.nS- IMAGE EVALUATION TEST TARGET (MT-S) 1.0 I.I |!0 IK u 12.8 112 13.6 L25 i 1.4 ■ 2.2 2.0 1.8 150mm V' *^ ^> 'TV ^7^ A /^PPLIED_j^ IIVMGE . Inc ^ss 1653 East Main Street .^SS "^ Rochester NY 14609 USA .^S^^ Phone: 716/482-0300 ^SS-—— Fax: 716/288-5989 O 1993. Applied Image. Inc.. All Rights Reserved v ^ CIHM ICMH Microfiche Collection de ^ Series microfiches 1 (Monographs) (monographies) Canadian Institute for Historical l\Aicroreproductions / Institut nanadien de microreproductions historiques \\ 990 Ttehnical and Bibliographic Notti / Notts techniques et bibliographiques The Institute has attempted to obtain the best original copy available for filming. Features of this copy which may be bibliographicaliy unique, which may alter any of the images in the reproduction, or which may significantly change the usual method of filming, are checked below. Coloured covers/ Couverture de couleur I I Covers damaged/ Couverture endommagte Covers restored and/or laminated/ Couverture restaurie et/ou peiliculte n □ Cover title missing/ Le titre de couvertu couverture manque I I Coloured maps/ n D D Caites giographiques en couleur Coloured ink (i.e. other than blue or black)/ Encre de couleur (i.e. autre que bleue ou noire) Coloured plates and/or illustrations/ Planches et/ou illustrations en couleur Bound with other material/ Relie avec d'autres dccuments Tight binding may cause shadows or distortion along interior margin/ La reliure serrte peut causer de I'ombre ou de la distorsion le long de la marge interieure Blank leaves added during restoration may appear within the text. Whenever possible, these have been omitted from filming/ II se peut que certaines pages blanches ajouties lors d'une restauration apparaissent dans le texte, me is, lorsque tela etait possible, ces pages n'ont pas ete filmees. Additional comments:/ Commentaires supplementaires: L'Institut a microfilm^ le meilleur exemplaire qu'il lui a M possible de se procurer. Les details de cet exemplaire qui sont peut-4tre uniques du point de vue bibliographique, qui peuvent modifier une image reproduite. ou qui peuvent exiger une modification dans la mithode normale de f ilmage sont indiqufc ci-dessous. □ Coloured pages/ Pages de couleur □ Pages damaged/ Pages endommag^ □ Pages restored and/or laminated/ Pages restaurtes et/ou pellicultes 0?ages discoloured, stained or foxed/ Pages dteolories. tacheties ou piquees □ Pages detached/ Pages ditachtes 0Showthrough/ Transparence □ Quality of print varies/ Qualite inigale de I'impression I [ Continuous pagination/ D Pagination continue Includes index(es)/ Comprend un (des) index Title on header taken from:/ Le titre de I'en-tCte provient: issue/ la livraison □ Title page of nt. Page de titre de □ Caption of issue/ Titre de depart de la I I Masthead/ depart de la livraison i/ Generique (periodiques) de la livraison This item is filmed at the reduction ratio checked below/ Ce document est f ilme au taux de reduction indique ci-dessous. ^O't 14X 18X y 22X 2SX 30X 12X 16X 20X 24 X 28 X 22 1 The copy filmed here has been reproduced thanks to the generosity of: National Library of Canada L'exemplaire film* fut reproduit grAce k la g«n«ro8it6 de: Bibliothdque nationale dv <^nada The images appearing he'e are the best quality possible considering the condition and legibility of the original copy and in keeping with the filming contract specifications. Original copies in printed paper covers are filmed beginning with the front cover and ending on the last page with a printed or illustrated impres- sion, or the back cover when appropriate. All other original copies are filmed beginning on the first page with a printed or illustrated impres- sion, and ending on the last page with a printed