13. $329. 
 
 !H 
 
 Exercise LXXXVII. 
 
 1. 6 days. 7. 750. 
 
 2. 25 cents per hour. 8. 11.30 o'clock p.m. (every lOi 
 
 3. A, $027 ; B, $2090 and C, $3443 hrs. ) 
 
 4. 3^ per cent. gain. 9. 31. 
 
 5. 700 bbla., 7 gala., 2 Iba., 14| 10. 9. 
 
 oza. 11. $140. 
 
 6. Rye, 70c. per bush. ; barley, 12. $kt.40. 
 
 50o. per bush. 13. A, $81 ; B, $90 ; 0, $108. 
 
 H 
 
64 
 
 ANNWrHH. 
 
 / 
 
 Bxorolw* r.XXXVIII. 
 
 1. lOdityt. 4. $1.75. 
 
 2. 7. 6. «:m.40. 
 
 3. A, $n2.2<) ; h. «tuj, 10 ; c, n. ;;()o foot. 
 
 (Outs, «t:Uil.HO ) 
 7. I W|i..ir., ^!>'MM.MJ, :8<hil«.01). 
 lHutloy.J6fL'!»;i,;W). j 
 
 H. 18 uhIIiiiin, '2 «|iiur>ii 
 
 \). :? 17.50. 
 
 10. 24 I)iisIi..|h, 27 lb«. 
 
 11. 2381400. 
 
 12. I 
 
 l.'l. A, rmo ; n. $420 ; 0, 
 
 BxorolRft LXXXIX. 
 
 1. 3 yearn. 
 
 2. 8701.10 not. 
 .3. .'i7 IxihIuiIh, 24 lh». 
 4. 41 cwt., l« lbs. 
 6. 14 acri'8, 15 roils, H \;inls, 
 
 2 ft., :{() iiu'luiH. 
 6. A, $27 ; B, !|3t; i C, !ii!46. 
 
 7. J?7.(M). 
 
 8. *!1510.00. 
 
 0. i:u,:{H4.(M)nij«?j. 
 
 10. 0. 
 
 11. .'{ CDllts. 
 
 12. 8 por cunt. 
 
 13. Sum of quutiuntN, 437. 
 
 1. 289. 
 
 2. 00 0,414,408; (6)180. 
 
 3. 80 pounds. 
 
 4. ^270. 00. 
 
 5. $945.00. 
 
 6. 05 cents. 
 
 7. 8 per cent. 
 
 Exercise XO. 
 
 8. JiJ(M20.(X). 
 
 9. .'to anirnula. 
 
 10. $75(10. 
 
 11. First,, $21.(50; Rocond, $18; 
 third, .ii«15; fourth, $12.60. 
 
 12. $17.00 and $8.20. 
 
 13. 84 inches. 
 
 Exercise XCI. 
 
 1. £96, 16 sh., 8d. 
 
 2. 36 cents. 
 
 3. $290.00. 
 
 4. 82 do/.ou and 6 egj^a. 
 
 5. 100 acres. 
 
 6. 18. 
 
 7. A, $450.00 ; B, $400.00 ; 
 
 0, $350.00. 
 
 8. 10 per cent. 
 
 9. 45 square yards, 1 square 
 
 foot, 72 square inches. 
 10. 90 times. 
 
 11. 3.65 o'clock, p.m. for it lacks 5 minutes of 4 o'clock, p.m.) 
 
ANHWHIU fi 
 
 I 7btiO ^2 X 'i X 2 X M M 3 X 8 X ft X 7. 
 18. { HS'.»0 2x2x3x3x5x7x7. 
 
 I 44 WO- '2 H 'J X ;u :i ,' ft X 6 X 7 X 7. 
 
 Now tliK ttmolhit Huli.ftinii of fartorN which cuntninii th« 
 
 fuotitrM of ttuoh ({ivuii iiiiiiiltKf U ; 
 
 [-< (2x2x2x;iK:Jx3xf») 7)x7 >• xft|— 2«;i.n»io IJ- M. 
 
 Atui till) ifiriititif sfli'i'tinii of fitt-tor'H coiiiiiioil t«i thuntf 
 iiuiiiltnrM in; 2x2x3x3x5x7-'^ I'JiiU U.C.i>. 
 
 13. (a) 21 yuttri i (6) 9745. 
 
 ExHiciHe XCII. 
 
 1. H of a ton. 
 
 2. 1(H) ruOa. 
 
 3. 1440. 
 
 4. 1081). 
 
 6. (a) «K)48 ; [b) 112320. 
 
 6. .'K)iiiiluR. 
 
 7. iiiilutt, 240 rinlN. 
 
 8. JJJ^J^ • 44362 eliiien. 
 
 9. <li^7t».43. 
 
 10. DU^'illotm. 
 
 11. $0(1.25. 
 
 12. <^V^ ~ 12G0 ume«. 
 
 13. 8UU. 
 
 Exercise XOIII. 
 
 1. 2040 dozen. 
 
 3. « 10,000.00. 
 
 4. 37i cents. 
 
 5. 40 biUTuls. 
 
 6. 15 iicros. 
 
 7. 8748.80. 
 
 8. .1 unit's, 19145 , Androw, 8132 ; 
 
 Hol.orr, !?11U. 
 
 9. 820. 1>0. 
 
 10. 842.00. (K:^ Ctsilinji thrco 
 
 times ordinary height.) 
 
 11. 820 too. 
 
 12. 817.00. 
 
 13. 815.00. 
 
 ) 
 
 1. i^S.P.^iC.P..- ^of80y<l.s 
 
 at lOc.-~,\ of S'J.IJO 
 
 2. 7UU .sum. 
 
 3. 90 <luy.s. 
 
 4. 854.40. 
 
 5. £(31G, l,sh.:^82998.11. 
 
 6. 240 rods. 
 
 Exercise XCIV. 
 
 II, 8r)r>0 ; L, 8440. 
 
 8. $1*)5(). 
 
 \). .$27.00. 
 
 10. i?20.59. 
 
 11. .^182. 
 
 12. 11,0*8, ICO. 
 
 13. (a) 8049 ; (6) 25%. 
 
66 
 
 ANSWERS. 
 
 Bzercise XOV. 
 
 1. $405.00. 
 
 2. 84. 
 
 3. (a) Reduce them to fractions liaving a coniniuu denominator. 
 
 (f>) lifh. ('^) t'3, ,¥5. f I- 
 
 4. 4,735,008. 
 
 6. 47 times. 
 
 6. 5 per cent, 
 
 7. 8 years. 
 
 8. $16.00. 
 
 9. 87^ cents. 
 
 10. 48 weeks, 3 days. 
 
 11. 50,424,201. 
 
 12. $18.00. 
 
 13. (a) $20.75 ; (6) $9,441 + • • • 
 
 Exercise XCVI. 
 8. 4. 
 
 1. $160 ; 400 dozens. 
 
 ^' ¥8" 
 
 3. 2 miles, 263 rods, 1 yd., 2ft., 
 
 6 inches. 
 
 4. $24.00. 
 
 5. 12| per cent. 
 
 6. 14f per cent. 
 
 7. $630. 
 
 9. 2 7' G> t> Fff* 
 
 10. 14. 
 2198^1 
 
 11. 
 
 ■2813 
 
 12. Ii5 lbs. 
 
 13. (a) 25 per cent. (6) 1 2 lbs. 
 
 Exercise XCVII. 
 
 1. 2 mile.s, 99 rods, 2 yards, feet, 6 inches. 
 
