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Ne« York 14609 USA i^a (716) 482 - 0300 - Phone SS (716) 5989 - Fax PJtl \ "F TTT TT- c ^ ^z-''^w^'ii-'': c^st -mzXI I ] ^ «! <^'«fle ^- <£o • 4H»thfmatiial ^e rud. 3 PRACTICAL PROBLEMS akitttmet: j r«»R THK I'MK «ir StNIOR C vSSHS IN THH PUBLIC SCHOOLS AHD MOKK KHPWIAM.V FOK THK rsK o. C.VM.IIUTM PRKPARINO FO.t KXAMINATI0N8 >r G. J. McCORMAC In^ptctor of P^UUic Srhoo/.,, Prince I'.h, ,nl hland. TORONTO : W. J. GAfJR .t COMPANY, L.m.trd 1902. •Jx f : ■ J M ■ ' Entered according to the Act of Parliament of Canada, in the oflSce of the Minister of Atrrirulture, by W. .T. Gaok \ Co. (Limited), in the year one thousand nine IiuiiilriMl ami . wo. PREFACE. AuiTUMKTic, it seems, is the subject which receives the lion's share of attention in tlie majority of our public schools; yet it is doubtful if the results attained are what they should W An old criticism on Arithmetic as generally taught in schools is tliat the work being done is only the guessing of so many riddles; that the pupil learns the rules in order to perform "a set of sums," and having learned "the trick" he hastens "to cipher out" all the problems under the formula in the same mechanical way. Certainly, there is in many schools glowing up a schoolisli dexterity in manipulating figures and finding answers, to the neglect of a proper undei-standing of the principles, or even the meaning, of figures. All the work given to the arithmetic class should be practical. Jt should be for the most part arithmetic dealing with the real affairs of life, rt should be presented in as interesting a manner as pos- sible, and the pupils should be required to direct their attention more to things and their relations and less to the figures used iu the soluti.m. Clear, logical and complete explanations of the method of solution of every problem worked should be given by the pupils. IV ntEFACE. It was at the urgent request of sorue of the leading teachers of Prince Edward Island that I compiled this little work. I have endeavored to give a great variety of problems, and also to have them as practical as possible. Those parts of arithmetic which have not been receiving due attention in our schools I have emphasized. My thanks are due to Alexander Anderson, Escj., LL.D., Chief Superintendent of Education for P. E. Island, for many valuable suggestions given me while engaged at this work, also for his kindness in revising the complete manu- script, and assurances of his approval of the Problems for use in the public schools of Prince Edward Island. G. J. McCOllMAC. Chakloitktown, P.E.I., January 2, 1902. 'n^m i^m^is^'i-'-m-^'m COKTENTS. Oraded Problems Miscellaneous . puoi'oution . Interest and J'eiuentaok Fractions . Present Worth ani> J)is( Stocks Mensuration Decimals . Problems Helatino to W Profit and Loss Taxes and Dutiks Square and Cube Ivoots Measurements . Exchange . Stocks Sharing and Partnershii' Answers »unt >UK page I 72 73 74 7«) 77 71) 82 Ki Si) 8(i S8 89 !K) 91 92 94 PRACTICAL PROBLEMS IN ARITHMHTIC ^ 1. A swimmer tukes 22 strokes a i„i„ute, aixl goes -i yards eacli stroke. IIou- l<.ng does it take liim to NW'im three-(iuarters of a mile? 2. The total area of three estates is ;j,:,;](J aeres If the areas v,i the two smaller estates be resiu-etivelv three hfths and two-thirds that, of the largest, find the "acreage or each. ° 3. When a person is 21 years old, what is his age in seconds ? 4. Wluit is the simple interest on 22 cc^nts for IT) ye-irs at 5^ % ? . ' ' ' 5. Find the value of ? ot £:> 7s. ] Id. + ^ of £20 r>s. 9^d. - -\.^ of £1 1 12s. Gd and reduce tlie result to the deciuial of a guinea. 6. How many demijohns, ench containing 2 gals .'] c.ts 1 pt., can he filled from a tank holding 14:3 gals '] ots' ot w4ne ? to 1 • • 7. If a room is 20 feet long and 16 feet wide, how many square yar.ls of plastering are there overhe.-nP II..W nmny yards of carpet 4 yd. wide will cowr the floor y 8 Pkactk'al Proj5Lemh in Arithmetic. 1. Simplify 2. A inuu failed in })iisiness, owing .1 $1400, ]i $4G00 and C $2000. Tho ca^li imxvcds of lii.s estatt/a.v $500o' 1I..VV inn..h can lie pay ou the dollar, and what anioi.nt does 7> receive ? 3. Find the area of a rhoinlioid whose length is 10.52 chains, and height 7.03 chains. 4. How many small ciil)es, a side of which is 4 inches, may be cut out of a large cube wliose side is 8 inches ? 5. Wluit is the cost in Montreal of a sight di-aft on Hahfax for $2000 at a discount of i| % ? 6. AiTange in order of magnitude : i) « ; a ; 2iV-25;4|of 1 1 + 1|. 7. If 10 sheep or If, lambs can eat 40 bus. of turnips in 7 days, how long will it take G sheep and 18 lambs to cat 30 bus. i 8. Two settlers in All)erta own adjoining farms of 300 and 5'^0 acres respectively. Th. unite their farms, tak- ing at tlie same time an additional partner, who pays them $1000, on the understanding that a third share of the land m future sliall belong to each. How is the $1000 to be divided between the original owners? 9. If the planet Mercury moves at the rate of 111000 mUes an hour, how fai- would it move in a year ? 10. Subtract .057 of 2 acres from 7.042 of 1 rood, and express the answer in square yards and the dccimol'of a square yard. on Practical Problems in Arithmetic. 9 1. IIow many childn'n can bo ncpominodHtcd in a w'hool room 27 ft. wide, Dd ft lonj:, ft. high, if loO cu. ft. of air shouhl bo aih.wi-d for each child? 2. Of two watches, ono h)ses 5 seconds and tlie other ji:alMs4 seconds in 12 honr.s; they are both corr«"ct at noon on a certain day; when will ono be 5 minntes l)efore the other, and what time will each then show? 3. Wliat percentage of the h-tters are vowels in the followingsentence:— "Anthmeti(! is the science of num- bers and the art of computing them"? 4. Divide .204 by .2; Vm:2--> l)y 24.:}; .*J7r>2.;j by 1(K)()()0. 5. Find tluA Present Worth of $.100 for 19 mcmtlis at HZ- G. How often must one go round a square field of 10 acres to run a mile ? 7. Find the proceeds of a note for $186 given for I] month.s and discounted at the l)ank the day it was made at 6% per annum. 8. Simplifv ^-^r ^-^^ ^ ^ " 9.7-6.4 9. If £1 sterling be worth 4.1 Pauls 9 Baiocchi, and be worth 2.")^ francs; show that a Napoleon of 20 francs equals 36 Pauls (10 Baiocchi = 1 Paul). 10. Reduce 11 ro. 11 pr. 11 yds. to inches and find what fraction of 3 acres the result is. 11. If the price of bread be proportionate to the price of wheat, and a 10c. loaf weighs 14 oz. when wheat is worth 80c. a bushel, what is the weight of a 10c. loaf when wheat is worth $1.12 a bushel? " 71-^ 3.1 X .m ""2.i.i ■ 10 PllACTlCAL PllOliLEMH IN AltlTHMETIC. 1. € (1„(.K liulf HM i.Mu.l, in a day us A ui.,1 B cm, do t.»-..th, r, and />' d.^.s Imlf m nm.-h aj,miu us .1 If ull t iivo wcrkinj. t.)jr,.th..r can mow 20 ucirs «f l.urlcy in M. .lays J.uNHong would eucli working by himself take to mow 5 acres 1 2. Divide 41. 26GG3(58 l>y .or)888. .'5. Wimt is the siiimre rot.t of l.')241-)7H7.')()19()r)21 f 4. Suppose u town h'vies a poll-tax of $21G 0!) go that each mau shall i.ny us many e.-nts us the be taxed j what is each man's tax t f). Write a number that may be classified as prime <>d< , concrete, integral, simpl.., and denominate. Define' each of those terms, G Find tl.e cost of i,ainting the walls of a ro.nn -20 n. hmg 14J ft. wide, and l;) ft. 4 in. high, at V.U.. per «q. yd., ullowuig for a fireplace 4 ft. by 4 ft. 4 in. and two windows each G ft. by .'j^ ft. 7. Express /.. of 12s. Gd. + A of 3 guineas + .v of i4 - -•'„ of 2,\d. as the fraction of £5. H. If a tract of land GJ juiles h)ng and 4 miles wide which cost $1.2.1 an acre, be exdianged for the samJ quantity ui the form of a sipiare, and subseciueutly be divul.-d into 100 e,iual and s.piare farms, ^ of which should bnng atsale$11.7r, per acre, f of them $12 an acre, and the remainder ^jilOl per acre ; what would })o the profit m the tran.^ .ction, and what the sum of the dis- tances round all the s(iuares ? 9. Of how many variations will the 26 letters of the ali)habet admit ? 10. Two ships sail from the same port; one goes due nortli 40 h-agues, tiie other due east 90 miles. How far are they then apart? PnAmrAL PnonLEMs ix Arithmetic. 11 1. A Siimnwrsidc ncrclmnt imirkM an- nrticlo 40% above ('((st ; ]u> hcIIh it m. ju'count at a discount of 10 % <.nthe niai'krt pri.-f; Ik, p„vs 20 7 of tlio d. l.„ for coi lectinj,' it. What ju'r wnt docs lie j^ain or lose i 2. .1 sold H of a piece of land f(.r what '} of it cost him f Wiiat was the piiu per cent? 3. Simplify 2,.,'„„ + l,,;-.„ + r)„„»,„- + 2.()(M)S7r). 4. Find the area of a s(puu-o whose hide is :J3.25 chains. r>. A cow is fastened to a stake by a rope 12 feet lon^'. What si)a<'e can she jrraze over i G. ExjJH'ss ISs. 4.\i\. as a decimal of £1000. 7. The interest on $S70 for ,.,, certain time at (i7 Ijcr annum is .$124.41. Find the tinn 8. The discount <.n $,')(;(;.50 for D numths is .$!().,")(). Find the rat( of interest. 9. Wluit is the value of .2.') of ,V of f "*" f of 8 j,niiueas. 10. The width of a room is twice its lieiglit and f.-i-t lii^rf,. How loun must, u lu.l.hr I,., to n-.K-li tin* window from flio opposito Hid., of tlio stircf, tliH KtnM't h 'iuir GO ft wich'f ** 2. Expn'ss hy Roman notation (a) lO.lO, (A) 1793. n. A and /; travelled on the same road in tliM wnme dinrtion-J at the rafe of ;{•/ mih-s jur lionr, ni-d /; at the rate <.f r..| mihs jwr hour. If A han Miff mill's the start, in liow many hours will lu^ Im« overtaken ]»v J!l 4. If I buy a liou.se for .$2!)1(), how larj;e a luite at six months must I have discounted, at G %, to pay for it? 5. How many acres are then^ in a circle whose eir- cuniforenco is one mile ? C. A reetanerular courtyard is 42 ft. 9 in. lonf? and G8 ft. 6 in. wide, a footpath goes -luite through it, and is 5 ft. C in. in width; the footpath is laid with stone at as. Gd. per yard, and the rest with pe])l,les at 3s. per yard. What will the whole cost? 7. The width of a phmk is 2G inches; what must lie the h'ligth of the i)art cut off, so that it may contain 1 yd. 4 ft. 72 in. superficial measure? ^ 8. What must bo the face value of a 3()-day draft on Charlottetowi' puriOiased in Toronto at a premium of li % to cost $3G2r).20, interest G % ? 9. Find the sum of £B*} and (9-fV-25) of 5s. and miUtii)lv the result bv '" ~ '*"''' •^"iV 3 ,% ' 3A-,^ S + 8-^-. 10. If 11 horses and 13 cowa consume 15 tons of hay in 45 days, how many tons wiU. 17 hoi-s, ., and 23 cows consume in GO days, if 2 horses eat^ on aa average, as much as 3 cows? i:f¥^:m:.-\;'^x_ PiarTICAI. PifOULKMS I.V AlMTHMETIO. 1 .'5 .nono.'jo X IKKKKMKMM). 1. Tlio (listji!H'«- round onch of two jrardi'tiH is 2.". rods: Olio is in tho forniof ju'ircl,., Mio other u s«nmn'. Wliicli contains tlio nKU-o liind, and liow nincli ? 2. Kxprcss tliefollowinirnnnilM'rs in Aral.io notation: i'CCCXC, DCCLXXXIX. Expluiu both systmis ot notation •l. Simplify: t (.(MIlH,-)) li 2 + 2 3 + 2 3 + if 4. A morcliant marks lln^ scllinj,' pHc.> of an niliclc which sells at }{':i.2.->, ALK, one whieli sells at >j«!).()() as TSII, one which sells at ^7(^ as l^M, and on(3 which sells at 84c. as I(^ What is his pri\at«^ mark, and what wa,s tho total cost to liim of (lie four articles if tho first article is sold at u^'ain of ,'50 7 on cost, the second and fourth at a gain of 20%, and the third at a jyain of i;5.\ % ? n. There is a liouso havinj,' thieo rows of wijidows and three windows in each row; the width of each window is '{ ft. 1 1 in. Find tho cost of Khizinj; the winch.ws at 24c. per sq. ft., sui»posinf,' the length of a window in tho firsr row to he 7 ft. 10 in., in the second row (i ft. 8 in., and in the third row 5 ft. 4 in. fi. Find tho contents of a rectangular hoai-d whose length is 12.J ft. and width 9 in. 7. A owes a sum equal to f of his yearly income. By saving y^y <»f Iiis income ann ,r five years he can pay his debt and have $1260 .. What is his yearly income ? 14 Pn.vcTrr .\L Pkoijlkm.s ix Akitiimetic. 1. .1 iM.iiirlit a Jiorsr. whicli he h«>1<1 io Ji at a 1i' wnt. n. Writ*' a m'{,'otia1»ln note and drflne it. 4. An ajr."iit ivrnvrd }f!n;]2,,l N) invst in cotton at 24.'. a H)., d.'du.'tinff n^ V commission. How many pounds did lio Imv? n. Suppose Mr. A. Canipboll Ixm^dit of Beer & Ooff, n.iirl.»ttcto«-i., dnrinf,^ the month of March tho following,' ^ ''^- 1<'<> l'''^- of ^*'^<,mr at tli.^ rate of 10 ll>s. for $1.(M), 20 U.S. of cofT.c at tlio rate of 5 ll)s. for $1.00, $2 M-ortli of tea at 4()c. a 11.. Make out a receipted bill for the goods, dated Aj.ril 1st, 1!)02. 0. A dealer mixed snpir which cost lie, 9e., and l.V per pi.und respectively in ecpial (piantities, and s(.ld the mixture so jis to piin 20 per cent. At what price per pound does he sell it? 7. The i.roduet of four numbers is 032.25; three of them are oG.,"), 1.1, and .r.:{. \Vl,at is the fourth ? 8. P^iud the amount of duty a M(mcton tobacconist must piiy on .30 kej^-s, each weighing 28 lbs., tare 5 %, which c(.st in Cai'olina IHc. a 11)., if the duty is 45c. per H. and 12.^ % ad ralorem, 0. The interest on $4.-«l for 3 >ts. 5 mos. 18 dys. is $7!).04. What is the rate ? 10. A and B can do a piece of work in 40 hours, and B can do it ak)ue in GO hour.s. In liow immy hours can A aloue do it ? msaiw^^^m^i ■m- ¥\ immisams^mmm Pkacimai, rijoniKMs IN Akitiimktk . 