or illustrated impression. The last recorded frame on each microfiche shall contain the symbol — ^> (meaning "CON- TINUED"), or the symbol V (meaning "END"), whichever applies. Maps, plates, charts, etc., may be filmed at different reduction ratios. Those too large to be entirely included in one exposure are filmed beginning in the upper left hand corner, left to right and top to bottom, as many frames as required. The following diagrams illustrate the method: Les images suivantes ont 6t6 reproduites avec le plus grand soin, compte tenu de la condition et de la nettet« de l'exemplaire film«, et en conformity avec les conditions du contrat de filmage. Les exemplaires originaux dont la couverture en papier est imprimis sont fiimds en commenpant par le premier plat et en terminant soit par la dernlAre page qui comporte une empreinte d'impression ou d'illustration, soSt par le second plat, selon le cas. Tous les autres exemplaires originaux sont filmAs en commengant par la premiere page qui comporte une empreinte d'impression ou d'illustration et en ttrminant par la dernidre page qui comporte une telle empreinte. Un des symboles suivants apparaltra sur la dernidre image de cheque microfiche, selon le cas: le symbols -♦ signifie "A SUIVRE ", le symbols V signifie "FIN". Les cartes, planches, tableaux, etc., peuvent dtre film^s A des taux de reduction diffdrents. Lorsque le document est trop grand pour dtre reproduit en un seul clich6, il est f;lm6 d partir de Tangle supdrieur gauche, do gauche d droite, et de haut en bas, en prenant le nombre d'images n^cessaire. Les diagrammes suivants illustrent la m6thode. 1 2 3 1 2 3 4 5 6 g^^ Xi. ^ U^Ju/ y^tt). &f< ^ I I Enf, ^««0f & Co.'0 examination i^rimrr ^eriw. PROBLEMS IN ARITHMETIC Ht* PUBLIC SCHOOLS ixtu iiix(j hih; Entrnnn' E.mmhuUions, Public School Learing Examinations, and Primary Examinations. HY C. CLARKSOX, H.A., PrinciiHil CKf- Soajorth Vollegiate Institute. "^Tcachere* (Bhiian. W. J. GAGE & COAfPANY, TORONTO. CSS ms Entered nrennliiifr to tlie Act of. railiiMiiiiit of (\iii:iila, in the year IMKi, in tlic offleoof the Minister ut'Agricultiirf, liy \\ . J. tUiiK & r«t., Toronto. PRHFACE. The tmchor of nn im-radM school hn.. tosolro a dimctilt question v.l...n ho comos to clHtril.uto hU avaihil,!.. ti,„o nuumg u n.„nlK.r ul ,'a*Hen at nil stagiM .,f progres. Ik-Iow tli,. I'uUic School Leavi,,., Lxamuwlion. ThU little voluino ha«. boen compiled to assist siioh i.-achors ,n oconon.i..i„g ii„io hy sotting senior p-ipih to toach th.-m- ■«i'lv..s Anthmotic uith u mininiuui of oral assistance. In view of //„ ,>roi^o>,ed iiureane in the difficult y in the Entranre and P. S Leavino ■..ram,n„t.oHH the full set of Entrance Examination PaiH>rs from tlie I^'gnming f.;rnishos the b.st possible proparati.m for onsuin.^ exami- nations. Uarn to ,.a>.Hthe examination b„ pasoing the examination H the lH,.t advice tha' can l,e given. Accordingly this clI.HJtion „f Miie.fi..ns cuirains a few carefully selected Revikw Ql'KSTIONS whirh are intend..! t., be worked in the order in which they are given' Next folh.w Tin: Entuante Tapers fro.m the imnssim inl878 to date These papers arc best utilized '., taking question No. 1 through the wlioh, set. then question No. • in each sot, etc., for the papers are generally somewhat grade,! from the beginning to the end. I hen follow the P. S. LEAVING Papers and a few sets of like dim- Top?'''.. J '"' '' '^l'"'^^ '^"'^'^"^'' collection of these pajx^rs in print. SKELETON SoLL'TK.xs, which enable the teacher to corrc-et his pupiPs " work in the shortest, possible time, or enable the senior pupil to h-arn for himself how to solve the problem, thus leaving the t<,acher free to snbw"'''" ".'"'