 2. 87120 times. 
 
 3. $339.57. 
 
 4. A, $1014 ; B, 2535 ; 0, $3549. 
 
 5. $0.65. 
 
 6. (a) 12 acres, 80 rods ; (6) $3250.00. 
 
 7. $6624.00. 
 
 8. $26.46. 
 
 9. 7 per cent. 
 
 10. 128,755. ' 
 
 11. 4^ miles an hour. 
 
 12. $3.05. 
 
 13. A, $6.12 ; B, $5.10 ; 0, $2.^4. 
 
ANSWERS. 
 
 67 
 
 Ezerciee XCVIII. 
 
 1. $34.15. 
 
 2. 3. 
 
 3. John $507 ; Robert $42. 
 
 4. $03. 
 
 5. 35 
 
 6. $40,32. 
 
 7. $1300. 
 
 8. 5. 
 
 9. 411 miles, 200 rds, 3 yds, 2 ft. 
 10. $00. 
 
 L.O.M. -840 
 
 11. 66. 
 
 TT.C.F.=16 
 
 12. 44 n>. 
 
 13. $147.00. 
 
 Exeroise XGIX, 
 
 1. 6. 8. 3 days. 
 
 2. $85. 9. 13 acres. 
 
 3. $8. 10. S., $420 ; T., 3 years. 
 
 4. L.C.M., 10^; G.O.M., J. 11. 7^ days. 
 
 5. 12 sq. rods. ,.> /Papering, $1.70 \ .a^ qn 
 
 6. 25 pur cent. ^"- ) Painting, $22.63/ «'^*-^»- 
 
 7. A, $108 ; B, $144 ; 0, $288. 13. $91.01. 
 
 Exercise O. 
 
 1. (a) 13 (H. 0. F.) ; (6) 7176 (L. 0. 
 
 2. $17.50. 
 
 3. Product, 69,010,080 ; sixty-nine 
 
 tliousand and eighty-six. 
 
 4. 350 tens ; 475 twenties. 
 
 5. 025. 
 
 6. 10 gallons. 
 
 7. $23.37i 
 
 8. (a) $25,000.00 ; (6) $21.40. 
 
 9. 13,089. 
 
 10. 20 cents. 
 
 11. (a) I of ^ of 1 ; (6) A compound fraction ; 
 
 M.) 
 
 millions, six hundred and ten 
 
 E 
 
 n 
 
 p 
 
 (c) 
 
 A 
 
 f 
 
 
 
 
 
 
 
 B 
 
 4 
 
 G 
 
 O 
 
 12. A, $20 ; B, $60 ; 0, $20. 
 
 13. $126.00. 
 
 Finish out, dividing 
 the whole Fig. E 
 GDF, so as toshow 
 it as composed of 
 eighths; then, A C 
 D B is three out of 
 the eighth, eighths, 
 or § of whole Fig. 
 EGDP. 
 
68 
 
 ANSWERS. 
 
 Ezeroise 01. 
 
 1. ^347. 50. 
 
 2. 27 cows ; 
 
 3. 115.75. 
 
 4. 9-44+.. 
 
 8. 1180.00. 
 !?35 each. 9. $276.00. 
 
 10. 25 cents. 
 
 11. 90 cents. 
 
 5. A, $4.00, B,$3.00, C, $2.<J0. 12. A .1?<;o.OO, B $72.00. 
 
 6. 6 per cent. 13. 150 per ceat. 
 
 7. (a) Book -work. (6) A, 4 days, 
 
 B, C days. 
 
 Exercise OIL 
 
 1. 24 cents. 
 
 2. G.C.M. = 329 ; L.C.M. = 29610. 
 
 3. 20 cows. 
 
 4. 93. 
 
 5. 31 acres, 130 rods, 27 yds., 4 ft., 72 in. 
 
 6. $3.50. 
 
 ^ 7. MnltipHcafion : Ex. 42 x 73 = 73 taken 4^ times as an addend 
 = 3006. Multiplicatian is a short form of Addition. 
 
 8. $22.40. 
 
 9. 43 f J- minutes past 12 o'clock. 
 
 10. -16. 
 
 11. 7 dozeM-i-3 + 2 = 30 marbles. 
 
 12. 30 days. 
 
 13. $425.00. 
 
 Exercise OIII. 
 
 3. G25 leaps. 
 
 4. £1291, 10 sh. 
 
 1. $380. 
 
 2. 9i per cent, 
 5. 163)0 -2x3'x5»x23. 
 
 113022 = 2x 3^x7x13x23. 
 161)533 = 3*x 7x13x23. 
 
 •. L.C. M = 2 X 3- X 5^ x 23 X 3 X 7 X 13 X 3 =8,476,650 ; and GO.M. 
 
 (orH.C.F.) = 3'x23 = 207. 
 
 6. (1) A, $70.20; B, $35.10; (2^ A, $67,80; B, 
 (3) The first nioile is the better one for by $2.40. 
 
 7. 2cwt., 24 lbs. 
 
 8. 1040 dozens. 
 
 9. 1 sq. rod, IG sq. yards, 8 sq. feet, 54 sq. inches. 
 10. (a) n ; and (6) yVy 
 
 11 21 cents. 
 
 12! (a) $4.80; (h) IGJ lbs. for a dollar. 
 
 13. (a) 17 ; {b) 49. 
 
 .50; 
 
ANSWERS. 
 
 69 
 
 Exercise OIV. 
 
 1. 810 dos. 
 
 2. 6 tons, 1950 lbs. 
 
 3. (a) Integral, Prime, Odd, Abatracfc. (6) Fractional, Vulvar. 
 Proper, Simple (representing 4 fractional units whose prime unft is 
 • »ne inch). Denominate. 
 
 4. 7 hours, 15 minutes. 
 
 5. $56.51 ; Receipt : 
 
 ^.^„ ., Burnside, May 13th, 181)3. 
 
 Received from John A. Bruce, the sum of fifty-six dollars and 
 fifty-one cents ($5(J,Vff) in full payment of account. 
 
 A. B. Burns & Co. 
 
 6. 24 sq. rods, 2 aq. yards, 2 sq. feet, 24 sq. inches. 
 
 7. £15, 15s. Sterling. 
 8 
 
 9. $30.25. 
 
 10. $198.76. 
 
 11. $1.50 an acre ; 128 acres. 
 
 12. 40 cents. 
 
 13. $4660.50. 
 
 Exercise OV. 
 
 1. A, $10.00 ; B, $2.40 ; 0, $2.00. 
 
 2. 64 tons. 
 
 4. $266.70. 
 
 5. $19.65. 
 
 6. 240 trees. 
 
 7. 13. 
 
 8. 11323. 
 
 9. A, 3 miles ; B, 4 miles ; 0, 4| miles ; D, 5 miles. 
 
 10. (a) The multiplicand. (6) The multiplier, (c) When both 
 
 numbers are afts^roci. (d) {'j^t^t + t + t^^''^ l-3y4-<iv'^ 
 
 ^ ' \4x3=3 + 3 + 3 + 3=12r •"^^*=4xo. 
 (e) 6x7. 
 
 11. 1980 
 
 12. 240 barrels R.I.G's. ; 420 barrels N.S's. 
 
 13. -0138. 
 
TO ANSWBIUi. 
 
 Bxeroise OVI. 
 