10 1. Fm.l til.- .lifr.rvii.M. iM.tw.rii ll,.> tni(. disi-oiint iiikI fhHl.ai,k .Iis..«nmfc of sfdiMM) fur ) vr. .'{ „„.s. i:, ,lvs at ' %• -. Tin- Icn^rfl, of ,1 j,iini;i."loj.ijM»l Is !) ft., l.r... 1, 2 ff. )f2() aiuldrpthls ill. Find its nolidity. ' "" ' 3. Find tl.o l..jr,d tinio of jimtiiiitv of tl.o followii.jr Mof.., till, u.i.xpind tin.o «i.d til.. i,ro<.n.ds, it iMi,,.. uis- ••omitcd Ai'iil KMli, l!)(t1, at (I ' : •tn.-».:.() '"' d.iionwnator of «Mio fra.-ti.a. iM-i,,^' ac.Md.-ntallv 'on-tt.-.i. Tli.. answ.T unv.., at til.. ...i.I of tl.o IxM.k was m. Ki,.,i „„. ,„.^^^,,.^ denominator. n. .1, Ti, and rstnrt in lu.sin.'.s.; l.,jr,.tli.T ; .1 p„ts in .+•..()()(», /.• ^mm, „n.l (' .t!>(.0(). At til.. ,.,Ml .,.' thn... ■"onths C l..,v..s, and at tli.. m.l of H-v.n months // i«'HV.'s, both takinj,' out th.i.- (capital with th.-m : hut thr profits a,v m.t divid.-d till tlio nid ..f th.. v.-ar, wh.-n (' n'etwcen a garden containing s(puire rods and one which is rods >;(piare. 9. ILiw much must I invest in Dojuinion bonds at 142, bi'okerage ^ %, to secure an income i) 41 ()0r)S0()f;2.')00 (h) r).774409, (r) 1 .-,.'] J, {,!) U3.-3G521. G. A person, after paying an income tax of 6 mills in the dollar, has $1090.40 income. What was his gross income? 7. How many times will a wheel which is 15 ft, 9 iii. in circumference turn round in going from Charlotte- town to Cardigan, it being 24 miles ? 18 PPwiCTK'AL PnoiJLEMS IN" AniTHMETIC, 1. Find the valm; of .7 of £1 + .n of 7s. Gd. -2 4,j o Is. Hd. 2. A toaclior, Lcinj^ aski-d how iniiiiy scholars he had rei)li('d, ''If I liad as many more as I now liavc, ono-lial as many more, onc-tliii-d as ni.-iiiy more, and on<'-fonrtl as many more, T slionld liav«> 2!H;." How niiniy had he! 3. A fjrroccr mixes tea AV(»rtli '}Sc. and 44o. rospoot ivcly. "Wliat mnst ho tlic sdlinj,' i>ri('o of the mixtni-t that ho niav f;;.in 1,1 7 (.ii tlio outhiv? 4. ITow many yards of paju'r, 30 in. wide, will Ix roqnin-d to cover the walls of a room lo ft. lonj,' 1 2 ft Avide and 8 ft. liiijh? What will it cost to plaster the walls and eeilinji^ at lOc. per sq. yd. ? 5. A hroken tree rested on the stnmp 20 ft. from the f?r() ixT cord, comes to 8;{7o(), what must l.o the Iciij,th of the pile ? 2. A watch whicli gains 5 sccojrIs in every ,'{ minutes was set right at (i a.m. What was the true time in the afternoon of the same day wlien the watch indicated a <|uarter j)ast -i o'clock? '.i. Find tlic cost of tiling a roof (,f a l)uilding vvho.se h^'iigth is;{() ft. and width H yds. j the eaves l.eing suj.posed to project 1 ft. on each side, and the i-oof n\ such a nature as to form a right-angle at the top ; reckon- ing at ^4.70 i)er 100 sq. ft. 4. In a ti-aiji containing 240 passengers, the nund)er of tir,st and third chiss passengers was 202, that of ■second and third chiss 1;J8. How many passengers were tliere in each class ? o. A merchant who.se cost-mark is " ('uml)erland," lias the cost price marked on an arti- !'^ as BLE. At what per cent advance must be the scll:;ig price that he may give a discount of 20 % fi-om the asking price, and still nuike 20 % on the cost ? 6. Find the value of 5 oaken planks at Gc. inv ft., ea(!h being 17A ft. huig, and tlicir widths as f(»llovvs: twd of loi in., one of 14A in., and tlie remaining two of IS in. at one end and 11 j in. at the other. 7. Simjdify: T4 - 7 of •] _ ^ _ i^'f "^ + •• «'f "> A+ Aof 3i-(Jof ^t-i^ '• dii-if^- 8. Suppose I remit to my agent at Halifax SloOO for the i)urchase of flour. The flour costs him .^r).00 a bai-rel. and his commission is 2.\ ^. How many barrels of flour shall I receive after deducting his coimnissiou? 20 PiucTiCAL Problems in AitiTUiiExic. 1. From a pile of wood 24 ft. long, 4 ft. wide, and 5 ft. high, there were sold 1 J cords at one time and half a cord at another time. What is the remainder worth at .*''{.25acord? 2. Find the distanee round a lot of land in the form of a right-angled triangle, if the longest side is 200 rods and the shortest 120 rods. 3. A cellar is to be dug whose length, breadth, and depth are each 12 ft. .'} in. ; find the number of solid feet in it. , 4. The capital stoek of a railway is $1437i.Mj, and its debt is 037,>()O. Its gross earnings for the year 1901 were $2r,()()()(), and its expenses 8132r)00. If the company paid expenses and interest on its debt at 6 %, and reserved m^O as surplus, what dividend would a stock- holder receive who owned 25 shares, par value $100? 5. If the population is now ten millions and the births are 1 in 20 and the deaths 1 in 30, annuaUy, what will the population be in 5 years ? 6. Having observed the flash of a cannon, I noticed by my watch that 6 seconds elaj.sed previous to my hearing the report. Determine my distanc*^ from the gun. 7. A detachment, consisting of 5 companies, was sent into a ganison, in '.*hich the duty required 228 men per day. The first company consisted of 1(52 men; the second, 153; the third, 144; the fourth, 117; and the fifth, 108. How many men must each company furnish in proportion to the whole number of men? ^^. Find the valup of f "^ f J" J'J, and take the result '7 X jt X u I from 10^3^ +71^ .-^fSS \\,, .:- J - TT- ■;¥■/■■:■ IF J the PliACTlCAL iMsoiJLKMS J.V AlMTlIMKTK . 21 1. IT(»\v iiumy acres are there on th»^ surface of tlie eartli, if it contains I'JTOOOOOO s«iiiare mih*s? Express the answer iu words. 2. A genth'uian in Georjifetown has two huil^linjr lots, one e«.ntaininj; 40 s(i. rds. and tlie other (10; a .y< iitlenian iu :\Ioi.taj;ue (dTcrs Idni a sijuare ti.-ld cou- tainiui^ four times as much hind as liis lots. How many rods in h'n«;th must each side <»f the sc^uare be ? 3. Multiply 3^ l.y ;5,'„ and divide "l^h.v '^l", and find the difffjrence Ix-twccn the sum and dilt'crence of these results. 4. What is tie diflferenci! Ix'twccu .77777 of £1 and Ss. G.6G48d. ? 5. .1, />', C, and /) enter into i>artnership. .1 and />' put in ei.'WO ; />' and T, 8131)0; f? and 7>, SISIO; ,1 and />, 81010; ^t and C, 61.J00. They gain 81152. What is the gain of each ? 6. A man huilt a house of three stories. In the upper story there were 10 wiiulows, each (iontaining 12 l>anes of glass, each pane 14 in. 1)y 12 in. ; the first and sectmd stories contained 14 windows, each of LI panes, and each pane IG in. hy 12 in. How many sc^. ft. of glass were there in the liouse? 7. Find the euhe root of 81 )96;]H4r)12000( )()()( )()(). H. If n is 10 years older than J, and C is as old as hoth .1 and />', what are their several ages, the sum of them all being 100 ? 9. On January l;t, ^1 began to trade with 87(50; on the 1st of February following he took in />* with 8.'340; on June 1st foUowing he took iu f7 with 8S00; at the end of ear they foujid they hud gained 8782. WTiat was ea< tin's share ' the gain ? 22 VllM'TUXL Ph'01JLK.M.S 1\ AlJITHMKTlC 1 Sinij.litA- \'t/" + ^^ ' - ^ 11 H.'..) 2. J, HUunVmg „u tlio l«.ft l,»nk .,f riillsl,„nMi.rl liivtT, (lis<-h;irp..s a f.„n, jin.l /,', „„ tli,' ..ppcsitc l.a.rk counts liv». pulsatmns <,f ],is wHst Ix'twrn tl..- flash an, tl.e iv].orf. If s.,un,l fiu-s 1142 tWt p.v s..<.on,l, an.l tla pulse ot a, iK-rson in lH..-,lfl, lu-ats 7.", sivokvs in a niinuto mint IS the widtli of the river ? 'i. If tlie unit of measurement l.e 2.{ vds., what is tin measure of 2i ft. ? - • » 4. Find the value of .02 of £1 +.();} of 7s fid +011 of 2s. 9(1. r>. If a i)ile (,f wood which is 2.10 ft. long, 40 ft wide and 40 ft. hiji:h, he thrown into the form of a eul.e and sold f,.r i of as many d(»]Iars as thv (Mihe would be feet long, what sum wt)uld the cube briu"- f n. A i)ieee of work is to be done in 3(5 {) ft. respectively. The distance betw.-cii tlie top <,f tower A and that of B is 1)7 ft., and tlie distance ]«-t\ve..ii the l.ot- toni of th<' tower B and that of (' is 70 ft. From th<-s,. (hita tind tlie folh.winjr distances: (//) Vvi,u) the top ,,f A to the lM.tt(»ni of IJ; (h) from the t..p uf ]i (o il,,. l.„(tom of A ; (r) from tlie l.oltoni of A to tlie hotlom of P, ; (,/) fn.m the bottom of B to the toi* (.f ('; (,) fn,ni the'l.ot- tom of (' to the top of B; and (/) from the top of B to the t(»p of C. 2. Sold 12S() bus. wheat at $1,'; commissi<.n ;!.]/, char^res.tr,1.4L>|. Invested proeccds in iron, ..ummi.s.siun' -.\ %. Find the sum invested in iron. ;]. The solid contents of a culte are 17l*S cu. ft.; {) tin.l the siirfac.. „f ,,11 its faces; (r) lind the h-nj^-th of the diaj^onal am.ss uiw face. 4. If /', of the i)ri.M' received tor an arliele is h.j^t, what is the loss jx-r cent ? 5. If a p<.le ]±\ ft. lon.i,' <-ast a shadow I)-,' ft. Icmih-, how lon.y must a pole lie to cast a shadow 21 ft. lon;,^ at the same hour of the day? (). Subtract l.Vl'; from 17,V, ; multiplv t..ireth works fur 5 hours on tlio first day, niid on t'lich of tli flvt" substMiuciit days an hour longer than on the prccrdin day; ^1 docs as niudi in 4 liours as li dors in 5 liouri If the 8uin total ]»aid .1 and 7> as waj^rs for the wee be 814, liow much shcudd cacli receive? 2. ITow nniny sqnai-e yards are there in a rliondtoi whose h-ngth is IJT ft. and hrcadtli ."> ft. '.i in.? .'}. Th(! lieij^lit of a precipice, standing l)y thf contaiiiing only at the rate c 8 lbs. to the srht a (|uaiitity of I,,,,,!.,.,, for S7(K) At what pWco must ],e st-ll it s<. that he n.av r<»^ression be T the «'oiiiiintii ditT'er«'iiee 2, iiiul the uuiuImt of tenuis ]'. whiit is tlie last term ? 4. There is ii ti'iaiii;idar eoi-iifteld who.se three sides jir l.'jO, 20(>, and 2.')() yds. respecrtively. Find th<^ (ro.st o reai>ing the eoi-u at $2.42 {u'r acre. ."). A j;roeer Itoujilit snj^ar amonntin^' to $725 o 1)0 days' time, but heinj^ (ttTei-ed 4 ^ off for easi borrowed the money at a 1)aiik for the time, less f;rae« at 9 7, and eashed the bill. What was the face of th note if (>. 2.") ]H'r eenl. of 2 is what jht eent. of .'{o.^ per <',enl of (i? 7. A ladder, 4<» fl. lon^^ may be .so placed that it sha reach a window 'A'l ft. fi-om the j^n-ound on one side o the street ; and by only tni'ninj; it over witliont movin the foot out of its place, it will do the same by a window 21 ft. hi.uh on the other sidt'. What is the width of th street ? 8. Tlie cost of carpeting a room IH ft. lonj? by 16 f wide, with carpet worth .$1.20 a yard, is $,")!. 20. Ho' wide is the carpet f *• V .^ % P|{.\rTUAI. PlMMII.KM^ l\ AlJll HMKTK . 27 > ides Jin* I iKTfs of land for H'l-'MMt; old onf liftli of it at .frj mi ni'i-f. oiif-tiiird of it at !fl»'ni for ••arpctin^r the Moor of ;i rootn, or for i>last«'i-in<,' or pa|Mrin«,' the walls and ceilinj; of a room, and ^'ivr the soli-ti mi in fnll. 4. The diaj;<»nal of a st|uar<' (h-ld is l_'(i rods. Kind tnt' area in at'i-t-s. 5. licdnce .48 of a sq. rod to tin- dtM-imal of an ari-f. G. If 1.') quarts (»f milk will niakf 2 llis. of hnltrr. and () lbs. of butter nM|Mirt' as innrh milk as ;i(» ll»s. of chccst', and 40 lbs. of chtcsf be ma months? If the milk sell at .")••. a (jnart. the butter at 2'u: a lb., and cheese at lOc. a lb., which would b<; the more ju-oMtaldc, for the "■ivcn tinic — tli,. selling of milk, the inakin' to^'ther can d(» a jfiecc of work in 12 thiys. If ,1 can ch. only ;^ as much as />', how loin;- will it tak(^ each of them to do the work? H. Find the area of a trianer[>eiidicular altitude l,"i{ yds. 111 ' •< •> ^ - I J I l<>i?-(4fU:5H) -1 x(4i <»f (;^+ .^)-!4>i of ((i^+ ••,! I •>• Simplify: I ,-j\ ";' ^u: + 2r. 28 PiarTK Al. ritOlJLKM.S IN Al{ITIIMKTi( . 1. TIk' iMtpulution of a certain town, af r there are altojjether. .'{. Sailing' into ('harh»ttetown harltor, I saw the ftti of a cannon, and counted H seconds l>y niywat<-h ltetw( the flasli and report. Find my distance from Pi Kdward. 4. A calde which is 3 ft. h)ng and 9 in. in circu fennce weijrhs 22 Ihs. Deterrvji; ;'i(« weij^ht of a eal who.se diameter is 9 in. and lenjrth 1 fathom. T). Feb'y 2Hth, 1901, I IxMifrht a l)ill „f jro,»ds amoni inj; to !{i(58r>.4(> on tlie following; terms: ".'> months n or h-ss 5 % if paid in 1,") days." How much will recpiired to .settle the hill March 14th? 6. Wliat must he th(> face of a note, .so that win di.scounted at hank at 7 % for 9 months the pr<»cee will be $:){){)? 7. The ])ase and hypotlienu.se of a right-an^ded t; an^de are respectively 7.6 in. and 9..") in. Find the pt peiidienlar. 5. A traveller, on reaehiufi: a <'crtain place, found th his w.iteh, whieh kept eurrect time for tli.- j.laee lie lei was 2 lirs. 2.j miu. slower tlian the local lijue. Had J travelled eastward or wcstwai-d. and how far? U'. VuA^ru .\L PifojJi.KMs j\ Ann niMKTlr 2'.) m fo tin* • >v«'r tlu' II ^uiu of wtw tbp inp cijfht iiiul iiiin' Veil Imn- il iiiiu'ty- is of ri('«* the flash l>('t\V«'(Ml Dm Port I circmn- r' a ('«l>le ainoiint- lltllS lU't. will be lilt when ixhil tri- thf per- 1111(1 thut ' lie left, Hiul he 1. A iiitrejiunt iiicroHHed l,is capital the first v,.ai- by •••"-M»»'-t"»- «'f" itself, the H.'eoM(l year hv two-fifilis. the fliird year he lost tvvi.-sev.„tl,.s of ,,11 h,. |,n,|. uimI* had *1.>(KM) remaiiiiii^r. \vi,„t was his capital at first ? 2. The (li.imeters of twoeoiireiitrieeirel.s are 1.-, and U» ft. Find the area of the rinj; formed hy these eireh-s. .'