.'" ^'*«''^*"^' ««mpo«ition. reading, eta, in which subjects our sohools are so generally deficient. To add to his perplexities the public school teacher in some rural sections is exnne.tAr) tn nmr'"»'n *n- . riv +1.5- . ' - 1 T- - „ . . ■ i--. !•,.." v,\o or tluw pupils lor the Primary Examination every year. To help this worthy class of teachers, who hr prepack:. are compelled to make oxtranrdinary drainx on health and strengt.h by doing one or two hours overtime every day, the FULL hkt ok Primart or Third Clahm Paperh down to date iti given. Tho qaestionn are roughly graded, ho that the bent plan of attack is to work No. I in each po'>"r throughout, then No. 'i, otc. until tho pupil h preprared to do a pai^er in full uguinnt time. TlIK Tka(;iibR8^ Editiom contuiua a complete not of aniiwnra to the whole and SKKLB- TON SOLL'TIONH to all the questions requiring them. It is h(>i)ed that toachors will try TUB Laboratory PIiAN, wliil>h'mH — is |>liic(Hl before the pupil and he receives directions how to set to work. Ho also receives books, apparatus, etc., and is told how to nmko uho of them. Thus equipped he is left to his own resources as much us |M>ssibla After going rather slowly for a week or two he begins to doi)end on himsolf and learns to teach ^imsclf with tho loast possiMo assistance from his teacher, whose duties bocomo largely of an advise >r\' kind. This plan has been fully tested in Arithmetic with groat success. The questions here given without the answci-s furnish tho matter to be investigated. If the pupil can write out full and explicit solutions he needs no help and roccivos nona If he fails aftvr duo trial the Skeleton Solution gives Turn assistance at tho discretion of his teacher, or it enables the teacher to ]>oint out in a moment tlio vicious stop in the calculation, so that timo is economise™« ..„„„,. c,„„p,„„ So. ,™ „78 to date i. P.'n. I. S .mK,r, Leavivo Exam,.vat„>x Papers, and .s-r! of Questions of the same grade •"». TVPE SOLUTrON.S ,. _ 01 •>• Tiiiui) Class avd PRrxfti.v t Papers, to date 7. Answers '• 105 INTRODUCTION-. I. The Temenc, of Recent Examlnatlo- has l«n toward, reducmg theory to a minimum and toward, clothir, ° few details in the form of problems and apphed questions It i« easdy observed that our examinations in ari.hm Uocofsi ■argely of problems containing in disguised form some oreo Ihe elfect of th.s is two-told. It prevents veiy eflectuallv .1,^ n^ere memorizing of dead rules without clear a^Xn" liZr"'"^' "'".? *^ ""'«' •'""^ " '^"-l"^ TcC™ o pass .ghtly over pure arithmetic and to spend most of their avaiS ■me m the solution of problems. Indirectly, thereZ ,h! tendency ,s to neglect mechanical skill, accrl y .nd ^^1?, analysmg appLed questions and problems. ^ « ei oi 11 Meehanleal Skill rs. Analytic Power.-Of these two a quu^ments the latter is in all respects the more importam Z f^af "r?'" ■"'"" V'' " •>'""«""' "'« ">e forme'To, vTry gxeat unportance; and, we may add, that for the purpose S doing a given amount of work in a limited time at an 2^ Ctr rr; '"■°"""'"'" "' ""'""'• -d a knowledroute shortest methods are equally as necessary as accuracy of Zglt ori^ "'"'""^ ""^ "«' " P-^Pa™ P"Pils for these 2 INTRODUCTION. I ! III. The Four Simple Rules should receive very particular attention and rapidity should be cultivated by every ingenious artifice and stimulated by appeals to every proper motive. Con- stant reviews, matches, puzzle questions, rewards, special privi- leges, etc., will readily suggest themselves. The main point is to place in some way a very special emphasis on the importance of unerring accuracy and of great rapidity in all combinations of the four simple rules as essential to success at the examinations. In many transatlantic schools this