 1. Q. 38984, Rem. 78 ; P. 37,050,342,912. 
 
 2. Q. 273, Rem 380. 
 
 3. A, $22.50 ; B, $24.00 , C, ^^6.50. 
 
 4. A, $3200; B, $4000 ; 0, $5040. 
 6. lOG lbs., 4 OZ8. 
 
 6. Oranges, 36 centa ; lemons, 28 cents. 
 
 7. 200 acres. 11. 65 dozen. 
 
 8. 16 bushels. 12. 3^. 
 
 9. 7 chains, 7 feet. 13. $49. 
 10. 64 cents. 
 
AVSWBBa. 
 
 fl 
 
 FIFTH CLASS. 
 
 
 Exercise I. 
 
 1. 64 and 6. 
 
 8. 192 men. 
 
 2. 159.40. 
 
 9. $1000.00. 
 
 3. 4. 
 
 10. 24 miles an hour. 
 
 4. 45 pairs. 
 
 11. 60 cents. 
 
 6. 17187 tons, 1000 lbs. 12. L CM., 45 ; H.C.F.. i. 
 
 6. 93 cents a lb. 
 
 13. 84 times. 
 
 7. 046. 
 
 
 
 Bxercise II. . 
 
 1. 64 miles. 
 
 
 2. 88cubiofeet. 
 
 
 3. $704.00. 
 
 
 4. A, $70 ; B, $42 i 
 
 0, $30. 
 
 6. 144 miles. 
 
 1 
 
 6. 70 bushels at 90 cents ; 130 bushels at 85 cents. 
 
 7. (a) 7h days ; (h) 15 days ; (c) $17.25. 
 
 8. 12 miles. 
 
 1 
 
 9. A, $40 ; B, $20 
 
 ; C, $40 ; D, $280. j 
 
 10. m days. 
 
 • 
 
 11. 45 bushels @ CO cents ; 75 bushels ® 80 cenfa. 
 
 12. 32 per cent. 
 
 1 
 
 13. 1987. 
 
 
 
 Exercise III. I 
 
 1. $373.06 net 
 
 9. $72.00. 
 
 2. 45 bushels. 
 
 107140G44 L.C.M. 
 
 3. $17.00. 
 
 10. 59292 times 
 
 4. $7.00. 
 
 1807H.C.F. 
 
 6. 7 brooms. 
 
 11. $04.00. f 
 
 6. 42 gallons. 
 
 1493382 L. CM. r 
 
 7. 30 hours. 
 
 
 345982 L.C.M. 
 
 ^^' - — 1122 and 
 1331H.C.F. 
 
 8. = 
 
 182 tiraea (1122) 2=1258884, \ j 
 
 1901 H.O.F. 
 
 13. 6ix)ns. ! 
 
73 
 
 ANSWRaS. 
 
 Ezeroise IV. 
 
 1. 21 lbs. ohioory ; 7 lbs. cutiee. 
 
 2. 04052.00. 
 
 3. 098H. 
 
 4. £300. 
 
 5. 90 X 90 = 8100 product. 
 
 6. 22ax3*x7xliaxl3-xl7xl9x2a 
 
 7. (tt) 02.88 ; (6) CO percent. 
 
 8. 20x3»x6x7"xllxlSxl7xl9. 
 
 9. 100 foot, 4 inches. 
 
 10. Green, IG lbs ; Black, 44 Ibi. 
 
 11. 9 lbs. 
 
 12. 6 per cent. 
 
 13. 2 feet, 9 inches. 
 
 Exeroise V. 
 
 1. 076.00. 
 
 2. 01875.00. 
 
 3. 01639.30. 
 
 4. 01752.00. 
 
 5. 28 sheep. 
 
 6. 0100.00. 
 
 7. 0112O.Oa 
 
 8. (a) 515 ; (6) 5 quarts. 
 
 9. (a) 225 ; <6) 330. 
 
 10. (a) 12 apples ; (b) 8 pears. 
 
 11. 0409.40. 
 
 12. 042.00. 
 
 13. 61-44 lbs. 
 
 Exercise VI. 
 
 1. 1st time, 9^ minutes past IX o'clock ; 2nd time, 22{f minutes 
 past IX o'clock. 
 
 2. With the Romans, the symbols used maintained their relative 
 values, no matter in what order they were written ; thus, IX stood 
 for 11, and was read eleven, just >'-.s XI; and XL stood for GO, and 
 was read sixty, just as LX, etc. Jheir system of notation was by 
 units, fives, tens, fifties, hundreds, etc., instead of units, tens, hun- 
 dreds, etc., as in our system, the symbols being written in that 
 order, and each one repeated in accordance with their syslcn of 
 notation — I and X might be repeated four times, but V cr D would 
 not be required to be repeated as two V'a = X, and two D's = i>I, 
 
ANawKi:s 
 
 78 
 
 etc., etc. In writing their down, place like symboln under eaoh 
 other, i.e., units under units, fivoa untlor fives, tens undtjr tens, etc. 
 
 (o) DCO LX 
 
 CC XXXX 
 DCCC XX Villi 
 
 (6) MM L XVIiri 
 
 MDCC XXV 
 
 MM CCC XXXXVmim. 
 
 CCCXXXXIlIIditJ. 
 
 (c) 
 
 MMC 
 CCCC 
 CCCO 
 CHHJO 
 CCCC 
 CC 
 
 XXXX II (d) 
 LXXXXV XXV)I\IDCCC XXV(LXX1I1 quot. 
 M CCL 
 
 XX 
 XX 
 XX 
 XX 
 X 
 
 D LXXV 
 CCL 
 
 CCC XXV 
 CCL 
 
 MMMDCCCCLXXXX prod. 
 
 LXXV 
 XXV 
 
 XXV 
 
 XXV 
 XXV 
 
 3. $7000.00. 
 
 4. 3 miles, CO rods. 
 
 5. $5070.00. 
 (>. $490.10. 
 
 7. $33.75. 
 
 8. 16 hours. 
 
 9. $5011.20. 
 10. Lose $1.. 50. 
 IL 270 8huL"p. 
 
 12. 117. 
 
 13. 233^ per cent. 
 
 1. 
 
 $20. 
 
 2. 
 
 $40. 
 
 3. 
 
 $45. 
 
 4. 
 
 $G0. 
 
 5. 
 
 $7. 
 
 6. 
 
 8 dozen. 
 
 7. 
 
 63 gallons. 
 
 Exercise VII. 
 
 8. $77. 
 
 9. 12 per cent. 
 
 10. 31. 
 
 11. A, $48 ; B, $72. 
 
 12. $05. 
 
 13. 54 cents. 
 
74 
 
 ANBWKHA. 
 
 I 
 
 1. 03^ barreli. 
 
 2. 3fi30. 
 
 3. 31 4*^7 quarts. 
 
 4. A, $200. 00 ; B, $125,00 
 
 6. 15(51 barrels. 
 0. 30 barrels, 18^ gallons. 
 
 7. $108. 
 
 Exercise VIII. 
 
 8. 81.00. 
 
 9. Principal, $350.00, tiino6 yrs. 
 
 10. (a) $1.20 ; {b) $2.00. 
 
 11. $2.00. 
 
 12. Principal, !|i'725, time, 7 yrs. 
 
 13. A, $27.00 ; B, $30.00 ; C, 
 $45.00. 
 
 EzerciBB IX. 
 
 1. $825.00. 
 
 2. $501 ).00 ; $300.00 
 
 3. $24 : $40. 
 
 4. $9.10. 
 
 5. 1444. 
 
 6. 4141. 
 