{. Find the e<»st of pnintinjr the fo„r sich-s and the iK.ttom of n tank 2\ yds h.njr. 4 ft. wide, an.l 4.4 ft. deep, at Sc. per .sq. ft. 4. If the iiumlu-r of s.piare miles in the Hritish Km- \ pire he 1;{0(iO(HM» and the i,opnlation 4:.(KMMM»(K), how many per.s.ais are there to the sipuire mile ? 5. If :> horses eat as mneh as eattle, and H horses and 12 eattle eat 12 tons .,f hay in 40 dnvs. how mn.-h hay will he n-ipjired to k.rp 7 h(»rses and" l.". eattle (I.", days? (». Redne,. .1 ,-);}( W};.") tons to ewt.. Ihs.. oz. I 7. A merehant Imnjrht tea at IS,., a Ih., ami mark.- ,.h,'sts awrajrin^' <0 ll)s. eaeh. Th,' pnivhaser havinj; fail .l hefo.-e pa\^- ment was made, a .'onipn.mi.se was etre,-t,-,l at 7S,.. on the dollar Did the .s,.]],-,. jrain or los,', ami how nnwh ? S. The lenjrth of rt i.ie,.e of timl)er is 2(M ft., the wi.lfh at the jrn.ater end 1 ft. 9 in. and th,. thi,.ki.,..ss 1 ft ;{ in • at the l,..ss,.r end th,' wi,lth is 1 ft. in. and th,. thi,.km.,ss 1 ft. What is th,' .soli,lifyy I !). Ascpiare mil,' has h,','h ad,h-d to the Hritish Em- pire evry 8 minntes of (^n.'.-n Vietoria's r,'ijrn. If h.r r<-ij:n dates from o a.m., .Iini.- L'Oth. ls;!7 f,, ,-, ., ni .Tannary 22nd, 1!)01, find tlie amonnt of l.-rrifav aihh-d to the Em])ire dnrinj,' her reiL'ii. ..(, 1>UA(TMAL PhoULKMS IN AUITIIMETK . 1 Tn .. citv of :.7S40 iuhaUilauts, .12.> of tin- mf'^^ ^ 1....^ ..ft<.n«l tilt' DuVtllc scliool^. how iiiiiny sHioliirs aTun„''• ';.,t-ai,i u i.id for a. Firnlll. mi,..,n,a i,,.. .vs, .m *l.i,(l t... -. xi- ■" .•„,;.,," 7.-, .n.l Vl-1 li.,Ks. ana ..,<■ l...-,,...,..-,,!,,, .1..- 8. W„a, V--;" ■;;';'\ ' . H, Uvay is ,1... .listau.-.. and Suniincrsule h\ i • '- '; . iM.tw.M'U Mount, Strwivrt aiul .>ouns .-^ . 11 .;- for 4?f)()(U» For wliat must ., Hou-l.t a l.ousi- and lov toi i^i.nui.. ^ T t it to ..-.un C. ' <"' n-.vino.u'V, and to i.a> ^-'-\;' ' T rent it to ^aiu . ^^ y , .» <,t ,„j„i,s,$22.r.OforiHsurau.-.',auatav..it l.» , ''';:r:.a..,.a,.«an.,.n...nsi,,-.uH._^^;^ ^vi"''-'''V'^:r; r- unL^^ ^'■^ su.d.astow..i^hSlbs.totl,.-s.,t^. Practical PuonLEMs is Auitiimetic. 81 1. What nnmiv, ',.; ti.at wliich bcinj; iiicrcjisoa by f of itself and thev ilonblod, j^i-es 4 more tliau the square root of 2704? 2. Simplify: u.:, X ;.t-42S/i x 1.07n92;{o X .;{ .6 X 2.!s.-)714i! X 2.;!(»7()!):> x 14..') .'{. What mm bears the same proportion to £.1 that VAs ll.i in. lonir and 11 ft. .'5 in. hifrli. How m.-my .sq. yds. does it eontain ? 5. A woodman hewinjj: timber strnek so vijron.nsly that I heard .-Meh stroke of his axe, aMor for .t2..-,0 ])er day on condition that h(> should forfeit 50... for everv (h.v h.' was idle At the end of 100 days he received .$190. How many days was he idle ? ^ . ■ 8. WHiat is the length of a rope extejiding from tho top of a pole 40 ft. high to the top of a stak.' 1.^5 ft. hj.^h standing 3.3 ft. from the pole? ^ ' 9. A cistern that holds 280 gallons i.s empty It has a •^"I'ply pipe that will fill it in 10 hrs. an.l a discharge pipe that will empty it in 7 hrs. If, after the supply pipe has been open 4 hrs., the discharge pipe i.s opened, in what time will the cistern be emptied ? s 1 T^mMWr>- .'r^mm^^._:yt. *;Lv»:ni^:^-:^i^^^«uA 32 PuACTKAL Problems in Auitiimetic 1. Multiply If) l)y sixteen Imndrcdtlis, divide the pro- duet by sixt.Vu tcn-tliousaudtlis and express tlie qiiotieiit in Roman notation. 2. Find the square root of tlie third power of l.G correct to 4 decimal places. 3. A S(iuare lot is l.ordered hy a walk 1 yd. wide; the lot and walk to^'ether occupy 2.\ acres. Find the cost of paving the walk at 25c. a s(i. yd. 4. Write in fitrnres: Eight hundred trillion, eight billion, eight million, eight hundred thousand and eighty. 5. A receives a, semi-annual income of $180 from (\P.R. stcx'k at C %. What was his total investment if C.P.R. stock is (luoted at 1 lO.J, bn.kerage i of 1 per cent. ? G. King Edward VTI. was boi-n on November 0th, '841. Find hi> age in minutes on November 9th, 1901. 7. Divide G dys. 5 hrs. 10 min. 30 sec. by V>, and multiply the result by 1 U. H Sold goods at a gain of 20 %. If Ilu> eost had been $(i() less, the gain w<.ul.l have been 25 %. Find the cost of the goods. 9. A brewerj' is worth 4 % less than a tannery, and the tannei-y IG % more than a boat; the o\Anier of tin }>oat has traded it for 75 % of the brewerj^ losing $103 What is the tannery worth ? 10. If the interest on $1 at (> % is $.0835, what is tlu time ? 11. Fiml the cost of 735 fence boards, each IG ft. lon« and 5 in. wide, at $14.50 per M. mik.m.. \^m WP^« PlfACTlCAL PhoHLKMS IV AlMTHM KTIC. i 1. It ni I'.Wli.yslfiOmni, working 9 hours a day, exca- vate a e..t 900 ft. long, ]:{ ff. d.-ep and .'50 ft. wide ,n limv many days .sluM.ld Or, men, M'orking H hours a dav .'x<-avate anotln-r .-.it 1l>()() ft. ]„ng, G.^ ft. deep, 38 ft wide' and 2i times as diflrteult to excavate ? 2 If in building the Belfast Kailway, rails weighin.^ SO ll>s. to the yard be used, how n.anv t<.ns of rails ^^'ill be re(iuired to finish one mile of the road ? ^. Divid.^ three ten - miDiouths bv five hundred- thousandths. 4 Find the cost .,f 24 planks 10 ft. long, U in. wide .-.ud 2i m. thick, at $L>;5..-.() p,.r M, board m.-asure. T). A stock of goods valued at eiH.lOO is insured for '' <'f Its value at 1 J %. Find the premium. r.. How many shares Bank of Halifax stock can b,' p.n-chas,.d for .t22:}7.7r, at 12!)=^, l,rok,'rage i per cent ? 7. Expre '" words 301 4,")Ofi.87.")4. 5 The r. • a roof is W ft. G in. above the eaves and the eav. .s are 55 ft. apart. Find the width of on.' sule of the roof. J). If milk weighs m lbs. to a cu. ft., and water (L\i li)s., what per cent is milk heavier than water ? 10. If the interest on $100 for 3 yrs. 4 mos. at G ^' per annum is $20, for how long must $350 remain at int^^-est, at U / per annum, to produce $42? irulVn"'*'??""'' "'■'• ''^ ^''''' ''''" ^'"^ ^•'^*"l"'''-eJ to make 1000 lbs. of bread, if the bread weigh 30 percent more than the flour used? 1 2. The factors of the dividend are 32, 2}, and 7 5 • and the factors of the divisor are ^ «, -OH, and 22i. Find th,^ quotient. m 34 pHACnCAL PhOIJLEMS IX AniTHMETIC ''Si 1. Miiltinlv f) rd. 4 v<\ 2 ft. 4 in. hv 9. 2. \Vvi\o. in words (a) 1240. {h) Mr^i^ (r) ./,«,, (e to each otliei' in ratios of .'5, 4-1, .">.', and (5 i'espeetiv(4y. ;"). The periniete" of a trianirle is 220 yds., and the sides are in the V'ltio of 4. 7 and !). t'nid the length of the longest side. (5. A liai'dware merchant sold two stov.s for .$.'10 each, piinini; 20 ' on one aner day for 10 days, and the tliird 12 hrs. per day for 5 days, how mnch should each receive? 5. A fruit pedler sold 41 oranires at 5 cents each and (is lemons at 4 cents each, after which lu^ invested one- tliird of his receipts iu bananas. Find the amcmnt paid for bananas. 9. Make a prol)lem in which the interest, principal, a?id time are given to find the rate per annum. 10. Express (a) .0007.") as a per cent. ; (h) 5 % as a common fraction; (c) 127.302 in words. 11. At 22 cents a sq. yd., how much will be the cost of plastering the walls and ceiling of a room Ui ft. by 14 ft., and 9 ft. C iu. high, if iV be alloweu for openiugs? I'l{\( TKAI, i*|;(HtLK.M.S IN AlMTIIMKTK 1. A spccul.-.tcc soM I.JO simns railway sto,.k at 941 and invested the pro ds iii Imnk ."stock at I'.U;. pax in-- hrokn-atro ^ 7, Imth lui- .s.-llinj. jiiid l.uying. Hmv ,uji„'v shaivs of tlie latter stock di''r yd., uails Gc. per lb. and lath $'^ per M. 30 I'ISACTK AL ]*|{«)H1-KMS J\ AiaTIIMKTlC. 1. Ill a lOO-vd. race .1 <'aii ])eat />' liv 4 yds.; in a (quarter of a mile ra<'<' C can 1)t'at ^1 1>y 11 yds. ; l»y liow miu'li can C beat li in a niilo race, sMi)posiii<; tliat the avt'rajifo spt'«'d of cadi man wlitii riiiiiiiuf^ a liundi-cd yards, a ((uartcr of a iiiilc, and a iiiilo arc pro- portional to 9 : 8 : 7 ? 2. A certain star is five million nine hundred and ninety-five tlionsand nine linndred and forty-fonr times as far from tlio eartli as is the siin. State in words the niimher of seconds which li^dit, travelling one hundred and eighty-six tJionsand miles per second, will occupy in coming from that star to the earth, if the earth is distant ninety-three millions of miles from the snn ; and express your answer iu years, supposing a year to eipial 3G5 days 6 hours. 3. Jacob, by contract, wa^ to serve Lal)an for liis two daughters 14 years; when he had occupied 10 yrs. 10 mos. 10 wks 10 dys. 10 hrs. 10 min., how many minutes had he then to serve ? 4. I bought of Poole & Thompson, Montague Bridge, the following pieces of lumber at $12 per M : 12 boards IG ft. long and 9 in. wide; eight 2x4 scantling IG ft. long; fifteen 8x10 joists 14 ft. long; three 8x14 tim- bers 24 ft. long. Make out a receipted bill for the above. 5. A dealer bought flour for $900 cash and sold it im- mediately for $1080 on 6 months' credit, for which he received a note. If he should get the note discounted at a bank at G %, what would be the gain on the flour? 6. How many board feet in a stick of timber 36 ft. long, 12 iu. wide, and 20 in. thick? How many sii-iare feet in tlie entire surface of tho stick ? How many cubic feet iu the stick ? J'KAtTK AL J*I{()1JLEMS 1\ AlilTHMKTK'. o< i 1. A s() sec, ^vlmt is fl.,- ,litr.'ivii.-<. in l..iij;if ...1,. ' 3. Fiiiu the nmoniit of a not,. f,,i- jfi'iLM, jriv,.|i July lOtli, ]S!)4, and paid O.-tolH-r L'r,th, l,S!r>, lu-ariior 8 / from date. 4. Find tli(> imn.l.(;r of s.j. ft. i„ tl..- sM-fa.-,. of a Ix.x •■{ ft. V) ill. L.njr, 2 ft. :{ in. wide, 1 ft. 4 in. liiuh. 5. A lu-iiitcr used ;{ ivanis 5 ,|i,iivs 1!» slic-ts of j.ap.T for i.rinlin.iT half-sluM-t posters. JIuw many did hv print, allowinjr 1 quire to a ream f(.r waste ? C. A farm has two of its four sid,-s parallel and two not parallel; the distance l.etwe.'n parallel sides is 7(1 i-ods; h'ligth of non-parallel si.les, SO rods and llo rods respectively. Find area in aeivs. 7. A man soM (I horses at $\:,i) v.wh -. ..n tlnve h.. -ained 30%- (,n the (.tliers h.st L'O '. Find oain or loss. 8. .1 can do a piece (.f work in S=| hrs.. ,| and /; in 4.:, hrs., and A and (' in 4 Imiirs. Find the tim.-, if /; and (' work toj^'ether. 0. .1 and B formed a partnership; .1 put in .^.'{OOO. and at the eh)se of the first y.'ar added $2()<)() ; Ii put in ■t4()(K), and at the close of the second year took out •f20()();^ at tlu; close of the third year the ju-olits amounted to $34o0. What wa.s each partner's sliare ? 1 0. A certain lot is 80 ft. hy ] 28 ft. How many ] G ft. hoards will be iv.piired to make a five-hoard fen.-earoun.l It? If the boards are (i in. wide, liow manv feet of lumber iu entire fence ? 38 PllACTlCAL PROHLEMS 1\ AuiTIlMETK 1. A solid wli«»st! luisc is 10 in. sciuun-, iiiul allitiuh! S in., equals wlmt purt (»f a lO-iii. culu'? 2. If tlicfo aim 48 cliiMn'ii in a room 20 ft. loiijr, 18 ft. wide, and 10 ft. liigli, liow many «*u. ft. of air to carli child f '.\. A waii-on ImmIv, 10 ft. lonir. .'5 ft. wide, and 18 in. deep, ludds 3(5 1)U.><. of corn. If its width l>c incn-a.scd in., how many hushcls will it hold? Il.id its hcij;ht hccn inci-cascd .'{ in. and its width remained o ft., how many hn.shds would it have held? 4. What is the wei<,dit of water in a full rectanj^'ular cistern 7 ft. hy :{ ft. l)y 10 ft., if a en. ft. of water weighs 1000 oz.? .'>. Divide $(>40 among J, /.'and (\ so that />* may have six times as much as A. and (' \.\ times as mueh as />'. (i. Find II.C.F. and L.C.M. of TJS, ;;S4, 7(iH, and 2:504. 7. Find the L.C.M. of all the prime nnndters hetween 2 and 17, inclusive. 8. A girl who attended school (iS days during a term, was marki'd sr> 7 for attendance. How many days was she absent'? 9. A man pays $'.]~7) a year rent for a house worth $,")4()0. Will he gain or lo.se, and how much, in four years, if lio borrows moiu-y at 7 % to purchase tlu' 1 louse ? 10. What rate of premium iloos 7 % stock bear in the market Avhen the invesiment paA,s G per cent? 11. What is the net tax of a town whose taxable pro- perty is assessed $4:50000 at 12 mills 'in the dollar, 5 % being paid for collectiug i i'KACTKAI, J'l{(»nKK.M.S IN AlMTllAIKTK ;{!) i IS in. ici«;lit j , how 'ciirlis worth J I I four f i I ie pro- I 1. A i.iun III vvalkinir tak.-s (Kloo sfrps in an hour- I,., ivarln-s (hu in-xt village i.i 40 imunWs. JIuw many M.-ns < istant is the place? Uow many miles, if each Jtei, 1... '2.7 teet? * 2. IIow many rolls „f ,,,,,„.,., each S yds. hn.jr ,,n\^:UU} tor the rent of a house. Would he gain or l...se, a'nd h<,w much, l.y investing $4000 of the $(J000 in a house on whwh he would have to pay a tax of 1l' mills in tlie dollar, and $10 for watei- rent ,' (k Miss Ellen Jones makes a dress for Mis^ Katie Brown for which she furnishes tiie following materials • () yds. percaliuo at ISc, 2 yds. sih'sia at 2r,e., .i yd ,n-a.ss cloth at 14c., f yd. velvvteeu at $2.00, 4 yds. hair cloHi at 4oc., 3 spools silk at 8c., I spool thread at 4c., 1 spool twLst at r.c., 5 yd.s. cord at 5c., 1 pr. .shi.'ld.s, helling l->c I doz. l,on..s r>4c., .-, yd.s. casing at 4e., 1 pi,-..,. |,i„aing nhhon iSc, work $11.00. Make out Miss Browns l.,ll and receipt it. 4i) rUAlTK Al, I'koUI.KMs IN Alii IIIM K I 1< . 1. If .',■; <»f 'A\ tiiiHs 1 Ih' imiltiplit'd liy I, tlir prodii.-l divided l>y fj, tln' (|uolicnt iin'i-ciisrd liy 4.'