mechanical skill is the strongest feature of the teaching. A careful observer reports that in an Edinburgh school some of the pupils "will multiply such a line of figures as 7,685,928,105,487,938,764 by 7, 8, or any other figure, in less than the sixth part of a minute. From such a line ,they will subtract another of the same length, in the ordinary way, in about seven seconds. In simple addition they will sum up seven lines of eight figures each, in the ordi- nary way, in less than one-third of a minute, and, if allowed to perform the operation while the question is dictating, in about three seconds.'" The gain in time is not the only gain, for with rapidity in the mechanical work, pupils acquire energy, decision, and quickness of mind that are of great practical value in all lines of study. From the earliest stages, tcork at hiyh speed should receive con- stant care, and the best drill is found in pure arithmetic with tolerably large numbers ; whereas, the most useful drill in analysis deals with small numbers and emphasises the intellectual side of the problem. There are numerous simple exi^edicnts by which the busy teacher can easily supply practice in long addi- tion, multiplication, subtraction, division, etc., without being obliged to work every question in order to test the pupil's result. All recent papers assume that pupils can aW"ed. It »f-iesoUddrtio„ anlrttt:? '"-""f™ """™"°" "' " in that way. Thus "„,ld 7 ■""T '"'' "'" ""•>" '" '^a™ it it is possible to sl2Tl rj^"" '"'"' ■*™-' ''a^'<^» '«-o, -^ -tion, an^ .„ r^l.tlr^ CL-^-t ^ '' 895493 ^' r>429971 -"t: lorav:r„^y7alv//"^;»-"'«»<•^» In each case the figure is 3,;t 11"'' ' * "" >" ^ '«■"!? 6 are 6. •inestion !s thought The^lT ' ?t "'"'''' '" "■« cental back" is avoided. This JC^ "f "borrowing and paying jdivisionveryrapidlvw hTaU 1? ■: ^ "'"•" '° ''" '™«5 multiplication and subtrac.on eZ^:!!""^ ""^ ™'"'"»'"'.' 13887 4064 j 56438971 1579^ 36065 35577 3065^ 2203 Write the quotient over the divi,1«r,^ i, ^ssisttheeye,andsayonce4a„drr' ^^^" «°"^enient, to farry one) ; once 6 are 7 and " « "" ^''' ^''''^ ^ ^^^ heare6 ; once 4 and Leare5 7-"'/' ' ""'^ ' ^^ ' ^^ ? : are 12 and ? s,^ are 18 thT^rn, T"^ ^''^" ^' ^^'"^^ *i"^es hree times is 1 and «k I " ' "" ^^ '-^^'^ .^^ ^"^^ ? -ero are 19 ; Ihree are 15. Bring down 9 % I %'' ''T ' "'^ '^ ^"*^? W ana it conduces to aclat anXi 1^-^'" ^- ^"« [Dun«uncly proves, and the rp«n]f . i ^ ^'^J' «« experience h™"--....nwithrtr^rt^-^- 'I 1 i I A INTRODUCTIOK. V. The Extended MuUiimcation Table is Of e^^^^^^^^^^^ ant. Experience soon teacl os a ^^ ^^^^^ necessity of ^-wing the tabl^^^^^^ to 60^^ ^ ^^.^^ ^^^^^ ^^^^ Five minutes a day for five ^^^^^ J ^ . ^„^ ^he same time „.astery of the table to '^^^^ ^^^^^M that the pupils will c rry a fourth <^ -^J;;'\^^^^^^^^^^^ subtrac construct their own table by successive ^^tiples in tions. Applied questions -^V^J^^^^^fCor^ J.nm, the memory, but they are a ^^^^^^^^^ .^^.^';' J^^itten papers if the table. It saves a vast amount ^^''^J^^^y^JJi.igY. the pupil can multiply, ^^vlde or -c -^h -mb^^ ^, ^^^,, as 25, and in this connection the squareb ana numbers ought t*o be learned as they occur. VI. Tcstin, ana Yerifying the ^or. is a ^^^^^^^ ..portance in business a^hitec^^^^^^^ ^^^^^^ simple means ^^^^^^^^^^^^^^^ the third class he ought examinations. When the pup .. ..^^ ^nd addition by to be able to test multiplication, d^^^«^°"' ^' ^^ ^^at he ^^casting out nines^> with great ea- ^tZtloZe^s. He may have confidence in his -sul^ as th^ wo^^ P ^^^^^.