 7. 30 cents. 
 
 8. CO per cent. 
 
 9. 90. 
 
 10. h 
 
 11. $2.00. 
 
 12. (a) 15. (h) The 7th. 
 
 13. 49 yards, 2 ft., 5 inches. 
 
 1. $180.00. 
 
 2. $1.80 an hour. 
 
 Exercise X. 
 
 3. $501.00. 
 
 4. 21. 
 
 5. L.C.M. 250208595; Quotients, C043, 3285, 4095 ; Sum, 14023. 
 
 6. A, $250.50, or S} cents a lb. ; B, ^90.30, or 7t'i cents a lb. 
 
 7. 24 days. 10. A, v7400.00 ; B, 88400.00. 
 
 8. $614.50. (See P.S. arith., 11. 21 miles. 
 
 p. 88). 12. 20 days. 
 
 9. A, $600.00 ; B, $370.00. 13. 6455763577. 
 
 Exercise XI. 
 
 1. L.O.M.=289,692, 179, 960, 6. $18.60. 
 
 656, 200, 943, 335, 120. 7. $448.00. 
 
 (Test question.) 8. $420.00. 
 
 2. L.C.M. - 783,029,520. 9. 4 per cent. 
 
 3. $892.08. 10. 5 years. 
 
 4. (a) 8641 ; (6) 2801 ; (c) 98079; 11. $73.00. 
 
 (d) 707 ;(e) 6041; (/)2841; 12. 13 years. 
 
 (g) 805.6. 13. A, $1690.00 : B, $1820.00 ; 
 
 5. (a) 506 ; (6) 287 ; (c) 4547 ; C, $1960.00. 
 
 (d) 407a 
 
ANAWKR8. 
 
 75 
 
 BlzeroiBe XIL 
 
 1. $84. 
 
 2. (a)«777; (6>«950. 
 
 3. $304. 
 
 4. A, «81.76 ; B, $245.25 ; 0, $nr.4.00. 
 
 5. 6. 
 
 0. I. The iMiinbor of oijii'l parts (fractional parts) of the primf, 
 unit, I Ih. II. Till' miml)iu of f •.•ictioiiiil parts (unitji) in the 
 friiction. III. Thnt th;' [)riiiiH imit, i lb. is divided into Jire enunl 
 parts.,) the nanu; of »'iicli part . tlin » eight (in this instanco) of each 
 part or fractional unit. IV. 1 lb. V. j^ of a lb., | of a lb., j^ of a 
 II)., ]^ of a lb., (Jl of a n..) VI. The terms of the fraction. VII. 
 Yus ; bocau.su it is the nuasure of a qiuintity, 
 
 7. 6'4 iiiclios. 
 
 8. «)8,3()0.00. 
 
 9. 15 lbs. 
 
 10. A. 
 
 11. 26; 27th. 
 
 12. 18 lbs. 
 
 13. (a) (1) Write out in Ruccession, the uultiples of these nuin- 
 
 l)ers : — 
 
 24 :-~24, 48, 72, IKi, 120, 144, 108, 192, 216, 240, 264, 288, 312, 
 336, 300, 384. 408, 432, 450, 480, 5^4, 628, 562, 576, 600, 
 624, 648, e_72, 09h, 720, 744. 7(:8, etc. 
 
 42 :— 42, 84, 126, 108, 210, 252, 294, 336, 378, 420, 462, 504, 
 346, 588, 630, «72, 714, etc. 
 
 Now we see, by in.spection, the common multiples of these num- 
 bers, and of these multiples 168 is the least ; therefore it is the L.O.M. 
 
 2. Write out all the pHme factor's of these numbers : — 
 
 24=2 X 2 X 2 X 3. 
 42=2 X 3 X 7. 
 
 Now the L. C. M consists of the smallest {leciat) selection of 
 factors that contains tlie factors of each given number; therefore the 
 L. O.M. i82x2x2x3x 7 = 168. 
 
 (3). 2) 24, 42 
 
 3) 12, 21 
 
 4,7 L.O. M. = 2x3x4x7= 168. 
 
<0 ANNWr^Rfl. 
 
 (h) (I) All fh« riH'aRuroB of 
 
 (FftctofM). (Co-f/ict<»r«). 
 
 WkI, 2, M, 4, «, a 12, 10, 24. 32, 48. 0«. 
 
 240— l,2,M,4,5,r»,8, 10,12,16. lfl,20.2».:}(). t0.4M,(M),H().l20,2*<». 
 
 Now tho awirnon vu'iimiir^ aro : 1,2,M,4,»»,8, l2,lf5,24.4S, n\n\ J^S, the 
 (pva^^-.i^of tlioHi'.cnntairiHuIl thootlior nuiisuruH; lu-nco it Ih thuG.C.M 
 
 (2) Writo out (ifl ptlin*' fiict(H'» of thusu nuiubura: 
 
 })a -2 X 2 X 2 X 2 X 2 X 3. 
 240=2x2x2x2x3x5. 
 
 Now the j^rofttost Holtction (»f iiujiisiiroH (factors) common to theHu 
 mimlursis: 2x2x2x2x3=48, tho (i.C.M. 
 
 (3) 90)240(2 
 
 192 
 
 48)00(2 
 00 
 
 .*. 48 JH tlie (J.C.M. 
 
 Ezeroise XIII. 
 
 1. 900 men. 5. SinoOO. 
 
 2. 32 per cent. 6. (a) 20 hours. (6) At stnrting 
 
 3. 5 dwts., 18f; grains. point, (c) A, 4 ; B, 7 ; C, 12 
 
 4. 33 days, 18 hours. tinios round thu islund. 
 
 7. Reduce to decimals of same order, then divide as in lonu 
 division, striking out a ti<,'ure in divisor every division, instead 
 of adding to the dividend by brin<,dnct <lown additional figures : 
 
 378-7878 . . . . )31G6«()()(;()0l> . . . .(83'G Ans. 
 
 30303 o;io:iO . 
 
 13(»3(»3()36 . . . 
 113G3()3fi3 .... 
 
 22727272 ... . 
 
 22727272 . . 
 
 8. 2-71828 ... 11. 6?f per cent 
 
 9. 60 yds., and $1.50 per yd. 12. 81)§. 
 
 10. 2100 ft. by 1680 ft. 13. (a) 5 ft.. C in.; (6) F., $1200 ; 
 
 S., $500. 
 
ANMWI'IKM. 
 
 TT 
 
 id 
 
 1. 13889.00. 
 
 2. 9116(MOO 
 
 3. inolioii. 
 
 4. A, $5187.60; B, $2812.50. 
 ft. (a)H58*)fHnoz.; (b) ^'i 
 
 of an uz. 
 
 ti. 600birdu. 
 
 Bxeroise XIV. 
 
 7. $85.25 gain. 
 
 8. 20 foot. 
 0. 210 m.luH. 
 
 10. 4. 
 
 U. £10:», 4i, Id. 
 
 12. 28 rodH. 
 
 13. 11)00 aquHre yM:d». 
 
 Bxeroise XV. 
 
 1. 6 o'clock p.m. 
 
 2. 6,'^ miiiiitoa pant 7 o'clock p. in. 
 
 3. 9 o'clock p.m. 
 
 4. 40]<>4^ HocoiidH uftor 4 o'clock. 
 6. 12jY2V socoikU uftor 5 o'clock. 
 
 6. 29f I seconds after 9 o'clock. 
 
 7. 50J{3^ Huconds uftor 1 o'clock. 
 