. aiil tlic .sum diiiiinislird l»y -, of itsolf, what is the rnimiiidcr? 2. I liuld Mr. Hlak.-'s not.- for $;{(;(»(», dated .laimary Stli, 1S!)(), due ill tint ycMi- williuiit iiiti'i't-st. What is till! ca.sli vahu- -Iidy L'ntli, iS'Mi, uK.n.'y Wring worth G / ? ;j. A cidn' iniiiKrsfd in a rcrtani-Mlai- reservoir :U» in. h>iif,' and Ki in. wide raises the water :5 iiu-hes. What i:^ the ed«i:e of the flllie ? 4. What nuinlter increased hy J."» ' of itself e(|iials ',•_*(»(>? What nniiil)ei- diniinished l>y 17.1 of iis(4t equals ;{().:;■:' 1 ll2 is 140 / of what nuinlier? (iO / (»t what nuinher equals *J, discounted at the bank, rat([. rds. '• ^^'^^ It a hill of ^^..ods lik.ly to 1... |Miivl,as.-d at a lianlwarc sii.n-, jind n'i' th.- n.st ..| th.- hoiis.-. What is th.' undi-rwritri--s loss if it hiinis? .'{. Alaiidlonl owns L';{(»4<» a,-ivs „f Imm.I i„ thr fun,, of a sqiiaiv. How iiiurh will h.' hav to pav a snm-vor to lay it oat into h.ts of Kid ;„.,vs .,„.h. if lir has to {,av +1.1.'.") ftu- i-vi-ry mile run ? 4. I have .tLNMIO „„ i„|,.,.,st -M (1 . \V1,,„ ,,,„„ ,„„^, 1 invest in S ^ hond.s, .s.Hii,^- ..,t !)s, to yi.Jd llic ^.•,„H. annual income? .'). A lanihei-man owns 74S(; Mcivs of timiMiv.l I.hmI in the form of a, .sq,iare. How ,„,,,,y „iiles aionnd it ? fi. The distance f,-oni ("harlottetown t.. S,ii„„ie,-.side is <■><» mih's. At $1 ajac-e fo,- posts and 7.-. a II.. to,- wii- what will the posts and wiiv for u tch-phone line cosi If the posts an; set oO yd.s. apart and a 11.. of wire stretches ,")() ft.? 7. A room floor contains 4:{L> s.p ft., and its breadth is t(» Its len-th as ',i is to 4. What are the .liinensions <.f the room ? S. How many barrels of flour at .+4 a l.anvl shall an Hp'iit s<'ll so tluit lie may remit to his princii.al .t-Jold, after dediictinjr a eomniissiou of 2.\ ' ? !>. How mudi will it co.st to paper the walls and ceilin,ir of a room 04^ ft. lonir, -M) ft. wide, and 10 ft (i in hi'di .•It 27iie. a si[. yd. ? ^ ' 10. T)educt ^ of ,: from ii of Jjf, ad.l to il„ ivmaiinler ,0, divide tlie sum by Gi, aud chauge to a deeimal. \'J. VHMT\i\\. l*i;n|,|.K.\LS IN AuiTllMKTir. 1. A mail (Inw :{() ' of liis l»aiik «l.|M.sits himI s|mii1 '2't ' of tlif iinnny (Ir.iwii to imn-liu.sc u ln»rsc for !i*!l7.>0 Find how imu'li ho hiul in the Imiik JM-t'oiv ilniwiiivr. •_'. Kiiitl IIm- fact! ot a !)0-(hiy iioto that wlu-ii di-s.-ouiitt-d ait 12 ' will pay foi- 1:{7'^ yds. «'loth at %'1'\ a yd. :{. An-a of till) ^alili' end of a house is ;{7s s(i. ft. li-ii^'th of liasr, 14 yds. Find lui.t,dit of ndj^c 4. A niinc-ovviM'i' iiiado a contnu't to dtlivor 1<>U(K Ions of <-oid ill 4 inonllis, I'lnployin}^ ;')()() iiicii to j^i-t i' out ; at Ihf fiid of :{ inoiitlis, with only :{ nn-ii struck. How many must he advrrtise for t< fullil his contract ? .'). Find the time of day if % of tin- time past midiiififh e«|uals tiie time to inidiii<;lit nuain. (■». Mv n<"vnt sold in Montreal 10(10 l.us. of wlieat commission 2 %, at S4«- ; invested proceeds iu doth, com mission 2 %, at S4c. a yard. Find number of yard iMiujrht- 7. Fxi)ress by Arabic ii(»tatioii twenty billion, niiieteei thousand and nineteen ; by l{<»miin notation six hundre( and live thousand; in ti.iruves, MDL; in words, ()•_»:>()•-•.'). ,s. Add ,Ia expressed decimally to G ])y ;}7.'). Find the i>rodu<'t o their quotients ami express the answers in words. 10. If (I m.'ii di^' a cellar 22..') ft. hmi?, 17.8 ft. wide, an 10 ft. a in. deep, in o days <.f 10 hrs. and L") min. eacl how many men will it reipiire to di^' anotlior, in 12 day of S.2 hrs. each, 1.") i"t. long, y4-;| ft. wide, and 12.8 f dee^> ? cx- ri;Aces of 24 do/.. oiiniLrrs -iieh did he buy! ^ r». Tf a farmer uses 1 p(.uiid of fertili;cer ..ii :; j.ie.., of irround 2 yd. .stjuaiv, how miirh will he us. ..n aere ? <'> an 7. Tf it eost $42.") to feneo a fi^ld 72 rd. hy 0>! rd.. what will it eost to feneo a square field of t!,.' s iue ar.'a .' 8. "What aro the eonteuts of a loj; t]C) ft. hiner 9tli, 1874, at a discount of G %. How mucli money was paid ? 7. Find the side of a square field ecjnal in area to a rectangular field 07(5 yds. long by 2r)G yds. wide. 8. How far from the house must the foot of a 2r)-ft. ladder be placied to reach the eaves, 2'-i ft. from the ground ? 9. How much cheaper would it be to pave a street one- fourth of a nule long and GO ft. wide witli asphalt at 22c. per s(|. ft., than to pave it with granite blocks at $.'{.10 per s(i. yd. ? 10. For what sum must a cargo of goods valued at $12:?G0 be insured at l'| % to cover both property and }iremium in case of loss? 11. What is the distance from the lower corner of a room 24 ft. long, 18 ft. wnde, and 12 ft. high to the opposite corner? Pkactkal Pkoulkms i\ Akitiimktk . l-*) l>ut 1. Make and solve a i>rol)]om illusfmtinj? tW i\\)\)]\. cation of s(inaro root in ftndinjr the side ot a ri^dit-anirled triiingle. 2. Wlmt will it cost to plastiM- tlie walls and ceiliix' of a room IS ft. l<,„g, 12 ft. wide, J) ft. hi^di, at 4()e. pcr's.,. yd? IL.w many cords of \v(K)d wonld the room hold if completely filled ? ..Simplify I 1^- "■•■•, '"-".« „YK,, J. 4. A boat whose rate of sailiiii,' in still water is 14 miles an hour, wasaceeh'rat.'d :].\ miles ])er hour in iroinj: down stream and retard.-d the same distan.M' in (..miinrr up. It was 4 hours lon<,'er in comiiies for $15 and sells them for l.le. a jK-ek, what is his gain per cent. ? G. A druggist bought 1200 ]l,s. of alum, avoirdupois, and retailed it by Troy weight. How m.wiv more lbs. did he sell than he bouglit ? 7. The rent of a sqnare field at £2 14s. Gd. p.-r acre amounts to £27 r,s. Find thr ...st of i.utting a paling fence around the field at 9d. a yard H Simjdify } of a - m of m ( W M ^ - 4 ( 0. If a mixture l)e made of ll)s. of candv worth 12c. a lb., 7 lbs. at Uic. a 11)., and 4 ll.s. at 2()e." a lb., what will 1 lb. of I he mixture Ix- worth ? 10. A sidewalk is l.-)0 ft. Ion and 4 ft. wide; it is nmde of 2-inch plaidv, crosswi.s,- on 4x4 sc:antlmg. Find tlie cost of the lumber at $24 per M. 46 PlUCTICAL PnoBI.KMS IX AuiTlIMETIC. 1. Goods l)oii<;*lit. at 40 % and 10 % off wer«^ sold at 12i % abov(^ list. If tln' lucrc'linnt's expenses are 20 % of his sales, does he make or lose, and what per cent, upon his investment? 2. A farmer's wlieat crop averages, per acre, I of -svhat his oat cro];) does, Init Ik^ receives i30 % more per hnsliel for it. If he receives !|!l.S(K) lor his entii'c croj) of GO ac. of oats and 40 ac. of wheat, lind the value of an acre of wheat. 3. I bought a horse in Liverpool for £;>() 9s. 4d. and sold it in C'harlpttetown for $K)4.7r), paying £0 2s. .'!d. freight. What was my gain or loss per cent.? 4. Find the number of revolutions made bv a carriage wheel 41 ft. in diameter while passing over tlie road from Georgetown to Cardigan, which is G mi. T). In a school of 28 scholars, 3 j)upils are l.lj yr. old, 4 others of 14-,', 3 of i;5,\, 5 of 11. \, G of Or, and 7 of S|. Find the average agt» of the scholars. G. Wiiat per cent, of 904 must lu; added to that number to make the sum lOOG? 7. If the unit of mcasui-emeut be f; yd., what is the measure of 3J in. ? 8. Express as the decimal of a week the time y huw^ht !<• pay S ? I 4. Exp-o^ .V of lis. lid. + /'. of 4 .uiui-as + '. ..D of *■■+ - IS oi 'A ,u .{ u.o. L>0 dy., u,(„M.y L.-ino. ^oHh r,.i / I per annum? " - /" I Mid San ^, .„...,..<, 4:^ d..^n...s 2/^ ..in. Mvst, ;ha . ^.no w.ll ,t ,. in X..V York wlu. it is u.x.n nt S I hrancisco? J 7. A jounn-y of HfiO „d. was nnul. l,y vail, stoanior jj.nd..a.4.. Tl. distan.. l>y ...h was on..fou..th and l.<. d.sta.uv by s.a tlnv,.-fourths of that hv rail Tla- I ^'-e I>- 'Mil., by ..<^,.h was double, and by s^, four-flf,hs I of that by rad. ^\ hat was th. .^xpenso of tho wholo jnurnoy, radway fare bcin^^ l.r.7142N,l. j.er n.il,>? S. IIow many onbic iWt in a ton of i,.,-, ifa <^•d]on of ,-t..r weighs 10 1b., n..asun.s 277.274 ... ^ I ''xpands on.'-tonth in frci-zini:' I 0. How many half-crowns are thr.v i„ n7()o jr„i„eas ? , m I invest. o<{ual sums i. ,4 .toek and in a ;] 7 90. \V hut IS the j.riee of th,' .{ p,.,- ,vnt,sf 4S I'UACTICAIi I'UOIJLEMS 1\ AlJlTIIMETK". 1. Sinii)]ify {a) :!.4i6 + l.OolOi - .24<'i7<"t ; (/>) divid .'57.4;j('i by .l;5!'t. 2. A sqiiai-o field contains 8^ ac. p^'ind tlio cost o niakiiiir a I'atli tlirco yards -wide inside tlie field, ronnt tile Itoiindary, at .'i2<'. per S(piare yard. ;}. Snlttract ..-'{Ts of Is. fi^id. from .37n of 2s. {)d. 4. A snin of money is to lie divided anionjjf 11 mei and ]S boys, and ') men are to i-eeeivo as mneli as ! boys. "When 3 men and •'{ boys luive received tlieii shares, wliat fraction of the whole sum will renniin ? "). Simplify: (2-' 400 , X .,: + ,- - U of ;i> ) -f- -y,\ + } of ui„ + ,^ C). Find value of ,'-, of £1 + ^' of Is. + ..'\ of a fjuinei + V of £1 (Is. Sd. 7. The circTimfereiice of the earth is 40000000 metres the lenyth of a metre beinj,' ;{9.;{707!) in. ; calenlat* the diameter of the eai'lh in miles, assnminj; the rati( of the cii-cnmfereiice of a circle to its diameter to Ix ;{.V) : li;!. * H. A watch, set on Fi'iday at 9 p.m., ^ains 4.1 sec. ii 12 hi-. ; what time does it show on the ne.xt Monday a .'> i).m. ? 0. Wlien silk is sold at 10 francs 25 centimes per metro find the eorresp()ndin<,' ]>rice ])er yai-d in .shillini;s an( pence ; snpposin.">.,')! 71 S4."), t(> T) jtlaces of decimals. - riiBif . ■•.-:> -iKi V. csarvi it-i^i.V 1- I*KA(TI( AI. PlJOIW-EMS IN' Ak" ITIIMKTK 41) 1. Tu-o cojr-wliools, one with 15 t.'otl,, tlie otlior witl, 18 tet'tl,, w„rk togotli,.,-. If the funuw t.m.s round 1(1 tn.H-s m 7A .s,-,... ],ovv many times will tlio latter turn ••ound in 21 see.? 2. An en-ine while driving machin-rv ])urns ooal at the rate of 1 ton 12 ewt. 2 qr. in 8 1.^40 n.in. Wln-n j thenrnvhineiy is not in motion, the consnmpti.,n <,f eoal I IS only ,', of this cjnantity. How mneh e(»al will tiie I "Mjrnie b,„-n in V>H4 In-., during i- of whieh time the maehinery is at rest f •i. A and 7? ride a raee of ,31 mi. on Lie voles The d.ning-whe<.l of .t's maehine nmk,.s .'{410 revolntions per iK'ur, and has a cireumferenee of 1(58 in.; that of li makes a:,20 revolnti<.ns jvr h(»nr, and has a eirenmfer- ''»<••' «.f ] r,2 in. Which will win, and l.y liow mueh ? 4. Add togeth.T ..']()2r, of £0 7s. fid., ]..3fi28 of 10s., and ■<»<'<4 uf 10(1., and expre.ss the an.swer in francs and'een- tnnes(l franc = Oid.). 5. An Iri.sh aei-e is to an Engli.sh aei-e as 49 is to 80} I1..W many English ac.res are th.-re in a farm <.ontainin- «.)2i Irish acres ? n. If a certain amount of worlc is done ])v 9 men l'> women, and 1.3 hoys in 11 dy., In.w long will the same work take if 18 men, ,3 w.nnen, and T, bovs are set to do It, a.ssuming that tlu* ratio of a man's w.»rk to a woman's IS as ,) to 3, and a woman's work to a boy'.s as 4 to 3 ? 7. A piece of timlier 15 in. square at each end, and 15 J t. long, is to be measured. Find its <'ont,'nt.s, and how tar from the end must it be e.it across, so that the piece ent off may contain 1 solid fo(»t? 50 I'l.'AC TK Ah Pl.'olW-K.MS IN AuiTII.MKTIC. 1, TlKTc is a tri!iii.-, hcMisos, cm-h lKMi.se 1ms 17 win- dows, I'l.cli window 4 iKui.-s, .'.-Ml ,.u..h imno uwnsnrvs IH m. hy «J in. What will lu- th.r cost of glazing ull tlu- windows at Gd. jht sqnarc foot? 2. A m-tan-ular cist.Tn lOi ft. in length, GJ ft in l.ivadth, and '^ ft. in depth, contains 14()^ cu. ft of water. What is tht. least nnniber of bricks, each 9 in longl.y4Ain.widel,y;nn. thi<-k, that must be timnvn into the cistei-n to mukv tin. wafr rise to the top, a brick iH'ing found to absorb Avater to the extent of '- its volume? 'i. Express .-,()()();{();] farthings in £ s. d. and subtract the result from 10021 guineas. 4 Two acres of land aiv t<. be cut from a rectangular held whose wi.lth is 2 chains fX) links, bv a lim^ paraUel with either end. What is the length of the plot? Jk a 9-months' note discounted at (J % yields $477.25 Find the face of the note. fi. If stock bought at 92 AviU i>ay 7 ;: on the invest- ment, at what rate should it be bought to pay 10 "^ ? 7. A pil,> of wood 128 ft. long, 4 ft. wide, and 3 ft S m. high, is sold for $:].; '» a cord. How much money is received for it ? S. An agent sells goods for his firm, paval)le at th,- tonowmgdat.'s:-$;20du.' 7tli .lanuarv; .fl.-JO due 9th February J $-200 du,> l.lth .March; $.-,()() due 20th May $240 due ir.th August. Find the average time of payment. 9. A room is 14 by 1 ft. l^luit wiU it cost to carpet the fioor-eai-pet scAved and laid at 90c. a yard— i^ 9 m. ar(> aUowvd for matching, stripes laid lengthwise earjjeting ^ yd. wide? 02 1*I!A( TK AI. TWOULEMS IN AltlTlIMKTK . 1. A owned il (»f a fiictorvuiid sidd '} of liis sluirc to / wlu) sold A of wijiit lie lioiijifht to i', \vlio sold H <»*' wlm lie l)ou«rlit to />. Whiit part of the fuetoiy did eueh < them own ? 2. A note for $.■)()() dated October 17tli, 1S{)0, was pai April 12th, 1902, with interest at G %. What was th amount i»aid? '? A ball disehnr«;ed direetly ui)wards returns to tli earth in IG sec. How high did it ascend? 4. A man travelled northward 24 mi., then enstwar HG mi., then southward 10 mi., then northward 4 m How far was he then from the starting point? 