^„ sbould also know as soon as possible how \^J'JJ ^.,^ of a problem by check calculaUons to test^ tsjnsist^^^^^ ^^^^^^ tL3 data. One correct ^^''^'\^'l^lJ^JZeI v^hen the method more marks than three inaccurate results even wne of solution is perfect. VTT Indicatinir the Work first and performing it afterwards •«.? of first-rate importance on examination papers. is an artifice of first rate ^^V accurately by AH written work can be done most ^^^^^^.^ ^7^, ^^^^jiem from separating as clearly as possible ^^^^^^^^^Z^^^ result, the mechanical operations necessaiT to obtain tn The examiner can iudge in a ^^^fj]t^ZTA^irnrn.rV.s rr ^:tr:::r^^;^ iii::^^ is not pro.^ nothing or some merely nominal marK. lous service ally import- ilesmen the les at least. :d class full le same time at the pupils and stibtrac- multiples in of learning tten papers if ihers as high Abes of simple cer of supreme c, and all the ice at written class he ought i addition by ity, so that he proceeds. He ify his solution nsistency with , usually count hen the method g it afterwards lination papers, d accurately by he problem from le correct result. )r the candidate ,ward him marks n is not properly mdidate receives t always possible i INTRODUCTION. g to make this separation complete at one stage, but the pupil must be accusto,ued to set dovvu the ground plan of his Zk first and make sure that he has done the reasoning correct" otherwise lie will l^ attempting to do two different things at th^ san.e moment Factoring and Cancelling must be learned as early as possible, so that the work ,nay be shortened and simpli- led Thus, in solving the foUowing question a little skill in factoring numbers actually reduces the mechanical part of the work to zero :— ^ "^ in l'an/^^!i**°' borrowed $5,000, and immediately invested it rnterrt!" ' '" ^"°"'^'' ^^'"^ ^^^'^^^ « % P^^ annum s'Lple Solution.~Sum received for land = $7500 (1 -06) T> «?""" P^i? ^^^k =$5000 (1-09)' Profit = 7o00 (I -OC) - 5000 (1-09), ^' = 7500 (1-06) - 5000 (1 0(i)'- 5000 (•O^'t = 2500 (1.06) -2500 (CO) = $250a^^' ^50^ard**'^*7O* ^i"*^!*^-" ^'T °^ ^ *^^^"SI« ^^'l^O'^e sides are 760 you, and 570. Applying the ordinary rule, ' area = ^(1140 x 380 x 190 x 570) ,= l<>0i/(114x 38x19x57) = 100 X 19 x 19 X 6 = etc. Vm. The Utility of the Simple Arithmetical Equation can zZ^Zfi'Trr ""^^ °^ '''-'' -ppingo":: reasomng m all k.nds of solutions. Every problem and question mvolves the equation. The addends taken together = tlesum akenrf "^d^ ^1 '""'^^' = ^'^ difference f the multi'li "d taken as an addend as many times as the multiplier contains the d .' '7 :.' ' ''' ^"'''"'^^ " ^^^ ^^^^-^ + 'he remainder = the dividend; the munber of the articles x the price of one tttlr ? T ' *'' ^^^"^'^^^ ^ *^^ -^ ^^ ^ X 'l^e years" larv t^Tt ll'^ ''"'^^^ "° '"^^ °'«'"'^^- - tL ordi- nary text-books has done so much harm to the learner as the g INTRODUCTION. omission of a chapter on the use of the simple arithmetical equa- tion, which is within the power of tiio youngest pupil, as it involves nothing more than the simple axioms that are funda- mental beliefs. Full and systematic solutions expressed m the form of equations dispel half the mystery that usually hangs over arithmetic. Very often the use ' e e.iuation, and a lit le Kkill in factoring numbers and canceliuig, shorten the work by more than one-half, and every minute saved on an exam.nat.on pai^r means two minutes gained. Abundant examples of this are given in the Skeleton Solntious of the following papers given in The Teachers' Edition of this little book and m the Tyre Solutions prefixed to the last section. IX Clear, DeflMito Aims are a prime requisite to success at any examination. . The student must know what he is exiK^cted to perform, and L must be taught how to do it at the least expenditure of time and labor. A careful study of the papei-s in this book will give a practical knowledge of the standard that prevails in Ontario, and will enable any pupil of ordinary mtel- ligence to know definitely when he is able to coi^ with the suc- ceeding paper. The best way to learn swimming is to plunge into the water ; and the best way to prepare for an examination is to plunge into the ex..mination papers and struggle through them some thrice. PROBLEMS IN ARITHMETIC FOR PUBLIC SCHOOLS. Review Questloas.