 8. 51,Voi^ hccoikIh after 2 o'clock. 
 
 9. First time, o2A niiiiiitoH after 8 o'clock 
 
 lainutos after 8 o'clock 
 
 10. 6 minutes too fast. 
 
 11. 6 minutes too alow. 
 
 second time, 64 ,", 
 
 12. 9 miles. 
 
 13. 24 minutes. 
 
 Exercise XVI. 
 
 1. 8 lbs. 
 
 2. 26 per cent. 
 
 .3. 6 miles, 110 rods. 
 
 4. .33.^ per cent. 
 
 6. 20 per cent. 
 
 8. 12 per cent. 
 
 9. 40 cents. 
 
 10. 12 rods. 
 
 11. (a) 1842 11)8., 4i9ff oza. (6) 9s<|. 
 
 ft., 90 «q. in. 
 
 6. (a) B's time i.s to C'h time as 12. Gr;ipos..930 00;ai)ples,$40.(:O; 
 
 14:9 (6) $1120, B's gain. cherries, 1^50.00. 
 
 7. UH per cent. 13. $40.00. 
 
 Exercise XVII. 
 
 1. $11,520. 
 
 2. $180. 
 
 3. 18 acres, 120 sq. rods. 
 
 4. 30 children i)urpo.sed going 
 
 and 15 went. 
 
 6. 10 lbs., 2 ozs. 
 
 G. 11 J per (jent. 
 
 7. $18,V 
 
 8. 25 per cent. gain. 
 
 9. l!) per cent. 
 
 10. 24000 bricks ; and 
 
 11. G boys. 
 
 12. 7033 and 9197. 
 
 13. $4800, 
 
78 
 
 AKMWlCltg. 
 
 KxfiriHo XVIII. 
 
 1. :(00»((nllonM(or M7i l>bU.) H. Ilult iumI Imlf; or 50 p^r cont 
 
 3. L9. liiiiiHly. 
 :», 170 M I vjl.'.MHn.O.M. U. ««H.M(> 
 
 4. 8 livuriit^ii imm. 10. ^loOH r»«). 
 
 6. 'I'lu) circuirMMiM, by $2. 11. A, i^lHO ; H, $'JiO. 
 <1. 7i K'^ll**!)*** I~- 1'^ iiiclioi. 
 
 7. .'(Oi( c.iiU a liiiHli., 30}^ IbM. la. U bulk 
 
 pur biixli. 
 
 Exercifle XIX. 
 
 L 
 
 12 pnr coiit. 
 
 
 8. 
 
 .'185 I'ord*. 
 
 
 2 
 
 *2(l".»7r>. 
 
 
 0. 
 
 ^'lo. 
 
 
 :{. 
 
 Oij p««r cunt. 
 
 
 10 
 
 #1000 M.; 
 
 ^(WWl W.; 8IH0 B. 
 
 4. 
 
 .'i liouiH, rt mill., nSjVo '*"'-'• 
 
 11 
 
 10 pur CPU 
 
 t. (liN(!ount. 
 
 5. 
 
 (\iNh, by .*(."»n. 
 
 12 
 
 . H pur cuni 
 
 iiu fi)iiiicran<l I0 
 
 0. 
 
 87^)1*0, H. of 
 
 <'. St«)ck. 
 
 
 pur cunt, on lutt(>r. 1 
 
 7. 
 
 A,«7r>(»; n, 
 
 *L'(M); U, ^.Ur, 
 
 ; 13 
 
 . (a) 70 cunts ; {b) 450. | 
 
 
 I), «I00 ; K, 
 
 «flilO. 
 
 
 
 
 
 
 Exerci 
 
 se ; 
 
 XX. 
 
 • 
 
 1. 
 
 87776. 
 
 
 8. 
 
 13 yojir.M. 
 
 
 2. 
 
 «6i. 
 
 
 9. 
 
 3: 1. 
 
 f 
 
 3. 
 
 $:i2,ooo. 
 
 
 10. 
 
 20^ niin.,28]( min. | 
 
 4. 
 
 $36. 
 
 
 11. 
 
 Jii<50.00. 
 
 
 5, 
 
 1001 hi. 0)45 
 
 cts. ; 100 lbs. (?J) 
 
 12. 
 
 '[\>U\Cum. 
 
 ^715.00; No. l.bls. 
 
 
 6(» ctH. ; 
 
 ;iOO lU. @ ItOc. 
 
 
 rt'Miitt 
 
 od, 4147. 
 
 fi. 
 
 £(;, «.sh, 6a. 
 
 
 13. 
 
 21 CO ballB. 
 
 
 7. 
 
 :{0 cHNks. 
 
 
 
 
 
 
 
 BxerciBe XXI. 
 
 
 1. 
 
 (ft) Town clock 15 minutes slow 
 
 ; Pnd (6) 10 
 
 inilua. 
 
 2. 
 
 75 bushels. 
 
 
 
 
 
 3. 
 
 40 yards. 
 
 
 
 
 
 4. 
 
 3 foot (loop. 
 
 
 
 
 
 5. 
 
 13 iiiiiuittis, 
 
 52^ seconds. 
 
 
 
 
 0. 
 
 25,000. 
 
 
 
 
 • 
 
AN^Wlim, 
 
 7 l>.'.r..V2l7nOI.Ti>i;U:M'JfT«>«rt (\ tho f.Mirth roirmin.lnr. in J ..f \i 
 tliu Ni>(*«tiiil i'l'iiiruiiiltti ; tlii'irfonf \ i>f i(, rliM tlm-'t hitriil>««r in <|iio< 
 Hunt, ia '2 wlutlt in I ho intki li ; ti** to Ni<t •lowii itt iJii'«|iii)ti«iii, uU).; 
 
 8. A, *l()2*-'0. \\, IfMii), 0,*5i.75, aad D, ^\n.2o. 
 
 U. <)«;oi»iinil r<7>'i(>, lOHpoctively. 
 10. A. :!«n70; n, K? 12.00. 
 
 12. I. 
 
 I:J, (a) «l iii-l ^'\:20 rMHjHvUvftly. (M Mari'i mto?* mll'Hon I i. 
 
 btiuiiiuH I'uto 2^ liiiluHttii littitr. 
 
 Ezoroifio XXII. 
 
 8. HI to. 
 
 9. (a) :{|'J7MI.u1Im; (6) ^g**, of 
 
 1. $25. 
 
 2. 25 yHnN. 
 .'l. 2»;0^ yiiiiln. '^""'''• 
 
 4. Khnclios. 10. 2H50. 
 
 5. Iji |MM'(;«'nt. (or 81 a sinrc). 11.2 iiiilos an liour. 
 0. 270.<H (ubioinuhes. 12. IkiIIh. 
 
 7. i. lU. A'h, by «l4«iO.(M). 
 
 >. 1.1.1.4. 
 
 Exercise XXIII. 
 
 1. 1140. 7. 20:j ciihio yards, 19 cui.iofoet, 
 
 2. «iOir» KMllonH,2q.i.irtH,l pint. 8. H.:\4\, 
 a. 441 boxo8. 0. i 
 
 4 $'Mm wholti profit and i^'JK'.O 10. 4 cwt., 10 !I)R., 2^ oza. 
 
 B'HHlmro. II. .^<;!H. 
 
 6. (a) 80 cuts ; (6) 77^ coiits. 12. .i?20(;55.00. 
 
 6. 41 gallouti. 13. 3 cubic fout, 5l4oul.io inoheB. 
 