5. What is the face of a di-aft due 90 dv. after si{) for S in..., f(.r li.,w loiijr ii time must 1 hnm him !ii4()(> as uu tMiiiivalciif ? 2. IT<»\v many s<|uaro yards were tlicro in tlic area of Solomoir.s Tempi.', whose (iim.Misions an- m.-iiti..n.-.l in I. Kinj;s, eluip. vi., r.'.-k.Miinj,' (li.' enl.it to l..- is in./ I Tf N.mh's ark was .*}()() cubits l.)njr, .">() wi.l.' an.l ;)() high, how many euhi.; yards did it contain ? ^. On.Mjuarter acre of frround is .'..v.-r.'.l with \v...mI I'iled 12 ft. high; how much is it w..rth at $;}.2.'i a cord ! 4. B(mght $070 hank st..<'k at 4 per .vnt. advan.v; s..!d at a discount of '2.\ ]»er cent. Find the h..ss. 5. The sides of a triangular h)t arc ]l.")i ft., 12S.\ ft. and r.iVl ft. respcctiv.'ly. Il..\v many board's will it tak.-,' and what will it cost to fem;e it with lumber at .$7^i [..'r M., tlie h)ngest boai-ds p(.s.siblc being used and the fenc.- being r> ])oards Ingh, the bott..m one 10 in. wide, two G in. wide, and the others 4 in. wide? _G. I have two pieces of cloth, ea.-h M yd. l.>ng; one is -•'* % hmger than it sli.iuld be, a" ' ' -ther is 2.") 7 shorter than it sh..ulMi 1 be tlie .•.)mbin«-.'i l.-ngth of the two pie.'es if each ^^•ls of the i.roper length ? 7. Copper weighs f).')!) lb. and tin 4(i2 lb. t.) the cubi,; foot. What is the w.'ight of 1 .mi. ft. of the mixture con- taining G parts of coi)per and 3 j.arts of tin ? 8. A note dated January 4th, 189."), for $9874.69 with interest at G %, had the following endorsem.'iits :— July l«t, 1895, i-eceived $.-579.28; Feb'y 18th, 189G, received $4.)8.74. What was duo on the note Jaiiuaiy 1st, 1898 ? "Jl riCACIKAl, I'lJoni.KMS IN Al.'ITll.MKTlC. 1. If it cost .tU to i.aiiit tln' walls ami wV .i^r <,f rooiri !':» ft. l.Mifr, L»() ft. wide, ami 10 ft. Iii^r],^ li.,\v' iiiir will it «'ost to i»aiiit tlit; walls ainl eciliii},' <»f u room 50 loiij,', 40 ft. Avidc, uiul 1*0 It. liij,'!!? 'J. Two men start from the snni) \»n'\t. Oiu! tniv« •■{() mi. (Iik; north and the other 40 mi. duo w.-st tlu' saiiK! tinu', aiud tlit-u th.-y l»oth turn and travel t wards cucli other jit their fortner rates of speed. WIk fiiey meet, Ik.w far wll eaeh luive travelled from tl comm«m startin<,' jtoint? -\. 9 lir. G min. S see. is what j.art of l:{ lir ;i!) mi 12 sec? 4. Fin / per annum < $.•{12.7.'), from S.'ptemher 11th. liJOl, t.» Xovemher 2;{r 1!)01. .'). Find the cost of a stair carpet for a fli«,'lit (»f ] steps, 7i in. ri.so and 10 in. deep, at (iS cents a yard, tl steps to include U in. tloor space at the top of tlio stair G. Aph)tof land 200 ft. wide ca- »e exactly dividt into lots 42 ft. fi-ont, 4S ft. front,* .)() ft. fn.nt. IIo many feet in lenurth must the j. ,; necessarily l)e i answer tlie.se conditions? 7. Find the value of *t I , Ol _ , , ;\ + (2;; of 1,\) - i;l (:i-\^ -^ z\) + ]r^ of .1282.-) 4.2 l(i 2.t 8. If I piircliase D. A. R. G i)er cent, stock at 99.J brokerajre J ])er cent., and at th(> end of fi mo. sell it i\ I04i, })rokerage ^ p«T cent., what per cent, do I mak on my investment? 1« . J*.i.V(Tl( AL l'l;n|!|.|.;.Ms | .\ A I.I TIIM i; n, ■ »•» •ig of a >\V llllK'll till ')() ft. V. Iniviils Wfst ill j'uvcl 1l) mill. iiiini on tri.-t i-*'j:;()(i(» iK-t is v..hd al III iiijr. Find tin- t '>^ "II .1 farm J asscsstd fMi- !f.,, ,..|. and ;!(; s., I rd. IS s(j. yd. ' ••{. Til.' n..t pri,.,- of an artiVI.-, alt.,- .Irdii.iiii.^ ,|is .■oiints of ;{;;,■ 7 „n.l 2:. -; fn.m tl... list ,„-i,.,.. u..,s $4.,s7.. What was the list pri.-.' ? 4. Til.- i.roc.M.ds .,f a 4-montlis' nut., nia.lr an.l ,lis. ••••nut...! at liank of X.,va S.-uiia, An-nst Hih, ]'.Hi] ..,1 <;% Iter annum wr.. $22.-».4(». Fin.l th.- f.„-.- .,f ll',,. IKttc. ' - 1 7 at 99^, H'U it ut I make •"». A m..r.'liant sold a <|naiitity ..f ......Is fur ^')H\r> .in.l th.-ivhy l...st = of what th.. -.h.,|s ,.„.st him. Fin.l tii.ir (•.»st. I (•>. A has )f;y an.l /; .^7, with whi.-h th.-v l.uv a JM.at tor I *!.). (' ^av.. slo f„, . i,„,.,,.,t i„ ,,,,. 1,,,^;^^ ^^..jj^ ^1^^^ I nmU.rstan.linjr that .-a.-ii ..f th.-ni shall ..wn ..mIv I .,f th.. I lM.ut. ll.,w nm.-h .,f th.. $1(1 r...-.-ivod from (' h.-ion-s t.. I -4 and li<»w nin.-li t.. /.'? " 7. Divide, th.. snm .)f .1 and .u l.y .1, and |„ fl„. ,,.snlt add .()(K)7. Divi.l.. th.. .-.■.snit thns „l,taiii...i Lv th.- 4,>.75 in i>,ank ..f P. F. I. 4 :' st.M-k at 119.1, hr.,k..r- !). Find tlu. altitn.l.. of a ri-ht-an-l...! frian-l.^ whos,. I hypothenus.- is .'{(Ki ft. and h.ts,. ;{(;(» n. 10. The princii.al is $9;J0, tlu- iutt.r..st is .$n.-,.;]2 an.l tile rate is (i . Fi,i,l tlu- tinir. "66 I'lar-n, Al. I'l.oni.K.M.s in AlilTIIMKlic, 1. \ Ciirin.-i' piii«l .t47.-jr. iiisiinuirr i.ninim.i ..n I'-.-i.i r- ,rs..s. tl... nih- iM-in^' 1 j /. How .niidi was I 2. ' of \vov -^ I nio u cord. l-\.r h„w irm.-h was it sul.l? •'■ I '-'. .111(1 (• trail- ill |.ai-|ii(.rslii|,. .1 furnislics the -a) .: ami i; to liavr i uf tlic ^ain fuv «'Xt >«'i-M.. V /; uml (' f'M-iiisli .f.-iiKMI racli uii.l flic ,^n\n $:)7(i'i V'!,'* .- ' .siiaivufrarliy ^ ^' -^ ' »' 'i ^vhat will itcost, to iHiiM til.' w! of a . •llai- J I < . ,,nir. IS ft. vvi.l.., an.] r> ft. a.'..p, tl wall ,n in 2 f:. thick Jiud to <'.\t.-ii 1,..xs than tlu- divisor. Wlmt, is tl divisor? (i. How many acn-s in a n-('tan.u:nlar ti.-ld \ mi. Ion and .' mi. hi-oad? 7. A hid- )i<;aiiist ill! foot , <»ii<' af •est {MT (led the at'h rc- What ijn'opcr I. If ,-; of tlii'Valil.* of 11 li,M-sfi;Mu, wliiit i.s Ihr valii.' of ca.'ii 2. A iiaiv is 70 Laps Im-Ioiv u Immih.I, an. I tak.-s .'» l..a|»s wliil.. 111.. Ihmiii.1 tak.-s :i: i„ii ;{ „f t!i.- Ii..iii,.|-s l.-a|.s .•.|iml 7 of th.- |,.n-,.-> |l<,\v nmny l.-aps will th.- IioiuhI t t.ik(! to 011(^11 the Imiv 1 \ :{. A v..mmissioii m.-r.-lmiit sol.l laoo 1.1.1. ,,r rl.mr at •f».7.» i».-r l»an-.-l, i-.-.-.-ivinu- ji (!oiniiii,ssi<.ii ..f :i\ \ ;,inl iuv.-sf.-,l tifi- pro. ,1s in .-otf.-.- at 1»S,.. a poun.l,' liist ••'■•I'l.-tinir 2 ;^ (■ommissi.,n. What was his (,,iti.v .-..lu- imssi.Mi ? How nmny p.)iin.ls ..f .-ntf.-.- ,li,l he buv .' 4. Find tin- date of niafnnfy of a not.- whi.-h falls (hw !M» .ly. lu-foiv Mardi ir.th, 1!)(»l»; „f „„.- that falls dn,- !»<) ily. uftei- March l.lth. 1!)((l>. •"). What niiinl»(-r diminished l.v '.l'.\.\ ..t" its IH) 7 l.-uves 24 ? ' • • /. n. If a man .-vny ."> m... s|m-ii.1s what li.- .-anis in 2 mo., and em-ns $:,;{() .-v.ry 2A m.,., how miieh ,l...-s I,,- sav., in a year ? 7. I I»ny hai-.lware, r.-c.-ivinj; :{() 7. 2(), , 10 ,.,,1 -,7 off. and settle- tin- hill with $!>:)7.(iO. What was Hi,- Jist price <.f the liill? H. Divid.j if!l20() iumm- J, /.', f\ and A s.. ,|,at the dilfen-nee h.-tw.-.-n tli.' ain.mnts n-.-.-iv.-d l.y any two .•onse.nitive per.suns will Ix- .$-20. 9. Redne.. ^ to a decimal fraction, mnUiply the resnlt hy 24-thou.sandths, snhtract 4 ten-thonsandths from the product, and divide th.( remainder l)y 5-millioutlis. O.S 1*j:a«ti( Ai. I'ltoni.EM.s in AiaTiLMETic. 1. Simplify {^: L' + 1 3 .)- L 1 1 V {^■^^-^'-i«j J I .075 "" ■>n .1.' + 1*. How iiiiK-Ii iimst ji watcli l.c murkoa tliat c(»st $1 so that 4 / may W dt'dtictcd and a protit of 20% made '/ ■I A n<)t(^ of $150, dated Marcli ;]()tli, 189??, was ps •Inly 4th, ISU;}, with iutorest at (> %. Wliat was t aiiiount ? ^V*!lat would have l>wii the amount at 7,1 % 4. Au ajiviit remitted $2S2!).0:> for tlie sale of ^'<)o< after deducting,' $2SG.3.'3 for frei<,dit ehar<,'es and 1 e(»mmission of ,") /, What amount was received by t ay:ent '/ "). If a tank G ft. h)ui.', 3 ft. wide, and 2 ft. dei (•ontains 4\ Idid. of water, how deep must a tank be th is S ft. h)n<,^ and o^ ft. wide to contain 22:| lihd. of wate 0. r> sells \ of his cattle to .1, g- to ''', ^ of the r mainder to />, and finds that 48 head is /V of what 1 has left. I low 7nany cattle had he at first? 7. A mail purchased a liorse, jLjfivMnj? in payment h ii(»te at () /'. At tlie end of 3 yr. G mo. he found tin he owed .$42 interest. IIow much did the horse coi liim ? 8. At what per cent, below par must 4| % stock I quoted to yield the same ])er cent. Ji, who afferwnrds sold 7 of i,is ' .nterest to C for .^2116. Find th,' valne of (he vessel at tiie rate paid by C. 7 Tlie trustees of a certain school distrj.-t wish to 'mild a schoolhoiise to cost .$:,()(). The cost of coJl,.,.tiM.- this snm,to-ether with several incidental expenses wiU amonnt to $lS.7r,. The total cost nu.st Ik- n.ised bv - |MX on property valued at $2(;;;()4. How much will I I have to pay on a piece of property valiu-d at ^22r>01 CO rUA(;TRAL Pi:()|{LE>:.S l\ ARITHMETIC. 1. T.'as at 59o., Goo., a.id 7Ge. per pound respective are mixed in eciual quantities and sold at 81 a poui Find tlie gain per cent. 2. Three men l)()Uf,'lit a fnetorv. A gave ^'^OOOO gave § m<.re than A, and gave 2o % less than the to iuuount paid by both the others. If a G % dividcMid declared ou the capital stock, how much mouey should receive ? ^ 3. A pole GO ft. higli broke into two pieces, such th I of on.. i.i.M.e e<,ualled = of the other. What was tl Icngtli of each, piece ? 4. How many cubic feet in a wall 2 ft. thick and G J high, built about a recrtangular celhir whosc^ interi. dimensions, when ihe wall is completed, shall be 20 1 long and IG ft. wide? 5. For how much must I make the fa.;e of a note, date .Tnly ISth, V.m, for .'} nio., in ord.'r to get ft-om the banl which discounts at G %, 8GG()0 ? G. June 12th, 1902, John Smith buys of Prowse Bros Charlottetowu, 3 yd. silk at 81.45 ; 2^ yd. lining at 20c. 3 pr. kid gloves at $1.25; 30 buttons at 25c. a dozen i doz. handkerchiefs at 25c. ea yd. long. How h)ng is the other? _ 2. A man reeeived S.'W.^O interest on a sum h.anod o yr. previ(»us at 7 %. What was tlie sum h,,,ne.i ? :}. If a dealer uses 14 oz. to the iM.und, huu- nuM-h d.ws a person actually get who ])uys 1 20 su.Ui pounds ? ll„w nnieh per eent. does the dealer gain ? 4. If 87000, H % stock, he sohl for 8ir.0, and procet.ls 1.0 invested iu 6 % stock at 105, find tli.. dim.rem'e in the :neome. 5. A man bought liats for 81.25 each. He sold h.-.lf of them at a profit of '^'^ %. The remainder he s<.ld at a loss of .8.50, and tli.Mi found that ho had ^r.M.uMl 8.^ 7 ou the whole transaction. How nuiny hats "did he hiivV G. .I's rate of working is to /?'s as 4 to 8, and ik is to rs as 2 to 1. How long will it take C to d,» what I would do in G days? 7. A bath can bo filled by the cold water pipe in 9 min and by the hot water pipe in llf min. A p.-rsou h-avs the bath-room aft.'r turning on both pipes simultaneonslv and returns at the moni.mt wh.'u the bath should W hlled. Finding, however, that the waste-pipe has b.vn open h.> now closes it. In ;j? min. more the ))ath is full. Ill what time would the waste-pipe empty it? 8. An estate is divid.'d among 3 i)ersoTis A, B and r so that A has ^ of the whol.s and li twic-e as nni.'h as r It 1 found that li has 27 ae. more than C. How lar.^e is the estate? ° 9. I t.H.k a risk at \\ ^'. re-insured ?- ot it at 2r,and \ <.f It at 2h %. What rate of iusuranc*^ do 1 g.-t on wliat IS left ? ^J:^ J'K'.vcrn al I'ijoklkms jv Akitiimktk . 1. An Kn^Wish I,ni„.rial jrallo,, is ,t moasnro which wi h«.M 10 Jl, avou-. of i,n.v wut,.r. A clue f.M.fc «f ,,„, «-.-.t^T wnj^hs <>n u sich> of 'Mnj i, FmmI to two phices of ch.(.inmls how many litres there ar 111 ji <>aIloii. 2. Sunplify 1 -; . <,f ! ,v, „f £:} :: ^^. „f ^.^ ,,^ j,^j _^ or 4, J l;s. j n. A fl«,or is 27.:; U. loMif and 2(U.-i ft. wide. Wha will Letliceostof coverin- it with matting 2. i ft wid( at GOe. a yard ? 4. The ext.Tual dimensions of a hox (witii a lid) are as follows: L,nj,tii 2 ft., widtii IJ ff., J,,i^.l,t, l ft. no^^ .nrniy cuh.e inehes of M.r are there in it, if the walls <,t tiio box are li in. tliiek ? n. Simi>lifv: / ^r - r «»»^»lo=> + 2:,", -j I'x (.0018:;)=^ " V ■":; /(.ts) X (.0(160 i) ^ (.Oi;i)x(.ol5) - 1 1 "< 1 2.i 0. A lalmrer eontra<'ts to work SO dy. for 7r,e. a dav and to forfeit oOe. for everyday he was idle durim, that: time, lie received .^2.1. How many days did he work ? 7 IIow mneh e<.rn at 42e„ CO.., n7c., and 7,Sc. n.-r .nshel must hr mixed t...,ether, that the cmipomul mav ho worth ()4c. per hiishel? 8 What is the eiy:ht root of 722204 i;{(i;50.S7;JG? ■^ms's^^'m- PUACTICAI. PkuBLEMS IX Akithme'] TIC. o;; lich will of pure ivo. is a .i):}7 ill. lere are MISCEI.I,ANEOUS. 1. A man ^ot his lu.te f„r ^]'2iH) at 90 ,lv. disronuWd •••^ <> /., JUicl ItMit tlio proceeds for a y,.ar at 7 Mv .vn..w.n.,. .very !)() dy., payinj. dis,.<>„„t, h. kept Ids not; 'M tl.. bank (ho wlH.le year. JIow nuu-h was ^-aine.! in the year by tins <)i)ei-ation ? ± What amonnt nmst be invested in :{ ^' stoek whieli sells at 92^, to fonnd a s<.holarship of .$L'()(i a year? r'!'-?" *^'i:;i ^'''"'^^i"" *>f tin. prop,.rty in a sehool .hstru-t 18 $800000, and the amount to ]>e raised bv Mssessment f(,r school purposes is $!>()]. What is th'e mte m the dollar and what will John Snnth have to pav >f his property in the district is valued at $L>7r)0 ? 4. .1 and /^ are partners in business, vl's stock is to /.s «s 7 IS to 11. After ;} mo. .1 withdraws ^ of Ids t^X TV'^r' ^"^- ""^^' '^'"^" t'-" y-"-'^ ^'Hins uf $4062 be divuled ? ^ t, i ;■). Simplify (.477 x .2;j) ^ .001219. Standard gold contains 12 parts of pure gold to 1 fart .