-Additlon. Exercise I, 2,IU,i^o^:?^^l«/e%":"- ''■'''■ '-'"'■ '*■'"'>' ^.'^o. (2) In question (1) take the sum of the digits of each number divide each sum by 9 ; take the sum of the remainders tW found and divide it by 9. Show that the remainder so found "s the same as the remainder found by taking the sum of all the numbers and dividing the sum of its digits by 9. (3) Ascertain by '' casting out the 7iines" whether 133,330 is q m" m ii' li^'oi a ^ ."n ^?f''' «o^-recting it if necessary :_ 3,985^502 ' ' ' ' ^'^^^' 12,190, 2,187, 12,424, 7,501, 6 71, 20o 3,28o; and test the accuracy of yo^ result by ' ' casting out nines. " j >■ yo^ resuic wil^l'''^^^''^'^^® r""'.^^'' °^ P^°P^^ ^^ a fe^ry was 1,648 for the whole week. For Sunday and Monday it was 1, 239 for Thurs- day, Friday and Saturday 1 84^ What ws- 41 ot. ; number per day for Tuesday and Wnesd^? '° '^' ^^''"^ 8 REVIEW QUESTIONS. Iliii (7) Add together tlio products of each pair of the numbers. 150, 225, 375, and find the difference between this sum and the product of all three numbers. (8^ The population of ten cities are as follows :— 65,539, 76,30(5. 150,844, 182,296; 19(;,3r.2, 2:;;;.41S, 242,731, 213,606, 358,989, 211,190. Find the total and the average. (9) Show that 1,500,090 is less than the sum of 161,415, i;j»:W 98,127, 174,192, 140,871, (52.481!, 90,334, 66,5»2, 73,148, 94,219, 99,928, 104, .301, 3(5,631, 44.0(54, 4(5,060, 13,977, 3o',350, 42,210. Test your work and give the correct result. (10) Find the aggregate of the following debts as^shown by the ledger totals iu a merchant's books :—S42. 17, J36.24, ?18 42 $10.71, $194.30. .$347.1(5, $40.C0, $12.94, $86.73, $07119, $103.07, $r00.50, §7.59, $11.44, $81.92, $110.10, $107'.09, $207.16, $97.20, $21.77, $150.15, $427.26, $316,42, $114.64. , EXEKCISK II. (1) Find the sum of all the numbers of three digits that can be made with the figures 3, 6, 9. (•^) The populations of five townships are 1,23(5, 452, 364, 516 and 3,430 respectively, and the average population of the six townships in the county is 1,256L What must be the population of the sixth township ? (3) What is the sum of 45 millionths, 45 thousandths, 45 hundredths, 45 tenths, and 45 units? a) The receipts at a ticket office for twenty-four weeks were ■IS follows :-$l,132.16, $327.40, $177.66, $94.57. $157.16, $27.96 $18 19, $276.44, $137.89, $372.22, $410.10, $56.00, $(l341 $48.50; $709.08, $320.00, $271.78, $152.(50, $39.46, $71*32, $173.26, $427.90, $194.32, $506.76. The agent returns the amount as $6, 160.24. The auditors detect the error. How much must the agent remit to rectify the mistake? (5) A collector receives ten payments but forgets to record the eighth. He finds on hand cash $422.10, and his book shows nine payments of $137.21, $142.45, $23.56 $24.06, $24 99, $12.75, $8.56, , $36.40, and $8.92. Find the sum omitted, and complete the record. (a) The head office of an Insurance Company has nine agents at work who remit the following sums for ten weeks, viz.:— • ISt^Mk, $89.63, $193.48, $193.59, $250.10, $181.50, $93.50, ) : :i REVIEW QUESTIONS. d ;its that can iisaudths, 45 1184.77, $90.80, and $174.49; 2ad Week. $95 7o «ioi qr, $179.45, $215.55, $300.95, $100.75, $r80?5, $9fe $66 53 3rd veek, $4.39.58, $189.19, $190.77, $319.32 $169 28 «95 05' J^J-O'I Mi>4.25, $42.75; 4th weeli:, $127.887 $409714 |.?4 J?' Jfifo- *ifo-'"\.P-^^L ^-^^•^^' ^-22.79, $47.18, $.38 9?; I ^'o^*^I^k ^^7??'i'^^«lS^21.9(), $156.70, $83.45 21.20, «13.5b, $234;73 7$96^7r$fn:55 ^:^^ $21.87, $75.01 8tk YOek, $85.20, $124.247 $<;7:7r;$26.7flloJ;'80 $57 o^' $45.2.5, $8.62, $21.65 ; Qth Veek, $4.88, ^39.85 "^o 05 U{i $3.0.3.,, $88.90, $44.25, $6.15, 121.52 lOthWMk $63 04' P?nft'hff?',' *'*•''' «24.