 Exeroise XXIV. 
 
 6' («) A- (N.B.— Tho «if7a of the nutnorator and denominator 
 of tho traction, r(.5[)rosontiii>4 tho siii)|.l.' inttTosi, tot nix thu tlciionii- 
 natof of thf fraction roproHoiiimu' tlm tiiio discount.) (6) $40.>.75 
 simple interest. 
 
 7. (a) *20; (;/>)8l; O')*!, 
 
 8. SSO-!. 
 
 10. .^!)l.!t2a^.,. 
 
 11. 'ik years. 
 
 9. 6yrs., 7.3 days, and per 12. 5 i)er cent. 
 
 cent. 
 
 13. $420. 
 
80 
 
 ANHWKItS. 
 
 Exercise XXV. 
 
 1. 2240. 
 
 2. 2 hours, 30 minutos. 
 
 3. 6 IbH. afc 6 centH, (> lbs. at 8 cents, 3 lbs. at 16 cents, aud 2 lbs. 
 lit 19 cents (other ssots of answers may bo got). 
 
 4. $80 first, and $120 second. 
 
 5. $404.20. 
 
 6. A, $300 ; B, $270 ; 0. $240. 
 
 7. 50 cents a lb. 
 
 8. $10. 
 
 9. 35 miles an hour. 
 
 10. $547.50. 
 
 11. 120 Iba. 
 
 12. 16 and 25. 
 
 13. 88 yards. 
 
 Exercise XXVI. 
 
 
 1. $1600. 
 
 
 8. :^ of cost (=7?7S. p.). 
 
 2. 12 per cent. 
 
 
 9. 25 per cent, (or ^ bf cost). 
 
 3. $330 and $1320. 
 
 
 10. $144. 
 
 4. $2703 and $8109. 
 
 
 11. 4,V per cent. 
 
 5. $2090.90 (or $4.185»^ per bbl 
 
 ) 12. 3^^ per cent. 
 
 6. $5520. 
 
 
 13. (a) $186. 60 J; (6) 24 days. 
 
 7. A. 
 
 
 
 
 Exercise XXVII. 
 
 1. 150 feet. 
 
 
 4. 3657i 
 
 2. $1125. 
 
 
 6. 1 per cent. ; 80 cents on $100. 
 
 3. m- 
 
 
 6. $180. 
 
 7. 91 yards. 
 
 8. (a) -0047619 ; (6) -142857 ; (c) The nature of the denomi- 
 nator of the vulgar fraction to which it corresponds. If the denomi- 
 nator is made up of no other factors than 2*8 and 5'.s, the decimal 
 will be finite ; if either 2 or 5 with other factors, it will be a mixed 
 repetend ; if neither 2 nor 5, it will be a pure repotend. {d) Finite 
 ileoimals ; and pure and mixed repetends, 
 
 9. $28,350.00. 
 
 10. $34.32. 
 
 11. 437 reams, 10 quires. 
 
 12. 4 per cent. 
 
 13. (a) 24.75 ; (6) 36 ; (c) 4213 ; (d) 2807 ; (e) 5004 ; (f) 7610. 
 
ANSWER!). 
 
 Exercise XXVIII. 
 
 1. L, 24 ft. ; B, 18 ft. ; H, 9 ft. 
 
 2. (a) $837.00 ; (6) 22|| per cent.; (c) 21? 
 
 3. 1202.00. 
 
 4. 7 feet. 
 
 5. 8|. 
 
 6. $5293.60. 
 
 7. 260 sacks ; 20 cents. 
 
 8. $1)46.80. 
 
 9. 19 cub. feet, 668^ cub. mohe«. 
 
 10. $9000. 
 
 11. $2500 @ 5 per cent. ; $3500 @ 7 per cent. 
 
 12. (a) 36^1 niin. past 7 ; (6) 42 min. past 7. 
 
 13. A, 60 ; B, $75 ; 0, $50 ; D, $30 ; E, $20, 
 
 81 
 
 per cent. 
 
 1. 5 per cent. 
 
 2. $1400. 
 
 3. $2060. 
 
 4. $22. 
 
 5. Gained $105. 
 
 6. Gained $75. 
 
 7. 6400 bushels. 
 
 Exercise XXIX. 
 
 8. $600. 
 
 9. 89°40'. 
 10 $600. 
 
 11. 900 barrels. 
 
 12. 5 per cent. 
 
 13. 6 per cent. 
 
 Exercise XXX. 
 
 1. (a) £5, 8sh., 9d ; (6) $1.00. 
 
 2. 8703 square yards. 
 
 3. $1.00. 
 
 4. 1 square foot, 81 sq. inches. 
 
 5. 8 per cent. loss. 
 
 6. 13 sq. rods, 26 sq. yards, 
 2 sq. feet, 35 sq. inches. 
 
 7. 6 sq. rods, 5 sq. yds., 6 sq. ft. 
 
 8. 2 sq. rods, 19 sq. yds., 2 
 
 ft., 116 sq. inch 
 
 sq. 
 
 9. $159.25. 
 
 10. 15 metres. 
 
 11. $9000.00. 
 
 12. $602.98. 
 (a) 39 sq. rods, 11 sq. yds., 
 138 sq. inches ; (b) Product. 
 478,687,021,724,583,756; quo- 
 tient, 53,693,500,996. 
 
 13 
 
 1A« 
 
82 
 
 ANSWKUS. 
 
 Exercise XXXI. 
 
 1. 25 lbs. for )i dollar. 7. HOSO-? foet. 
 
 2. (1) 45 tons ; 535^ bushels. 
 
 (See P.S. Arith. p. SS). 
 .'1 171 cwt., 92 lbs., 7 0Z8. 
 4. 8^ barrels. 
 6. 250 acres. 
 
 8. 216if barrels. 
 
 9. $126, 
 10. $18,900. 
 11. 
 
 12. 14 gallons. 
 
 6. 6840-S-d=-855. 
 
 iS. (a) 15 cents ; (6) 792 yards. 
 
 Exercise XXXII. 
 
 1. $38.50. 7. 06. 
 
 2. 13. 8. 72 gallons. 
 3 18. 9. 9^ years. 
 4. 34 lbs., 11 ozs., 14 dwts., 10. $126. 
 
 9grs. 11. $4800. 
 
 6. 1620 lbs. 12. 50c ; ^percent. 
 
 6. $26.25. 13. -923076. 
 
 After the first division we have 3 as reinaindor, which is one-fourth 
 (jf 12, the numerator of the fraction ; now, complete the repetend 
 from this point by reducing cacli remainder to tenths of the next 
 lower order and dividin;< by 4, e.y. : — 
 
 \^ = '9, and 3 as remahider ; now 3 is ^ of 12. 
 ^ of 9 (first figun; in u.;cimal), etc. 
 = 9 .^ 4 = a and 1 over,— 10 x 1 + 2 = 12. 
 12 ^ 4 -= tJ and over,— 10 x + 3 = 3. 
 3 + 4^0 iin.l 3 over, —10 x 3 + = 30. 
 30 ^ 4 = 7 and 2 over, -10 x 2 + 7 = 27. 
 27 -i- 4 — e and 3 ovtr,— 10 x 3 + 6 = 36. 
 36 H- 4 = 9 and over, etc. 
 Dec. = •9230761)2, etc. 
 = -923076. 
 
 (N.B. — The operation should be performed mentally.) 
 
ANHWKIIS, 
 
 S3 
 
 irda. 
 