>f <.opper, and 20 11,. troy r.re coined into 9:J4.i sovereigns. Find the weight of pure gold in a sovereign' 7. Sold wheat at $1 per bushel and gained $.'50 on he quantity sold; had I sold it at $1.12A I would did 1 SIT" ^'' "^ ^^""^^'^' ""'''■ ""^^ --^- '--^-' ' J. How many men must be ..mploy-d to uiow lOO ae >- i-o. in 1^ dy., if 21 men can mow 72 ac. in r, dy. ? crown. 04 PiucTicAL Problems jx Arithmetic. 1. The true discount on $572 for one year is $22. What is tlie rate of interest? 2. If I transfer $3294 of 3i % stock to the 3 per cents, sellftig the former at 9S,^ and jjun-hasing- the latter at 91^, what do I gain or h)se by the transaction ? li. Three workman, A, B, C, did a certain work, and were paid daily wages according to their skill, ^'s eflRciency was to li's as 4 to 3 j ^'s to C's as G to 5. A worked f) dy., B 6 dy., and G 8 dy., and the whole amount paid for the W(n-k was $3G.25. Find what each man receives daily. 4. Find th(; value of 5(fiH 2i) of £1 + ?i^| i'f I >f U of a , Express the answer in Canadian currency. 5. If the People's Bank stock sells at 147 and pays a yearly dividend of 7 %, and the Merchants' Bank stock sells at I.IO and pays a yearly dividend of 8 %, what will be the difference l)etween the annual incomes whieli A will receive if he invests Sr)()()() in the stock of each bank ? G. Find the value of £1.1.'> + 2.(>(;2.') g uineas + .00781 2r) of 32s. 7. What stim must be put out at 5 %, compound interest, to amount to $2()()() in 4 \'r. ? 8. Explain the difference lu'twci'ii true and l)ank dis- count. 9. Simplifvf^^Ji^^^l-^^).. 2142857. .■M^ 'i^nsrwimw^'^-w^'- Pn.vcTicAL Pnour.KMs i\ Aritiimf/i TW. 1. I oxohaiiye an estato, wliose valtu. is £2r)4:]4 KJs Sd stjT., for st..c.k whose pivsmt valuo is $7Gl'()().H "and the foUowiiif; shares in s' " is £SL'.'{4 iSs. 4(1. s)j vahie is $9!)J)0. II* hips : I of one whoso wliolo valne find if of another whose wliolo <»\v nineh wonld I h.so or piiu hy the t.ansaetion ? Express the answer in dollars and ee.'its. 2. A ean do a j.it of ^ork in 2.-> dv.. 7? can d -0 dy., and C in 24 dv. Tl o it in + : 3+^ X f .000729 i + 2 3 + i 6i+ig-4i-n ■ ^"Y >/.(M)62()01 6. Find the cube root of 7| to three places of decimals. 7. The .specific gravitv of atmo.spheric air, compared with water, is .0012 ; thfc specific gravity of common gas. compared with air, is .45. Find the specific gi-avity of common gas compared with water. H. An army of 215296 men is drawn up in lie form of a solici square. How many men are there on each side? 9. A detachment of soldiers are drawn up two deep, so as to form a hollow square. How many men are there if the face of one side of the s(iuare shows 10 men? PjtACTlCAL rK01iLE31>» 1\ AurniMETIt . 67 1. Siinplify .niilft X .->,M ?:?■• " -^^ •>■-• ••■ . 1 ,( 1 '75 • •* ;i 5 li - X .2:; it 1.1 o8. ^h of I -• ^>:i»»'«'^« ill Aml.io notation CXIV, mid in I notation ]l!)S;j utniiin ir. per Vl\\\ il 1 nuin les as )onn! J + H +^ + i + I; 8. Compose a i>ro1>k'm of wliich the sohition nniyl)e as tMllows: £m - £.-,() Ss. = £12 12s. jrain j.er hogshead. Then £.-,0 8s. : £12 12s. :; 100 : £2.",, jrain p^r cent. 0. What is theeost of 3 hn. 1 i)k. ."> qt. of l.erries at 1 ov. a quart ? 10. How much will an anetioneer r<'oeive for sellinjr a piano for $4,")0, and furniture for ^'.WA), at (>J % com- mission ? 11. Find tlie sum of 6 and 428 thousandths, 23 and 73 hundredths, 18 and 4oG thousaudth.s, and 15 and J)07 thousandths. C8 Practical TifoiiLKMs in Akitiimetic. 1. Two nion, A ami //, liin, a paKture for $01 0'). A I)ut8 in 4.^0 8l„.(.p f„r 7 wk, un.l /; ;»;:, Hhcr,, f,.r S U Wliat should t'ucli pay ? 2. A del)t of ^r.'.i.r)-, ,vns dur .Afnv 2U\, 1MS(» l.ut was settled N<.v..nil.tr 9th, 1874, at a discount of y. How much money was paid f 3. Find the value of (If-i.;)x.()L'.-, y.oi HxSxi'-x ,', X J^. 4. Find th., face of a si^dit draft costing,' $50.40 wlicn cxchauj-e is 2J % premium. T). Fiiul tlu! side of a square fi.'ld equal in area to a reetanyuhir field G7() yd. lonjj l)y 2:)a yd. wide. 0. I rented a Louse for 7 % of its value, and in ,no IH dy. I received $122.08 lent. Find the vahu, of (he house. 7. Write out a prol.leni of whi.-li the solution is as follows : 100 % - 20 % = 80 % left. SO - X 140 / = ll-> 7 112%-lOO%=12/i.ain. ' ^" 8. A hoy sold f bu. 5 pk. -} qt. if j.t. of herries at ."ie h pint, and with the proceeds bought sugar at .{ 'e. a p.)und How much sugar did he get 1 9. Tliree men enter into partnership. A puts in $4000 for 8 mo., B $0000 for 7 mo., and G $3500 for 1 vr They gain $2320. Divide the gains. 10. A person owning 10 shares of 3 % stock sells it at $/4 per share. With part of the proceeds he buys enough 5 % stock at 105 to yield tlie same income. H(iw much money had he remaining ? Pr.\ctical Phohlem.s ix Auitiimetic. 69 1. A l-OOMl is 10 ft. lonjr, 14 ft. wi,l,., n.Ml 10 ft. l.ijrl, it 1ms ;j wirulow.s (j ft. l,y ;j ft. ;{ ii, , l» ,1 Hiid tli») bast'luxinl is f) loorsT ft. l.v.'{ ft. t«'riuf< tho room jit !.')«. | ui. \vi(l.'. Find t )»'i' sijium^ V!irv .'}. Fiiiil the 2-/X7J, S !» ft. wido, witli z 4. Simplify: A + .2:i + L* t of liniiiii: )i tank 14 ft. louj;. 7 ft. .l.'cp, iKi ut 40(!. [u'v stpiani yanl. . 1 L'.i + + lKS JN AkiTIIAIKTIC. tMMM 74.028.!; (r) divi.lu 27.(ir)i l.v llMl. 2. ('0 Fiii.l H.,,i„n» root (»f ]()i»();{()4();i()L>()i ; (h) fi,„i ciihKi root of 410G.](i2.>. ^ '{. Siuiplity: 4r)()|--3.; (H «»f .? - i «'^' ;o : (14J X ;/,) Hiid rrduco tlio unsw.T to fiv,. pl.-u-rs of (Ic-inials. 4. Find tho compound infcnst oii £:>()() for .T yv ut 4 "^ 5. lutho sr„t,Mi(.e, "Of all tho suvv.s that ev,r I saw saw, I ,„.v.-r saw a saw saw us my saw saws," what ...r contage of th. lett.rs are c.ousona..ts, wliat iu..rnuJ. of he w..nls are nouns, and hy Low nni.-li p.-r ..nt. do th. ->alnundx.r,,f tho lottors fn tho voH.s exocvd the total nnniber of tho lottors in tho ni.uns 1 0. Ilowdoosa s.i;uire diffor from a cuho? A solM-ro romaouolof An an^lo from a trian,.iof A pv.anud from a eouo ? A cyiindor from a prism ? 7. Tlie markot price of an article is $2.r)(). Tlio mor of 3^ y ""^1 t"r:"f ''\ -'' -' ""'^ «*^^^ "^'"-^ '^ l'-"t "t J.ii %. Wliat did tlie doalor pay for tho artido ? 8. A merchant l.ou-ht 4(iO bhl. of flour at $:] 75 p,., barnl Ho s.nt tho flour to an aj^ont, wiio sold it at an advance of ^ % and char^.o,! J /^ commission. The nnr- / cluint tlicn sent the not proco.-ds to an agont to purchaso niolassos, after d<"ductin{r a conimissiou of 1 j -/ ij^w many galh)ns, at GOc, could tho niront puroliasoT 9. If 200 men in 12 dy. of 8 h.-. <....oh can dig a trench 100 yd. long, 18 ft. wid.> ..nd 4 ^=1. ;\^.., days of 10 lir. each will 90 ju< 4 yd. wide, and 3 yd. deep ? 1>, i;i liow man 11 + J.s;"i 4- .(■; ^ l of th»» result.* .'{. Expns.s .;{7.") of a jru in< )llld tillll lilc |i|t' a n-own 4 .;; of 7s. r»d. ^ U of LM. as th.' (l.( inmi of 1(1 4. Find Uw siiuaiv r.M.is ,,f .;j. l(;.:{r,;jf>;;(i^ j | j^ o-,,, .{- 1, iind .(MJo. .'). Divide £110 aniui;,' K 11, •'hilcb'fii, so tli;«t each niiii!'. -I, of 2 women, and the .{2 woin luueh as the 4S childreti. •"IL \Voi.ii.|i, III,,] \s wii' «'iiial tlie ^||,|(•es uiil r, r.-iv,. twice as Kii- siini is .">1 and 0. Find two nnmlKTs, such tiial il their difference 1.'). 7. At the Canihridjre local exiiniiiiutions the muni junior stn7().l(il, SOfiTTr^JSKil, and 2.5. 10. Simplify. 2 i \ of 1 J !__■ '^l 2.] ^ • ^ 7 ^ l(».i i 3 + 1 1 (:;r-\i^J X 1 '>' 72 Practical Pkoblems iv An ITlIMETic. 1. If 1 oz. 4 (Iwt. 9 gr. est £1 lis. ()J,1., what is the pricu of 5 oz. 17 dwt. ? j , t i.> i,u PROPORTION. 2. If i„ 2(U(; dy. of Hi l.r. .,.,.1,, 12 ,nn. l>„i],l a wall ->(> ft lo„^ 28 ft. hi,.h, a,Mi li ft. thi.k, in how ,n,.nv Onys of 2 h... ea,.h will 9 men build a wall 9G ft. lo„. -'1 ft. Iiij.h, and IJft. thick? ^ ■I The tax to' bo raised in a town is .SIGS?.",, and the assessed valuation of the property is 8ir,()(MM)() wint amount (,f tax will a man have to pav wln.se pro,>ertv is assessed at -SGoOO ? i i '.v i^ i. A and n can plougli 22J nc. of land in 3 dv • /; and C c.m plough 6 ae. in 1 dy., and .1 and C 13 'ac! i„ - (ly. How many acres <;. ■ ach plouj,'h per day ? 5. If A can do a piece of work bv himself in 1 hr 7? in 3 hr., C in f, hr., and /> in 7 hr., in vvliat ti.ne can they do thn'c times as much, all working together ? G. If 120 men In 3 dy. of 12 hr. each, can dig a trench 'JO yd. h.ng, 2 ft. broad, and 4 ft. deep, how many men would l,e reciunvd to dig a trench 50 yd. h.njr G fl deep, njid U ft. broad in 9 dy. of V, hr. ? 7. A tract of land 7495 ac. 3 ro. 32 rd. is to be divided among a regiment consisting of a colonel, a major 5 <-uptains, 9 lieuteiumts, G ensigns, 20 sergeants, and 450 privates, so that a sergeant is to have twice as nmch as a ' private, an c.isign 8 shaivs. a lic-utenant 12, a captaiix 20, the major JO, an.l the eolom-l 50. Find tho shai-e of each and the value of the Juud at 83 an ar-re. > ^W^'^&^rC: Xvif :^^:, .jfW. PitAcTR'AL Problems ix AuiTiniETif, 73 1. A alone could porforin a pii-eo of work in 12 lir. • ^l and f ' t()j,^('ther could do it in o hr., and r"s woi-k is to /i's us 2 is to ;J. The work must ])c coiupl.'trd l)y noon. A bej^'ins work at o a.m. At what hour jiuist />' .-lud (' join him so tliat tlie work may be complctfd in time? 2. If 4 men and 18 l)oys working together can do three times as nuieh w<»rk i»er day as 2 men and 4 l.ovs together, compare tlit« work of a boy witli that (.f a maii. 3. If battleship having 1S()() „i,.,i on ])ojird and pro- visions enough for l.i yr., sliould lose \ of lier men, how long would the provisions lasl the remaindi-r? 4. If 1.") men, working (i hr. 40 min. per day, can diir a trench 48 ft. long, 8 ft. wide, and :] ft. deep in 12 dy!^ Iiow many hours a day must 2.') men w(.rk to dig a treneli 3G ft. long, 12 ft. wide, an end of 2 yr. what amount is due .-i person who has deposited f}2o at the beginning of each iutere.st period ? ^■;si-^.':l:;^£l 74 VRAVncxL VmULEyiS I\ AKIXIlilE-J TIC. 1. A Tiu'ivliunt bought goods aiul .sold them for P4'>()0 losing 10 %. Wluit did the goods eost liim ? ^ " ' 2. Find the eompound interest on eiOOO for 2 yr. at 'H %> payable quarterly. 3. What is the amount of $600 for 168 yr. at 6 7 simple interest? ' ^° 4 A note for .^2500, dated July 1st, 1;S9S, was to be paid October 2i,d, 1900, with eompnund interest at 6 %. Find the amount to be i)aid O(!tober 2nd. 5. 11800. Annandale, Septemlu-r 10th, 1900 For vahu^ received, T promise to pay Patrick Ri'ee or ord.T, Kiirhteen Hundred Dollars /'.;;, in one year' witu interest at 6%. C. 0. Howled t. A^ payment of .^6(H) was made „u January 25th, 1902. What was the balance due July l,")th, 1902? 6. I ho]?lA)l Practical Pkoulems in AuiTiiMEiic. to 1. Express jis a decimal : 60 ! .19 1 + ( ()(» Ol ) 2. Divide the sum of 4i], 7'^, 3,^^ ^'V tlie difFereiiee between ]J ami 8,^, and multiply the result by 7.\. 3. Simplify: ( + Ir. + .37;-) + C.lM .oor.!?: _'.j 4. Simplify (789 - JH!)) (.7.") - .07 ) X ./.)<» f S) — - - .00090. llH■^ .04 i 5. Multiply 7. ;■{(■) by 3.:297 and ••xpr.-ss th tj answer as a decimal fraction. 6. Simi)lify •U + 4^ - m -;- 3?) 3 + o + ,i42sn7 7. If the difference lu'tween 7.") and ;:' of 121? + =^ of 4S§ be t«,ken from l.lOi, by hoAv many timt-s f, of 1 ^ of 4 - 24 should the r(\sult be multiplied to ])roduee 342 ,';,'„ ? ■S. Find the value of (1?. -*)x(i-,"o) . ^of bi i of 4i of ) I (2H+3i)x(H', 4.i) 2H + (3ixSi, -4i 21 + }% ,1 ^ S •_• 1 .! T 1 + 1 i_ ••« 70 PiucTicAL Problems m Arithmetic. 1. 7f 1 of -i-(§^>fl.^) , o , what will ^•^'^''^•^i)- 2.5 PMS^NT WORTH AND DISCOUNT. lM.Na 1,. ,2 „,o. l.en,.., u.mI sol.l thoTu at once for $07-, r^Q 4. A ],ill of .$;j;527.50 dmwn on Jannary Isf, 1901 at 8 nm. IS discounted by a ha„kor on the ] tb Apri io ;>--.^ at 4 %. What does the hanker .ain by Sno ' in- interest instead of true discount / J. Find tlie present worth of a note of $:mM ,h,e 80 dy. hence at U 7. (i. A l.ill of $SL>.-) w,is drawn on 0<.tol.pr 24tlr iqni .,. 1 111(1 the present worth of it. <'"nnted 146 dy. before bein^ due, at T, %. «. A merchant bouo^ht 50(» bbl. flour at $6.o() per '-•■'-1 and sold it imn.eork a bill of $7:} due in 1 mo., and sold tlie ]M)rk at onee for a note of $S7 at 4 m(». Find the niereluint's jraiu or loss per cent., interest at Ah %. 4. Show that the diflFereiu .. between the interest an?, 1 may hav<' a, net in- eonie of 4 % on mv outlay? S. I invest $2n") f(.r 8 yr. at 7 % and tln-n buy bank st(.ck, 12 per cents, at n4.i. ITow mueh stock (hi I get ? 9. The income (»f a railway company would jiay 4 ^' dividend were there no preferejice shares; but $200000 of the stock being of sueli shares and guaranteed f) %, the ordinary shareholders receive only ?>h %. What is the whole amount of stock? /8 P«A(TI( AL PaoiiLKMS IN' AhITILMETIC. ^ H^ < ars at 90 H.Hl n.vesf .nj, in 4 p.v c.nLs at llo ttiu.^ ar. j«. After rcceiVMM' a Ji-ilf v,.....'. ,t • i ^ " ^U,K What was tl.o original sum inv.stod ? ^ .^ 1 invest .r)40 in fi jht ocnt. stock at O-i . *i«>(K ac :^)i, conunis- •^1011 i ^^. Ilou' much stock do I receive ? 4. mat sum Tuust be invested iu 4 per cent slock at on m order tliat after paving an inco/ne tax of 4 ,, th.' doHar, I may liave au inc mie of $400 ? proceeds ,n 4 per cent, stock at 76 ana the rel' .