«9; $29.57, $48.69? $7? u', |l6:89: tmd the total amount received, the amount remitted by earl, 10, 11, 19, 24, etc. :_$14, 763.84, $33 076 90 gi? 061 '-Iq' $18,242.76, $47,364.96, $8,410.3l', $1^ ,724 27 ^- ' ^••^^' «22'i;il-27, $40,16.3.5.5, $.32,189.60, $9,200.00, $1,807..36, $56,768.72, $90,807.08, $28,763.81, $37,196.75, Test your result. $81,742.73, $3,451.09, $36,180.4.5, $3,719.84. $56,317.66, $7,063.21, $63,024.27, $4,230.61, (8) At a bank tlie cash receipts and payments for a week I73917; Rw 'w r'^Y' ""^^^'P*^' ^^^'^ l^-'- 3^., payments fill i«!" ??7 ^f "«lday, receipts, £854 lU. lU; , paymen s l59'7o/^%^''«'/Y^^' '"^^^P*«' ^"«« 17*- 6c«.; payments i'-nj^ 11 A Id. What was the excess of the total receipts over Zmt^'IClt'-^^iT^ "' "■" "Pl^^ '<=" hand corZ . ^Tvi^ ^ "P *"® horizontal 1 nes :— '> 016 4 910 1 «^r q oRrt ^,*=4, 324, 2,124, 4,820, 1,764, 3,960, ' Mb? 3,2(&,' i,SI; 10 REVIEW QUESTIONS. ' I ! ! 2,844; 2,880, 720, 2,520, 360, 2,160, 4,856, 1,800,3,600, 1,440, 3,240, 1,080; 1,116, 2,916, 756, 2,556, :596, 2,196, 3,996, 1,836, 3,636, 1,476, 3,276; 3,312, 1,152, 2,952, 792, 2,592, 36, 2,232, 4,032, 1,872, 3,672, 1,51 J ; 1,548, 3,348, 1,188, 2,988, 4:52, 2,628, 72,2,268,4,068, 1,908,3,708; 3,744, 1,584,3,384,828,3,024,468, 2,664, 108, 2,304, 4,104, 1,944 ; 1,980, 3,7H0, 1,224, 3,420, 864, 3,060, 504, 2,700, 144, 2,340, 4,140 ; 4,176, 1,620, 3,816, 1,260, 3,466, 900, 3,096, 540, 2,736, 180, 2,376. Now add the vertical columns, the horrizontal columns, and the two diagonal columns. Do this 10 times and record the time required for each operation. Note. — In commercial life Addition is by far the most im- portant part of Arithmetic, and the pupil is recommended to construct gymnastic exercises like No. 9 and do them against time. Let each member of the class furnish one in turn and let the time required be recorded until the addition of vertical and horizontal lines of figures can be i)erformed mechanically at high speed. , Eeviev Questions.— Simple Rules. Exercise III. (1) Add together 804,959, 186,402, 700,077, 9,450,068, 20,047,300; subtract from the sum 670,076, and divide the remainder by 87. (2) Find the sum, the difference, and the product of 1,234,568 and 4,321,089. (3) In a question in di'usion the dividend was .'51,884,740 and the quotient was 40,930 ; find the remainder. (4) Divide the product of 999,999 and 1,955 by the continued product of 37 X 13 X 17 X 7 X 23. (5) Find what number subtracted from the one five hundred and eighty-third of the product of 31,472 and 974 will leave exactly 100. (6) Multiply 129,847 by 468, commencing with the figure 6, next by 4, and lastly by 8. (7) Add together 567, 496, 341, 827, beginning at the hundreds, next the tens, lastly the units. (8) Subtract 34,876 from 7-^ 093 anrl A,r^j • process. '-,"JJ, and explain every step of tl.o (9) Divide 550,974 bv 1 472 an,.t "s\tr*r„'d.""^ "« ""-.*» (3) Multiply 4,327 by 814. (4) In Question 3 take the sum of f].« t u , . Phcand (4,327), divide tl at 1 1' bv 0^' an /^ the mmtipij. remainder; take the sum of thofL / r .^'^ ^^^ '^own the divide the sum by 9 and set dowf ?i. ""^ *^'' multiplier (814), these two remainders togethe and ivMn T'^'^'^r ' "^"^^'P^^ down this remainder ^ud Z^lrt Zf -l ■ 'i'.'^^""* ^^ ^' «et ^^.amder obtained by <^eX^ ^ 1''.^.^^- ^ ^^"^l^^^i^^ practical value, and multiplication hel,erform? It L , l^^i? ^'' !