 I 
 
 Exercise XXXIII. 
 ^' ^22(M). g^ 30034 .^(^,„^re root. 
 
 2- ^1040. 9. a^^ . Kern. = Divi.lend - 
 
 3. 42!; percent. (Divisor x <.<|u..tiont.) 
 
 4. Focal elite, Af)ril 0, 1887 ; 10. 15 rods. 
 
 Bal. due, Jan. IGth, 1887. II. $1742.25. 
 
 6. 40()0 barrels. 12. 280 dozons. 
 
 6. 20 per cent. 13. $19(].37 per acre. 
 
 7. £40, 10a., 6d. 
 
 Exercise XXXIV. 
 
 1. $1200. 
 
 2. B, $1200 ; 0, $1700. • 
 8. $14400. 
 
 4. $98.55. 
 
 6. 25 per cent, discount. 
 
 6. $280. 
 
 7. 28 lbs., loz., lOdwts. 
 
 8. 16 boytj. 
 
 9. $48.44. 
 
 10. ni; ( vvt., 15 lbs. 
 
 11. G a(;res, 28 aq. rods, 15 sq. yds., 
 
 1 sq. foot, 18 sq. inches. 
 
 12. 93|. 
 
 13. $6.00. 
 
 fourth 
 )eteTid 
 ) next 
 
 Exercise XXXV. 
 
 1. 29i^ per cent. 
 
 2. June 17th, 1893, 
 
 3. $5915. 
 
 4. $81.25. 
 
 5. I per cent. 
 (). 53f cents. 
 
 7. 303 lbs., 12 ozs. 
 
 8. $350. 
 
 9. 4vMba. 
 
 10. 1188. 
 
 11. 225 miles. 
 
 12. $820; $H-2m. 
 
 13. $300 first ; $240 second. 
 
 Exercise XXXVI. 
 
 1. $108.64. 7. $1012.^0. 
 
 2. $20,00); $225,000. 8. 46 and 40. 
 
 3. $990. 9. $79.50. 
 
 4. Bal. due Nov. 25th, 1892. 10. 90 cents. 
 (Focal date, Dec. 0, 1892.) 11. 72. 
 
 5. $1600. 12. 180.96. 
 G. $10,000. 13. $3930. 
 
84 ANSWRRS. 
 
 i 
 
 EUeroisd XKKVII. 
 
 
 1. $490. 8. «3. 
 
 
 2. 2 oza., 2 dwt., U grs. 9 8108. 
 
 
 .*{. $103.56. 10. 2 Metres. 
 
 1 
 
 4. 25 times: a hours, 30 min. 11. l."):! M., (» dm.; $116.20. i 
 
 5. $62.02. 12. 1 OS 10751 K> 1841269. l 
 
 
 6. 1400 iiiile.s. 13. $'J0O. 1 
 
 i 
 
 7. 020002667306849580698412. 
 
 Exercise XXXVIII. 
 
 9. Compound Rules ; 1 oiibia 
 
 metre (volume or capacity)* 
 1 gramme (weiglit), or capa- 
 city! weight! il cu. cm. ilg. 
 
 10. 400. 
 
 11. I47-754 interest; $297*764 
 a)iiount. 
 
 1. $1.00. 
 
 :.. -2449786837 138s268849206:i. 
 
 3. $960. 
 
 4. A, $80 ; B, $120 ; C, $160. 
 
 5. 1 Kl., 4 111., 5 Dl., 2 L.; 
 145 Mg., 2 Kg. 
 
 6. $2475. 
 
 7. 5 Dg.,7 G.,9dg., 2 eg., 1 mg. 12. 23. 
 
 8. 68 Kg. 13. $1560. 
 
 Exercise XXXIX. 
 
 1 . 130 acres, 
 
 2. Diminished by 36%. 
 
 4. 3. 
 
 5. $455. 
 
 6. A, $3900 ; B, $4950. 
 
 7. $1.20. 
 
 8. 40 shares. 
 
 9. £45, LOah., 6d. 
 
 10. $1.20. 
 
 11. 6ij%. 
 
 12. 7h%- 
 
 13. $700. 
 
 Exercise XL. 
 
 1. A, $1200 ; B, $1500. 
 
 2. $862.13. 
 
 3. $1500. 
 4. 
 5. 
 6. 
 
 7. $6.00. 
 
 8. 44 yards. 
 
 9. (a) 16^^ min. past tx 
 lb] 
 
 80% gain. (b) 24 
 
 (ft) ^ (^) h (c)i^2V 10. 48 min. past vii 
 
 $1140.88 (or using 25 qts. to 11. (a) 2 pks. 1 gal. 
 
 the cub. ft., which is prac- (b) 4 days IM\ min 
 
 ticallv wrong for grain, the 12. 7%. 
 
 answer would be $1120). 13. $810. 
 
oil bio 
 
 ity)- 
 
 capa- 
 I7-764 
 
 AN8WEKS. 
 
 Exercise XLI. 
 
 1. 12 lbs., 8 lbs., 32 lbs., ivspeccively. 
 
 2. G.Muitl 1430, 130 and 715. 
 
 3. 13 
 
 4. I(jblb8.,2501b8. 
 
 sr^ 
 
 5. (a) 
 
 pie ilt}T'''^^^' 
 [{b) Improper. 
 
 1. Sim 
 
 1. Vulgar 1 2. Mixed. 
 
 3. Cuiiipouiul. 
 
 [4. Complex. 
 
 fl. Finite decimala. 
 
 2. Decimal J 2. Pure Rep.. tends. 
 
 l3. Mixed Rejieteiids. 
 
 1. Vulgar 
 
 (b) (I.), lA; (u.), ^, ; (rir.), ,4.^ ; (IV.), | ; (v.), .42651. 
 
 ^2;Kr;l^r^^'^^-'^^'^'^- 
 
 3. Compnund : ^ of rf*. 
 ^^^ J 4. Complex : iji. 
 
 1. Finite decimal : '025. 
 
 2. Mixed Repetend : '138 and -426.^1. 
 
 3. Pure Repetend 
 
 2. Decimal 
 
 •2«>. 
 
 6. Lumber $34.65, Posts $13.00, Labor 
 
 7. 272 barrels ; and 72 minutes. 
 
 8. 30%. 
 
 9. 280 twenty-fives, 720 tens. 
 
 10. 91 and 161. 
 
 11. $8018.75. 
 
 12. A, $152 ; B, $12 ; C, 
 
 13. 40 feet. 
 
 $7.35 ; Total ^66.00. 
 
 L 25625 and 10250. 
 
 2. 6i%. 
 
 3. 290 rods. 
 
 Exercise XLII, 
 
 5. A, $280.80; B, $646.00 ; 9 96 
 
 C, $458.64; total, $1285.44. 10 •>o°/ 
 
 ?• B, 5 25%. 11. 60 dozen. 
 
 7. o40 acres. 12. A 
 
 8. $321.36. 13' 2'feet 2 inches 
 
HCi 
 
 A NSW Kits. 
 
 I. 
 
 'i. «< 
 
 4. 
 
 6. 
 
 12. 
 
 I. 
 2. 
 
 3. 
 4. 
 
 (i. 
 
 7. 
 
 8. 
 
 0. 
 10. 
 11. 
 
 Exercise XLIII. 
 
 A'r, 200 ; lis. .<«:)( 10. G. duvs. 
 