^ n ^^1- cents at 114. mat is the alterati<.n in 1 -/i;;; o a 89I'" ^^'^'VT-"""' ' •^•"-•'« •^■•vidend he sells out at 89,. The whole increase o Wliat did he invest? ' '-^ -Ti — 7 A person holdin.s,^ ,£l.-iOO st.Tlinjr stock in 3 i>er »"•). tuul the g-ain in uifojue if £1 ^ $4^7. S. I invest .$10000 in the T, per cuts .,t 0". ir much nnist I also invest in tlu. r "^'"/'^ ^•*- ""«• X .u.so in\(st m tlie G per cents at V^O tint myinc•■'• vllJit riiALTICAI. I'liOliJ.KMS IN A IMTHM KTI( . 7!) I I MENSURATION. 1. What is tlic /JifT'.'n-ncc hctw.-.'n S s,,. ff nnd Hft square? The dittVirn.-e m a.va l.eiween 1 s.,. ft. and" J 1 ft. s. Thirty-two yards of carpet. 2^ ft. wide, an. used in niakui-a s,|uare rii- winch is laid evenly in the centre "1 a reetaniiidar room 24 ff. }>-, Is.i ft. Find the dis- iMuee the carpet is fn.ni the suh-s of the room, and what IS the area of the uneovfred portion of th<. floor? f). A room is 21 ff. huiir. 1') ti. (I in. wide. 10 ft hbrh • It contains ;{ windows, th- re.-ess.-s of which reai-h" t/» 'Ik- c'duio., and are 4 ft. G in. wide; there are in it 4 doors, (>aeh (5 ft. (i in. hij^h and ;5 ft. :i m. ^^■\do, ■ the fire place IS (5 ft, wi.io .,na ^ ^^ ,,i^,j^ . ,^ ^j,;,.,;,,,, , f, ^ .^^ deep nnis ronnd the wall... Find the cost of paperin.^ Hie room at .jc. p.r .Mjuaiv fooi. ' Find thr ar<-a of a s.inar.' wli<..se side is 17.02.1 ch. ^. Wliat i.s thf a?'ea of .;i triani'!!- vc'.in-fu- \;^^i. ;. - o -■ •h. and altitude 0.4 eh. : 80 PltAr'TTfAL PriOIlLKMS IN AlUTIIMKTIC. 1. II'> c'u., also the perpen.lieuhir is 5.1:. eh. Find the area. "" r>. Find tl,e,an.a <.f a hexag.ni whoso side is 14.G ft and pei"pen,4. ' ' ''' 7. The length of an irregnlar figure is 50 vd. and its hivadths at seven e,,ui,lisfunt phiees are 5.5,*G.2, 7 3 G 7.0, 7, and 8.G. What is its area? ' ' ' 8. The diameter of a eirele is 34 ft. Wlutt is tlie length ot the cireumferenee? 9. Find tlie radius of a eirele wliose are. is 1 ro. ^V\ Find the area of a ein-le wh<,se einMunferenee is 11. The differenee between the diameters of two e.m- centne e.reles is 5, the greater diam.f.r b,.i„g i.-,. Find tiie area (.f the ring formed by the cireles. 12. How many imperial gallons will a tank in the torn, ot a eube eontaiii if one side of the eube is 7.5 ft. ? wJ* 7'"\V"'"/^'" ""^'^^ <*'>»<<'n^sof ablo<.kof granite whose length .s 10 ft., Us width 5^ n., and depth ^J ft. ? I'KA< IK AJ. PUOULKJIS I\ AkITMMETIC. 81 1. Find tlie si.li.lity of a oylindcr wl 15 ft. and (tircuinfeiviKMi of its Jmse 2() ft. lose height is 4.G ft. < I 11(1 its II 7.3, G, s tlio "^e IS J ' con- Fiud I the ft. ? initc ft.? 2. Find the solidity of u <'oii(', tlui diiuin'ter of whose base is 18 iu. and its altitude l.j ft. :;. Fiud the convex surface of a sphere who.s<. diameter is 18 in. 4. Find the .^olid eontents of is 18 ft. 'i. What are tli a sphere whose radiu^ e eontents ()f t\v(» niahofrany plank.s, •'ueh 12.^ ft. lonj; hy 11 in. wide? f). Tlie lenjrth of a pieee of .'uinan-d tinil.er is 49 ft. and its ends are eiinal scpuires wliose sides are eaeh 1.04 ft. What is the solidity ? 7. The eireuniferenee of a tree in four diflFerent plaees is as foHows: in the first ])laee, 3'^ ft.; se<-ond place, 'y^ ft.; tliird place, 4^ ft.; fourth place, 4,"., ft.; and the length of the tree is 15 ft. What is the solidity ? 8. The weight of an iron sliot used yearly at the Caledonian sports is IS 11,. Wliat is it.s dianuierf Another shot weighs 12 Ih. WHiat is its diameter? J>. The three sides of a triangle are 12, 20, and 28. What is the area ? 10. Wishing to find the lieight of the flagimle on Anuandale st;hool lawn I procui-ed a staff 5 ft. in length, and i>laeing it in the sunshine, perpendicular to the horizon, I founole ? 11. A tract of land in the form of an obtuse-angled triangle contains 1 ac. ; two of the sides are 20 ant tJie tlirce answers. r, A,U1 the followin.ir ,„„ni„,, ,^i^|,„„^ . ^nu.tH.ns:-;i.Ow, 2.0G;i, 8.210, 4.5<>, mui ^i.m. (y. Add tojrethor .5 of n ),i„f i .,k ., . __ .> of u peck and ^.pt. '^- ^ l**^' - 4t., .7. ot n,n., 7. Simplify-: ■ S.i of . Ss. + ., •)..-. „f2.tr„iii,.H.s 4-1. ,S« ,f Ds. 5 1 AHV^ ^ ■""> ■^K 2o l,y 8. Divide !(20() + .()2-.nx.,s{+(.,si ,.,- ^., „. -,,, -'.07of .^x300x,f)0.:j • ^ ^ •'-n.x.f of ,•)! PRACTtCAL PuoiiLKAIS IN AumiMKTlc. H'J 1. Simplify: (;;47.H4-=- 10.87) X i(.0| (lOHO X :].-27) ^ 10.90 _ (75JO-: ;{.y:,) ^ '^•' ' "hi:; '2 i \ 5i -0.042 2.4 + 7.^ \ "~ -. FilHl tii(3 Villllf of .1 -J 1 7 » • f3. 1 2 + fAmiry .< X " »( >«;(;.-) 4.;{7.") ^80 - f .01 .( )(»()(). O 7 7 - I I I •*{. Find iUr valiui of £.(;:{4:!7."> + .02.') of 2.'»s. +- ..'J2."i of •iOs. - 2.1 j.i of .Is. 8-^i. (liviiK'd hy 4^ 4. Find tiu' vidiu) of llUiid milrs. "). Simplify: ( '.07.') X 0.07.')) - (0.00.1 X 0.00.')) 0.75-0.05 ^ snim.imn. PROBI^EMS REI.ATING TO WORK. dy. of ■"> hr. cacJi ? 7. If yi can do a piece of work in 5 dy., /i twice a.s Muich in 7dy., and T four times a.s much in 11 dy., in wiuit time can ^l, 7?, and (! together do three tiniys the amount of work ? 8. A boy hired with a farmer for Ifi weeks fo i and a coat. At the end of 10 weeks the hoy (luit.s work and receives §6.35 and the coat. Find the value of the coat. - i-'r- MICROCOPY RESOLUTION TEST CHART (ANSI and ISO TEST CHART No. 2) 1.0 I.I 1.25 ■ so 1^ 1^ 2.2 13.2 ?r 14.0 2.0 1.8 ^ APPLIED IIVMGE Inc Sr 1653 Eost Mam Street r.S Roctiester, New York 14609 USA ^S (716) 482 - 0300 - Ptione a^ (716) 288 - 5989 - Fax 84 PuACTicAL Problems i\ Ahitiimktk . 1. What will it cost to paint a room 20J: ft. louj,', 18^ ft. wide, aud 10 ft. high if there are two windovvs eaoli 7 ft. by 4 ft., aud the work costs 62^c. per square yard ? 2. A aud B agree to do a piece of work for $36 ; A could do it in 9 dy. aud B in 12 dy.; but C joining them, the work is done in 4 dy. How should the money be divided ? 3. If 15 men dig a tren-h 48 ft. long and 2§ yd. wide in 14f dy., in how many days would 25 men dig a trench of the same depth, but 12 yd. long aud 12 ft wideP 4. Tom, Dick, aud Harry, working together, can do a piece of work in 5 dy. Dick can do half as much as Tom and Hairy together, and Harry can do J as much as Dick and Tom together. They rec<'ive $45 for the work. What is each person's share ? 5. Eight men were hired to do a certain work. By five of them failing to appear the work was prolonged 44 dy. In what time could the eight men have done the work? 6. Write out a problem of which the following is the solution : 12 X 7^ dy. = 87 dy. work to do ; 12 x 5^ dy. = G6 dy. work done ; 87 - 66 = 21 dy. work to do by the 4 men; 21 - 4 = 5|; 5J - 5J = | dy. Answer. 7. If the rate of wages of a man, a womau, and a child be as 6, 3, aud 1, and 25 men, 30 women, and 10 children get $320 for 10 dy. work, find how much 32 men, 36 women, aud 72 children should get for 8 dy. work. 8. A, B, and C mow a field for $12. A mows as much as B aud C less 5 ac, and 7? as much as A and G less 10 ac. If A receives $5, how much should B aud C each receive ? Practical Pkodlkms i.v Auitilmetic. S^! PROFIT AND I^OSS. 1. A dealer sold a caiTiaj^e tor $7(5, and tliere])y clcart'd ^ of his luouey ou it. If lio had sold it for $.SS what would ho have gained jxT cent. ? 2. I bought cotton for 8^c. per yard, which was 20 % less than the asking price, and the asking pi-iee w.-is 12| % more than the cost. What did the merchant gain or lose ou each yard he sold to me ? 3. A schooll)oy htiys slate i)en(!ils at "x-. a 'lozen k»i<1 sells them at the rate of 3 for 2(;. "What does he irain per cent. ? 4. By selling 10 lb. of tea for $r)A{) I gain 12^ %. What do I gain or lose per (!ent. by selling 2.> lb. of the same tea for $14.25? 5. A grocer mixes 68 lb. of tea at 32c. a pound with 36 11>. worth 28c. a pound. At what jjrice mu.st he sell the mixture to gain 13 i\c. a pound ? 6. How mu'jh per cent, above cost must a man inark his goods so that he may take off 30 % from the market price and still make 30 % on the cost? 7. A btiys a tract of land at $42 an acre. If he sells i- of it to B at $21 an acre, J- of the renminder to C at $()3 an acre, | of what then remains to J) at $12.7.j for \ of an acre, and the remainder, 193 J, ac, to U at $72 for § of an acre, what is his gain or loss ? 8. A man bought a farm of 165 ac. 2 ro. 32 po. for a certain sum and sold it immediately at $33.50 per acre, and took a note for the amount, payable in 5 mo. 15 dy. at 7 % simple interest. He got the note discounted at once. How much money did he make on the transac- ^ tion if he bouglit the farm for $4986 ? 86 TlJACTK AL PlIOlJI.K.MS JX A KITII.MKTl, 1. Tin. 4 iHT n-i.ts an, .s.-Uin^, ,,t l;{(i :uul ll„, ;j „,.,• n'Mts ut 102. Uovv „„,.•!. would T pti„ or ],.... in Uu.L kv s,.!],,..- cut moi) stu,.k iufh.. fonn.-r an.l iuv.stin- tlic procH't'ds in tli.- latici-? * 2 A irKMrluint failing, iu Lushu-ss can pav 70,.. <,u th. dollar. JI.. cm.rs to pay ],i.s whuio iud.l.h.du.'ss iu r, .vcars If h.s nvditcrs NviU allow l.i.a to ^.„ on witli his •>u«iue.ss. Ills off.T iHMuj. ac-rptr,!, ],ow luuc-li will his .•mlitors lose iu the 5 y.-ars if niou.'v is worth 7 7 simido i,,l.r,.st ami the merdmut pays no iutercst on lii^ mdt'btt'dness? 3. A luerc'hunt pur.-liascd in ]\Iontreal p.ods oostin^ *-0G0 on the foUowinj,^ terms: G nio. credit or .1 7 off toi- cash. Ho cliose the latter nn.l kept the goo.ls for (.0 days before sellinjr them; he sold tliem on 1 year's credit at 20% advance. What were his profits on tlie whole transaction ? 4. What was the cost to tlie wholesale dealer of L'oods sold by the retailer for 140 ^ndnc.is, if the whoh-sale .• w:--'* I*i:a(ti(al I'|{oi!lkms in Aimtifmktic S7 1. A ^r.M'(T huys ]:>() 11,. rolfcc ,il llr. [k-v ixmiikI, :iimI :'.!) 11). chicory .-it G.'. per pomid : lie p;;ys ;m import duly ol' \2.l y,atl r, I Ion' III, una mixes uiid sells them at 2r,e, |)cr ixmiid, hut l.y the us.- of a fals.' wcii-ht i-aius J-o/,, .►u every pound sold. Find (he perccntaj,'e"of prolii made on the outlay. 2. J)efiue (^0 a tax, (h) direct tax, (r) p„ll tax, (S04(>9(;. 4. Siinpiifv >'™^''"i + rmummi '). Dividi! tlio culKM-oot of H:i7Al')(HH) hy | ,'. ,,f 12,^ of -.^ "f (I+r!- 7)<»f !;;! and diniiuish the result liy the sTst G.C.I), of 945, 1560, and 22683. I'KACTK AL I'ltOMI.KMS 1\ AlJITirM KTIC. St) 1. Prov(^ )>y nil example tliiit tlic s((uaT-o root of tlic lirndiict of two or moiv imiiilu'r.s is niiuil to tlif prudiu-t of tlR'ir !S(|Ujire roots. 2. Tlic square of twice a iiiunlM'r is liMi. Wliat is the iniiiilier? MEASUREMENTS, ■ i. A eirele and a sijiian^ eaeli li.is a eireiiit of l.'».i ft. W'hieli lias tlie greater area ? 4. Apiece of land is .'{:;(! ft. Ion-,', and .•ontains M sij. chains. What is its width ? ."). How many sleepers, placed 2 ft. apart, and Imw much iron u.siui,' 2."> 11). t(> the yard ut rails, will 1»e re(iuired to CO nstruet lo mi. of the Belfast Murray Harbor Railway 6. Find +he cost of the lumber for the dre.ssed dnov facings t.f 30 doors, each 7 ft. high r.iid L'g ft. wide, the facings being G in. wide, at $18 per M feet. 7. A box whose 1»ase is s(pian! (contains ■• 1 cu. vd. 10 ft. 1)4.3 in., and is 2 ft. .'{ in. iiigh. Find its width. 8. A garden is 24.^ rd. hmg and l.Jj i-d. wide. Kind the cost of digging a ditch round it 2^ ft. wide by 4 ft. deep, at G^c. per cubic foot. 9. What will it cost to survey 12 mi. of the Belfast Railway at $2.2.") a chain ? of 10. If the diameter a semicircle I'ornuM of a circh is 12, what is the area 1 from it V !M ' 1*JL\( IICAI. J'lJOlJJ.KMS IN Ainni.MKTK EXCHANGE. I. Find tlui cost of the f«»lIouiii}r (li-uft, t'xdmiip. '"'"J^' :} Z l>i-«'iiHum juid iiitcmst G % :— •*<>««• Clmrlottetown, P.E.T., May 1st, 1902. Thirty (lays jiftcr si^ht i)ay to W. P. (}uiuly <„• b.-aivi-, six liundtvd ei^'lity-cijrht dollars, value received, and charge the same to the aecoiiiit of rc- mium can be jmrchased for $740 ? 4. If £1 stg. exchanges for 24.8 fr., and the Frencli a per cents are selling at 70.2 fr., what sum of English money will I pay for 19041 ^ ^; -; of the French 3 i,er cents ? 5. A gentleman in Moncton wishes to pay a bill of $1400 in St. Paid, Minn. What mnst he pay for a 60- day draft, exchange being | % preniium and the rate of discount being 5 % ? 6. Define (a) exchange, (/>) domestic excliange, (e) foreign exchange, (d) bill of exchange, (e) drawer, drawee, and payee. 7. A merchant in Liveiix)ol owes a debt of 1750 pistoles to a gentleman in Barcelona. Does he gain or lose, and how mucb, by sending tlie amornt to Barcelona by way of France, tlie exchange being £1 = 24.4 fr., 19 fr. = 1 pistole, ar.d 4 pistoles = £3 ? 8. What is the face of a dr.it on St. Petersburg wliich can be pmchased for $047.50 when the rouble is quoted at $.505 ? P|{A<'<' = $..'{"J.*J, wlmt will !»<* tli.> cost of ii lull of t'xdmiijye on the Hank of Calcnttii f(»i- LMmX) nii»'«- Ixnight lit St. Jolm, t-xchanpt Ixinj; 8 % pn'niiniu ? 2. A man h-avinj? ('luirlottctnwn for Sonth Africa wishes to carry witii liim two l)ills (»f cxclianjr*', one on a bank in Brazil for ;}00 niilrcis and the other on a bank in Chili for sncli an amonnt as he can pnrchase with $282. Find cost of the Prst bill of excluui«re and the face of tlie hitter, the milreis beinjif (]noted at $M2 and peso of Cliili ($.91.')) at G % preniinin. STOCKS. 