 (r/)0'jM((. ft-,. 102 .s.|. iiicli.-s. 7. $147.84. 
 (b) 7cu. ft. 1254 011. ill. lies, 8. *iMK 
 120 of fill iii(!ivuso. 0. !M). 
 
 :{feut. 10. 78125. 
 
 75%. 11. 7. 
 
 lOtK? s(|. 3:ir.lH. 4 Hr|. ft. 72 s(). inches, 
 (a) 4121-412(10) t- 1. 
 
 = -^ 4l(lO)-f-2 [-(1.0)4-1. 
 
 = 4l(l(»)-'+2 10) + 1. 
 
 ==4 ; ^IO) + l ;-( 10)2+ 2(10) + 1. 
 
 r-^4 lO)' f I(10)'-i+2(l0) + l. 
 
 -4121. ^ 
 
 (/>) 4121-^515(8)+!. 
 
 = ■> 04 8)}-;; ;-(8) + i. 
 =(;4(8)- + :{(8j + i. 
 
 = -; 8(8) + 0^8)-+ 3:8) + 1. 
 = 8(8)'i+0(8)-+:)(8) + l. 
 = 8031. 
 
 Exercise XLIV. 
 28 miles. 
 
 One parh 142, fciie other 8. 
 *10(H). 
 355057 03125. 
 
 ^B, $3.00 '^ 
 
 P, $9. 07 U- $15. 00 total. 
 IR, $1.0r,]j 
 
 24%. 
 
 lolimf I!''- '^'"^'■']-=«736| lbs. in all ; or 3 tx)n8 736 lbs. 
 1 20491 lbs. slate, J lo ozs. 
 
 A, $1.00; 13, $.3.00. 
 
 
 (a) 3 ; and (b) 484 '84. 
 
 24 ft. 
 
 $8500. 
 
 12. $53.29. 
 1.3. 80 planks. 
 
 Exercise XLV. 
 
 i 
 
 1. 6. 
 
 2. 25 .\ lbs. to the cub. ft. 
 
 3. $ii92.32. 
 
 4. 1.3. 
 
 5. i?8070.00. 
 
 0. The latter ; $5 gain. 
 
 7. $1.00. 
 
 8. .«10350.00. 
 
 9. 40 feet. 
 
 10. $77.50. 
 
 11. $22.50. 
 
 12. 7. 
 
 13. 200. 
 
I 
 
 I. 
 
 2. 
 :{. 
 \. 
 5. 
 <). 
 7. 
 
 
 
 A NSW K lis. 
 
 
 Exercise 
 
 XLVI. 
 
 A, ^'JHOO ; B, $4200. 
 
 
 8. !i<:u;. 
 
 .«;{r.o. 
 
 
 
 9. $U\QO. 
 
 mm 
 
 
 
 10. 48 llw. 
 
 lL'474 H([. inches. 
 
 
 
 II. ic«.'U5.«0 
 
 IS"/ 
 
 
 
 12. $5243. 
 
 22 iiiiimtes. 
 
 
 
 13. 406. 
 
 )i!$926. 
 
 
 
 
 67 
 
 >8. 
 
 Exercise XLVII. 
 
 4. 
 
 5. 
 
 6U%; 12J%. 
 
 6125. 
 4 (luys. 
 *10840. 
 $150. 
 
 r(a) .^7.00 bill. ^ ^,^_ ^ 
 
 I (/>) .70 discount off. Ifr ™ ■^'^^' ®^<'-' see P.S.A. papres 
 
 J56 
 
 and 57. 
 
 /. 
 
 8. 
 
 9. 
 10. 
 11. 
 
 12. 
 13. 
 
 (c) $6.30 cash. 
 $VXV.)0 
 $3000. 
 419. 
 Gained $2.73. 
 
 51480 2x"2x2x3x3x5xll y 13 
 3346200 2 X 2 X 2 X 3 X 3 X 5 X .-. X n X 13 X 13. 
 
 (i) L. 0. M. = 2 X 2 X 2 X ;5 ":{ x 5 x 1 1 xTi x 5 x 1 3. 
 
 G.C.M. 2x2x2x3x3x5x11x13 " " 
 (ii) Qu()fient = 5xl3. 
 
 (iii) Quotient = 2 x 2 x 2 x 3 x 3 x 5 x 11 x 13. 
 o. 
 
 12. 
 
 Exercise XLVIII. 
 
 1. 
 
 »> 
 
 w. 
 
 o 
 O, 
 
 4. 
 5. 
 6. 
 
 $1500. 
 
 (a) 87 .V cents ; (h) $712.80. 
 
 A, 200 acre.s ; B, 300 acres ; 
 
 C, 450 acres ; D, 600 acres. 
 
 8160 lbs. 
 
 $6.25. 
 
 $300. 
 
 7. $37500. 
 
 9. $15015. 
 
 10. 45 \ urds, 
 
 11. $:u'5. 
 
 12. 3 minutes Hi seconds. 
 
 13. 13%. 
 
88 
 
 ANBWKRJi 
 
 Exeroise XLIX. 
 
 1. an. 80. 
 
 2. (a) 1,'4 .•icrcs, 47 n<| r<»«ls, 18 
 Bq. yds., \i n(\. ft., 'M\ hij. in. 
 (/>) 7'><1<M» |.lunk,H. 
 
 4. £•;{. lS.^liilli||;fH. 
 
 6. 6<i] cents ; and (5^% ^o^s. 
 
 7. #107.50. 
 
 8. li^'JfL'.uO. 
 ••>. 'J8i''/j. 
 
 10. '.i'2 iviits. 
 
 IJ. 2() t. „t. 
 
 U. 30. 
 
 13. (a) ^li2000; {h) 15 yardH. 
 
 V 
 
 Exercise L. 
 
 1. •i<i«;f5r)r,752. 
 
 
 8. $8250. 
 
 2. /'2 and iJ. 
 
 
 9. 07„. 
 
 3. 5<)7. 
 
 
 10. 4. 
 
 4. 2720 11)3. 
 
 
 11. 3 days. 
 
 5. !i?l440. 
 
 
 12. 33i /,. 
 
 0. 26contfl. 
 
 
 13. 12 inches. 
 
 7. 46 feet. 
 
 
 
 
 Exercise LI. 
 
 1. $4.00. 
 
 
 8. $1000.00. 
 
 2. 50% ; 37n. ; 
 
 and 12^7,. 
 
 9. $-077.00. 
 
 3. S2:;51.00. 
 
 
 10. 72 cents. 
 
 4. $«3r)0.50. 
 
 
 11. Vr 
 
 5. 110.50. 
 
 
 12. $75.00; I 
 
 0. $9.45. 
 
 
 13. $5000.00. 
 
 7. $11200.00. 
 
 
 
 Exercise LII. 
 
 1. 40 biishel.s in all ; bailey 6 
 bnsliols, rye 20 Imshels, 
 corn 15 husliels. 
 
 2. 12 lb.s. 3 OZ.S. 
 
 3. 8 hours 20 minutes. 
 
 4. $250.00. 
 
 5. 8 d.iys hours. 
 
 6. S., ;;J2«00; C, $4200. 
 
 7. $4.80. 
 
 8. 50 pairs shoes, 112 pairs 
 boots, 108 i)airs slippers. 
 
 9. 125 barrels. 
 
 10. 10 ft. () inches. 
 
 11. 38 cub. ft. 804 cub. inches 
 
 12. $045.00. 
 
 13. March 27tli, 1894. 
 
Ih. 
 
 "),iirs 
 
 '8. 
 
 les. 
 
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