3. I can olttain $0 more per annnin by investinj^ a certain snin in 5 per cents at 12S^ than in the 3 per cents at 81 . Wliat is the snm ? 4. A person laid a certain snm invested in 4 % stock. Ho sells it at 11 7^, and invests lialf the jiroceeds in 2 % stock at 90, and the rest in 3 % stock at 99. He tln-n finds tliat liis annnal income is rednced by .^20. What anumnt of tlie original stock had lie? 5. I receive an income of $i:n2.r)() fr<»m oOO sliares of $')() each in a stock comi)any. What is the rate of dividend? 6. The capital of a mannfactnring concern (consists of $.j()0(M)() preference stock, paying 4 ', and $70()()(K) ordinary stock. The Avorking expenses amonut to $2r)()00 a month, and the receipts average $1000 per day. Wliat dividend can be declared on tlie ordinary stock after $24000 is added to a reserve fniid ? 7. If I buy $1000 of 3 % stock at a discount of 3^ y, sell out again after the stock lias fallen to 82',^, and in- vest the i>roceeds in 3.^ per cents nt }.;!r, wliat do I lose in capitad by the whole tian.sjiction ? 'J-' l*IJ.\(TI< ,\l, I'lMHtl.KMs IN A|{||||MKT,( . 1. TF stork hnnfrhtnt 10% pivinium piivs 8" n„ tli. inv..stnM.nt. what j,,., ..t. w.m.I.I it pav' if lM„.ul.t at 10/^ (liirieouiit y 2. A p. son invests r.n4()0 i„ tlu- H i.c nts sellin- ut a .liscoui.t of G /. Wli.-u tlMT rise to ir.A 1„. seJJs .mt $L>()(H)() of Lis stoek, UM,! he sells the re„„.imler when they have fulle,, to S7J. He then invests the pro. Is m the r> i,er cents at 108. What does he p,in or lose hv the transaetioi. ? '' 3. AVlien the 3 tx-:- cents were at !)(). I fouiul that hv sell.n- out -n, but in 1902 /> retired from business and sold his share in cpial parts to the ori^ri„al (,wncrs. If J's iuul V\ interest in the estal.lishmeut is now worth $79:>r),^, what is the value of /i's share ? 6. A man divides among his sons William. Louis aud Henry the sum of *948 so that three times the sum Wdhara receives ecpials five times what Louis gets and eight times what Henry gets. Divide the money. ^.^••i^*^- .»■..•*' PlfArnr \h Pl;ar*tn.i's share? :{. John licll s
»i<»rc than he pive to the library. Find the valne of the estate 4. .1 and D enter into partnership and a^nce to divide .he in-ofits accordinfjr to tli«^ ea[)ital invested ).y each. A puts in .l!SJ)() in cash, /.* puts in $(172 in cash and a note at .'inio. for!i!;]4S. If lh(! note is i)aid at nialnrity how should an annual profit of !|;70() l»e divided Im-I ween the partners? "). A and li enter into i»artncrs]iip, ^1 coiitril»utin<,' $.")()() and /.' $;|()(); iit tlie end of 9 mo. tiny take C as a partner, who l)iin«rs witli him acaj>ital<.i jfilOOO. The i>rofit.s, $1()(((), heini; divided ;it the end of aiK.ther 9 mo., what .shares did they each rec-ivc? (J. A iM'i-sou owes .'f!l(t()() to thre<' credit). rs, .1, /,'. jiiid C. Ilisdel' lo /; is 1.] of wli.-it he owes to T, and liis del>t to C is ].', of 'vhat he owes to .1. T(]( Htii St'.- i. io."Jj|(;i ImI^^' v.. 1. 58. I'a«ik 9. 2. hi -joul.rs. -,„!,, Ui^so...to ,aj„.: 2n.in. 13> see. aft..r4a.,n ;;• 30:, /. ». |;t-(i,.25;.20; 2(K» ,iii 10. 50 leagues. 9. II. 10 (.Z. .'. 700.80. 3. 12.3h-.«78!». . 4oa2i>l401 l:>0(;o.-,03.-.58 4(M)OOOO. Paok II. l-i%f:ain. . 2. 12i%. 3.10.0045. 4. 124 ac. I ro. 1 p.,. :,. r,„.on.-,fi s.|. yd. 0. .OO09187-, 7. 2yr. 4 mo. ISdy. 8. 4 7. ., 3^ 10. Len-th, a-2(t.; l.rciultli, l(i ft.; heij,dit, 8 ft' ' " '1- ■'■'742, •'„ 11,. 1.." •»««"/ la. 105! U s<, yd., 20^ 94 Anhnveius. 9.J Pahr 12. '•yy*- 2. (fl>MrWA)MI)CCX(||| •J. »lir. 11 nun. r.\' ] m.-. _,. j- „, ^ ^.-JiifM.. (,. £|7 i&s. «!i,|. i(». ;{2^j. ft. 2i in. I. rirrle; 10? J r.l. J. Hliicksniitli; !ffl l.3:ij. «i. Og s.,. ft. I'AilK l.'». I. $14.40. 5. !*. 6%. 1'a.;k 14. i. I %. 3. — . 10. 120 hr. •• I II Oil II. 7. «I520. I. 4r.7142. 7. $235.57. Paok 16. 1- 125. 2. 834275. .3. 2^1 yr. f». 82O90».r.I. (5, 400 ft. 7.178332. !). 822740. 10. 1,7^- ,iii. 4. .Tune 8th, 1901. H. 3" sq. 1(1. 1 -r^" Paoe 17. 2. 2.50 11.. 3. 840..3f). .-.. (a) 2039750, (/,) ;j,|(,:{, (,) 12.4007, {,/) 3789. 7. 8045? times. 4. 12.h', fr. (>. $H!00. Paok 18. 1. 16s. 7d. 2. 96. 3. 47.1.5c. .5. 7.3.44 ft. 6. 24 dy. 7. 8ii«. 9. 889ti.M(i!J.HM..'-.3j.; 40038? 2 L'i ) 90.97 +ft., (c) 84.71 ft., (d) 9,3.45 ft., (c) 1 13.26 + ft, (/•) 129.74 + ft. 2. $1,304.61+. 3. (a) 12 cu.ft., (/>)864 .sq. ft., (c) 17 ft. nearly. 4. 27i % ^- 26if. 6. 11. Wu. 7. .322830+. 1. A, $8; B,$6. 4. $7176.96. 7. 201.22 ft. Page 24. 2. 21 sq. yd., 5 sq.ft., 36 sq. in. 3. 302.97 ft. "'>• 1"3 %gain. 6. $1114.74. 1. S^ 2. 72^ ft. 5. o id. 167 ft. 9+ in. 7. 20 dy. Page 25. 3. 600. 4. $1280. 6. No; 88 cu. ft. yet du& 8- lo^Ts pure wine. Ansavtrs. 07 Pa(!K 26. '''fi. 2. 12 J ft. 3. •'>r, «742.40. 6.2.^% 7. .5Gft.7|in. 4. .^7.. 50, K i'4 ft P.vcJK 27. $4000gain. 2. 8l.r.7i. 3. . 4. | ac. ■""•^- 6. 45000 qt. ; cheese hy gi7r,() aiid f^ir^oo ' A, 21 dy.; B, 28 dy. 8. 141.062.-3 yd. 9. f «. Pa«!E 28. 1. 3600. 1. 4. 7. 1. "). 9. 8r,.-,2.08. fi. r>28.03. 7. 5 7 in. Eastward, 36* 1,5'. Pa(;k 29. SI 2000. 2. 24..3474 sq. ft. 3.-) nearly. r,. I3i^ tons. Gain $132.30. s. 37.476.'J625cu.ft. •i- 1 M. mi., nearly. 4. 434.26 11>. •3. .?io.ns. 6. 3(\vt. (ill). 3r)z. 9. 4180680 sq. mi. Pahk ."JO. '230. 2. .58. J780.40. 6. l.-)l69.sq. linb $464. 3. $-2HH. 7. 12.20.J rd. 10. £-35 las. 4d. 4. $1790.93,' 8. 39 /. Pa(;k 31. 1. 9. 1. 4. 7. 10. IG. 2. .00.-)9372.34+, 1 WOSyd. 6. 22» ac. 9^ hr. 3 18s. !,(!. 7. 20 7J. n. 99 yd. 7. $ir,.r)0, ^22.5(t, $ir.. 8. ^\.rti). '<>• -075%; riu; . 11. «12.54. 3. $1.50. G. $G0. 9. Paoe 35, 1. .'')2 sliares, 2, 984| ft. J. .()0r,[Ki:-2:M+. 5, 37i. 7. 3|min.; lOjiii. aiihour. 8. $17.53. 3. $4. G. J, §120; J{, $180. 1. 112.G4y(l. 3. ]41G3r>0min, 5. $147.51. Page 36. 2. 4. — -; 95 yr. 6. 1820ft.; 195 J sc,. ft.; 60 cu. ft. Page 37, 1.2 mi, 2. 48 hr. 45 mill. 5 sec. 3, $1020.70, 4. 3lAsq-ft. 5. 3000. 6, 44i5. 7, $8.65 + . 8. 2li"hr. 9, ^,$19.50; ^,$1500, 10, 130 boards; 1040 ft. 1. i 4. 210000 oz, 7, 2552.5.-), 10, I Kit Page 38, 2. 75 cu, ft, 5, .4, $50; 7?, $240; C, $360. 8. 12 dy, 11. $4752, 3. 39 bu. 42 bu. G. 128; 2304, 9, $50 loss. 1. 4400 steps; 2i mi, 4. $3.91. Page 39. 2. lU rolls. 5. $22 gain. 3. 16i%. 6. 1 « 2 3- I • o 3 a u • 4. 960 ; 44 ; 90 ; 1 50. 7. $317.32. Page 40. 2. $3501.26 + . 5. 1 /, ft. nearly. 8. $438i. 3. 1 ft. 6. 28034 lb. ■rwmifm-i Answeiw. {M.I 1. . r>. \:i.v,H mi. 8. 900 bbl. 1. 81300. 4. 3450 men Paoe 41. 2. $127.3,\. 3. $1!).",. 4. 8U.70. (•>. f 255.-). 52. T. 18 ft. wide hy -') it. loiij;. 9. ^104.23 noaily. lo. .078834 + . I'a(!k 42. 2. $372.44 A. 3. 18 ft. __^ 5. 3 i).m. G. ixji. 7. 20000019019; DCV.; 1550. 8. 5900. 9. 500; .002; 0,10. 10. 9. 1. $20.86 + . 4. $20 gain. 7. $420. Pack 43. 2. 800 trees. 3. $(58.75 increase. 5. 12 boxes. 6. 1 ton 16 cwt. 1 787. Pa(!Z 49. 2. 276 tons. 3. j „i„.s l,y J „ii. i"). 13801? Eii<,'lisli acres. (!. 1 1 dy. 24 times. 88 f. !;3c. 28.12.J ft.; 7.68 Page 50. 3 ac. 15 [H).; §6.00. A, 40 ft.; ]}, 30.00 ft.; (',41.42 ft. 28.284 + rd. 6. 1 mi: fur. 27 + rd. £47 10s. 3d. 8 chaiiis. §51.33^ Pa(;e 51. 2. 1437 J bricks. 5. $442.47+. 8. May 2 lid. 2. £18 lf).s. 8id. 4. 526^ 7. 30 ac. 3 H). 38.88 IK). 3. £.5313 8s. Oid. 6. 64|. 9. $29.02 i. Page 52. A, ^V; B, A; C, -,^', D, A. 2. $544.39. 30 mi. $3 13. 17 A. f). $1800. 3. 1029.12 ft. 6. $.3.20U. 5 mo. $03.05. 510 1b. 8. 5.33.43 ft. 9. $3752.95. 10. 108 ft, Page 53. 2. .300; 56250. $56. $0.12. 82Ac. $2.30. 1.1. 5. 295 boards; $7.09 nearly. 8. $10754.75. Pv«;k 54. ■2. 51?, 68^ ,3. |. 0. 330 ft. 7. 12;? Page 55. 2. 4 ac. 20 pn. 26 yd. 81 in. 5. $130. 41c. 8. $152. 9. 66 ft. 3. $3318.05. 0. 32 yd. 4. $0.1192808 +. 3. $9.75. 0. A, $6, n, $4. 10. 2 yr 24 dy. *?. ^'p,.'\w f /: ANSWEltij. 101 Paoe 56. 1. 845. 2. 874.8U. 3. ^,83240; />', $1260; (7, 812RO 4.8306.72. 5.28. 6. lOSUi ao. 7. 30 ft. 8. 81200 each loiin. D. 82JOO to son, $750 to wife, $750 to daughter. 10. 4623^. Paoe 57. 1. 8270liorse; 870 harness. 2. 35lr.ip3, 3. 8405.90; 25247 H.. 4. Dec. 15,'inOl ; June 13 1 902. 5. 120. 6. 81526.40. 7. $2000. 8. A, $270; //, $280; C, 8310; /),8320. 9. 1720. Paoe 58. 1. i?. 2. 8150. 3. 8152.37; $152.96. 4. 83566.35. 5. 4i ft. 6. 1280 cattle. 7. $200. 8. 8^ /. PACiE 59. 1. 89000. 2. 3hr. .3. /I, 8193.55; ^,8206.45. t. 811.57. 5. 42.52+ ft. 6.814812. 7.844.15. Pack 60. 1.50%. 2.82160. 3. 25 ft., 35 ft. 4. 960 cu. ft. 5. 86703.07. 6. . 7. 8 1 20. 8. 855000. 1. 120 yd. 5. 480. ■2. 895.40. 6. 16 da. Page 61. 3. 105 IK; 14f%. 4. 840frai, 7. 6s I. in. 8. 216 at;. 9. .,^4%. Paoe 62. 2. £10 8.S. 3. 84.'».10. 5- JTTTDVfftroff. 6. 52 dy. 7. 14 ® 42c., 3 ® 60c., 4 @ 67c., 22 @ 78c, 1. 4.54 litres, ,1, 4. 2835 cu. in. 8. 72. ml I ip I I II iMii II .-»=• 102 Aj^sweics. Pi*oK 63. MISCELLANEOUS. 1. «9.12. 2. eo 1(5.60 5. 4. A, $2352; /;, $2310. 6. 4dwt. 17?iiijgr. 3. loSuC. in dollar; $1.84^. r>. loo.iooi. T. m bu. 8. 3<)2. Pauk 64. 1-4%. 4. $15. 00. 7. $164.50. i). VAWo 2. $9.09. .3. A, $2.50; Ji, $1.87. J; C, $1.56. 5. $28.57 i. 6. £1 2s. ajd. 1. $8855.04 los.s. 4. £7 16,s. 4d. Pagis 65. 2. 22i «ly. 5. $375. (!. I .3. 5.0420168067. 7. 1262. Pace 66. 1. $5500; $5078i. 2. 7.92 in. .3. 7 dy. 4. 1 11.. feathers, 2 oz. 1 1 .Iwt. ]6 ^r. ; 1 ox. gold heavier Ijy -12.J -r. 6. 1.966. 7. .00054. 9. 64 men. 5. 101.854 + 8. 464 PA(iE 67. 1. 6T,¥/«. 2. 114; X.MC'MLXXXIII. 3. .338500. 4. lOi?; ij)§. .5. 4808880. (! 800.000. 7. 63J. ^' • y- $1«.35. 10. i-;50. 11. 64.521. Pack 6S. 1. ^1, $47.25; y;, £4.3.80. 2. $40.5o. 3. 621^???. 4. $740.66. ■^- -H«y«l- 6. $2180. 7. . 8. 43,2- |,, 9. A, $640; /i, $840; C, $840. 10. $110. Pace 69. 1. $7.57J. 2. 1.291875. 3. $19.9U. 4. .'AVA- 7. $12.50. T"- .jar'-^^.L. 'ix itsaax. t:atijv. . se^fi^ . f^.-K : "»Tj»: - Answers. Paok 70. (a) 18267.37698. (//) r!8.8616, (r) 1.6.')n26. (a) 101010, (/>) .M.'-,. 3. .22"23r<. 625?%; 16ii%; 60%. 7. jJi.50. 10 dy Pace 71. 27 ; .816; .7ry; 8.175; 135.1940625. 54772 4.044; 10.535; 16.104; .06,'?24. Men, €35 ; women, £56 ; ohilclren, £35. 785. H. 10'," niin. .2154; 32.1; 4321; 1.357. 10. 168iSJ,gJ. 10.'] 4. £62 8.x. 7J(1. 8. 3006 gal. 3. .6875. 6. 33, 18. Paoe 72. PROPORTION. £7 9s. 2. 300. 3. 873i. 4. A, 4; Ti, 3j; C, 2J; 1 hr. 47 min. 23,-, .sec. 6. 180 men. Soldiers, 9 ac. 12 rd. ; sergeant, 18 jic. 24 rd, ; ensign, 72 .10. 2 rr 16 rd. 11 sec. ; lieutenant, 108 ao. 3 ro. 24 rd. ; cap- tain, 181 ac. 2 ro. ; major, 272 ac. 1 ro. ; colonel, 458 ac. 3 rd. : $22487.8.5. Paoe 73. 1. 10.34? a.m. 2. Boy's work is to man's as 1 is to 3. 3. 2yr. 4. lOlir. INTEREST AND PERCENTAGE. 5. 17 yr. 6. 9^ %. 7. §762.50. 8. §1? 4. 9. S78. 50. Pace 74. 1. 85000. 2. §72.14. 3. §1200. 4. §2851.14. 5. §1274.50. 6. Fehy. 14th, 1885. 7. §17425. 8. §35.10. FRACTIONS. ' 9. JsisB- Paoe 75. 1. .51. 2. ]22,V,-. 3. 2411- 4. 77,^2. 5. 24.28009*^, 6. 2 075645161290322580. 7. 3 times. 8. 50697 2 9 7 3 It • aismzs"rii~-s:tis.'ii:^€^maa .-. . 104 Answers. 1. $6100. 84!).+. 7. 70. $300. $10000. 86c. 3. $126.18. 7. $100. 4. 84r. 8. $320.62j. 9- 4 %. Pagk 77. 2. $195,124",. 3. i%l<)88. 4. «i. $706ii. STOCKS. 8. $243. 05 + stock. 9. $600000. Page 78. 2. $1960. 3. $.r;8.31. 5. $19.79j loss. 6. $69418. 8. $16000. 9. 114. 1. 4. 7. 10. 13. 1. 4. 7. 10. Pagk 79. MENSURATION. 56 sq. ft. ; none. 2. 645 sii- rd. $247.15. li ft. from sides, 4 ft. from ends ; 20g s(]. yd. 3. $146.31i. $20.95. 61.498 ac. 5 ac. 1 ro. 9 fur. 342.08 sq. yd. 38.51672. 201 J 6u. ft. 477.48 cu. ft. 24428. 20 ^t. nearly. 53 ft. 7. 31 sq. ac. 10 jx). 8. 40.32. Page 80. 2. 67.74. 3. 6347ift. 5. 553.6.32 sq. ft. 6. 130..381. 8. 106.8144 ft 9. 19.624. 11. 98. 175. 12. 2629J gal. Page 81. 2. 8.83575 cu. ft. 3. 7.0686 sq. ft 5. 23 ft. nearly. 6. 53 ft. 8. 5.039 in.; 3.78 in. 9. 60^3—. 11. 58.876. An»vv£Ks. loo 3. 41.803; 12 ft. pAor, S'i I 20 in. 2. 42.5195. DECIMALS. 4. (n) 2.04.5, (h) d.Ooht\ (r) G9.6H7M3, (,/) H0.738350lA. 5, l«).01397. 6. 1 bu. 2 (it. 1 pt. 7. £31 2s. «ilM 8. 99.84436, Pack 83. t. 258.0645 4-. 2. .010418448*. 4. 3 lui. 2 fur. 21 jKt. 4 yd. 1 ft. 6 in. PROBLEMS RELATING TO WORIC. «• 3dy. 7. 3dy. 12hr. 46 ■+• inin. 8. $6.40. 3. 48. 4i*7d. 5. .29752. Paob 84. 1. 849.93i. 2. A, $\G ; B, «;2 ; C, $8. 4. Tom, $18.75; Diik, $15; Harry, $ 1 1.2.5. 7. $372. 8. B, $4; C, $3. 3. 9if dy 5. 2ii dy. 1. 20 :=>«%. 5. 44c. Paok 85. PROFIT AND LOSS. 2. He los.s. 3. 60%. 4. 18|%gain. 6. 85? %. 7. $272.34? gain. 8. $.386.86. Pace 86. 1. $26.47 nearly, lost. 2. 2?c. on the $. 3. $261056,^0 nearly. 4. $584. TAXES AND DUTIES. 6. $7200; $675. Page 87. 1. 82. r/ nearly. 3. $3^^1.89 ,V 4. $18.55 +. 5. 6^ %. <« $1394 nearly. 7. $26000. um ANSWKUfti. I. $31.04. Padk 88. SQUARE AND CUBE ROOTS. •2. 7(M)4Hli4. 3. 8.027 an.l .(J064. 1 _ » s. 35.8 + in. 10. 1!). 11. |. iW,»* 7. «i.ir. 2. 7. Paok 89. MEASUREMENTS. 3. Circle. 4. lua ft. .'>. 3s)601 hIccikts; 132(XK)0 11.. in-n 6. «.54. 7. 3 yd. 2 ft. 8 ill. 8. $185,301. 0. f lOM) 10. 66.548 +. ' . ' Pacik 90. EXCHANGE. 2. $1747.18; $1740.04. 3. $740.44. 4. £53U. I. $08.M,3. 5. $l38y.50. 7. £3 83. lojd. 8. 1148»0l roubles. 1. I!?697.68. 3. $.3078. 1. yJ 7o- 5. $404 4 ^ Paoe 91. 2. $168.00; 300.35 jieso. STOCKS. 4. $200O. 5. 5i%. 0.3%. 7. $141.2a. Paoe 92. 2. $700. 3. £3078. 4. $173.92*. SHAPING AND PARTNERSHIP. 8. W., $840; L., $288; H., $180. Paoe 93, i. $35000. 2. F., $3870.09; J., $2807.31. 3. $.•J847.s.^ 4. A, $357.20; ^$348.80. 5. $384.61 A, $230.76tif, .I3.s4.6l iV- 6. $600. 7. $700 to one, J?450 to each of t! ? others. *