^ every case of '» actual practice ff will not flil !.. •^^'^^l^*^^^ infallible, but out an error. "°* ^^'^ °"«« ^^ 10,000 times to point ^o^^^'^'^^et^:^^^^^^ *^-aP^d -thod of per- to apply it at%very stag^of his worL""' '"^ ^-<>-agethe p^pil (5) Multiply 123,456,789 bv 987 find ^oi [by casting out the nines. ^«^«>«4,32l, and test the result ,.l?l-.^^*jPJy 57,298,492,692 by 700 809 nsooc. -^. ancwci re detect any error in the wor't ' ' '""""^ ^" ^^"^ H RKVIBW QIESTHH**. (7) 4^ro is a ntRr u ose distiinre from the t'tirth is 674, oHa,- '« 2,8.'l7, IM.nOJ) times more distant tli second star from the eartii. (R) Construct a multiplication table for yourself from 13 times 2 to 19 times 10 and learn it by heart, one column to bo learned each day in IT) minutes, (9) Multiply 234,578 by 18 in one line of figures rtn«l test your answer. (10) Multiply 924,840 by 95, using tlie factors 5 and 19 so as to save addition. (11) Find the continued product of 12, 17, and 19, using the extended table of (juestion 8. (12) The quotient is 17 when 9,281 is divided by a certain number and the remainder is 373. What is the unknown divisor ? i (13) Arrange 15 dots in rows, 3 dots in each row ; also arrange 15 dots in rows, 5 dots in each row, and from this show (a) that 5 X 3 == 3 X 5 ; and {h) tl at in both cases the multi- plier is an abstr.icr number denoting the nnmlm' of times that some other number is to l)o repeated as an addend. Review Questlons.-Subtraotiea and Dlviilon. EXEUCISK V. (1) Subtract 123,456,789 froni 087,054,321 and n'-ove the result by addition. (2) Subtract 584 from 721 and prove the result ns yo.', pro ceod thus, 4 and ?— 7 make 11 ; 9 and ?— 3 make 12 ; (J and ?— 1 are 7. Apply this method to Question 1. (8) Y'^Ti'te down ten examples in subtraction, eacli containing ten Cgu •;■ Do these examples over and over against time until you ce.n i' ;*\ . i in ton seconds each. (4) V"r"t.: ov>ri ita exarni)les as in Question 3 and obtain the correct :;.~.s" 3 -a one mi' • v?. KEVIKW yut> IONS. 18 d n-X'Ve the id obtain the (^) Take the number J.>;ti -,;7 soo o i v i . by i;{, then hv 1!, ,,, , " '; "^p^'*^ "'"^ '^'V'do it by 12. the,. plicHtio,.. do tbroMKh 1 .is\:ruursti..T' '^ •'''''"" ''•'' '""J^'- those l;{ divisions and 1 J h n *"""''' V,' *^'^'='' ''-'"l ^o d,. yourrecnnl a. ouch t.ial "'"'^''''"'^'^'O''^- -Kndoavor to break (7) Divido24,r).'j;j 07J) J I.,., t> , the ro.uaindor, 4;{i; f.onx the divrd«?yr '''^'■^■^;''^ ''.V subtracting remainder, on casting o t „i'.e ' '^o ' H °'"'-'';''""^' ^^'^^ »''« product of the remainders le ton c^L T-'' ""'"« ^ «« ••'o and quotie.it. " °" ''"•^''"fe' o"t nines from divisor 17.'J,28(5,L)95,04(>. "^"^^ remainder 8,5;M,57n in the numbt!r (!)) Observing that 432 = (i v « ^ ,, ,. , ,, the tme ™,ai„der i„ Q.^Mon^^Tjtr " ""' '"-^ ""'"■'e (11) Divide l,79n '>qo i,„ in- correct remainde;, 102 ^ ^^'^ "«^"S f^^'tors and find the correct remainder when ^^(13) Prove that 58,,;70 « „„ exact divisor of 2,808,330 . na;i'S^'tl^,^„;,»',/;^-«;j.««'^«r,.3. «^„a,„. a!„o„, result. *''^® "10 share of each. Test your Exercise VI (1) 153 = 9 X 17 • 144 _ o and W4 ? Express' their'r! I^J" i^^,"?!!.'' 'he H.C.P. of 153 — . .» e,„., to their product d7vaad"l>y';^ir G.'SV''"' "" 14 REVIEW QUESTIONS. II ^ I 1 (2) What is the greatest number that will divide 32 with remainder f) ? What is the greatest number that will divide 24 with remainder G ? What is the greatest number that will divide 32 and 24 with remainders 5 and 6 respectively ? (3) What is the greatest number that will divide G8,130 and 107,275, leaving remainders 27 and 49 respectively ? (4) The product of two numbers is 24, their H.C.F. is 2 ; find their L. CM. (5) Resolve 1,287 and 6,281 into prime factors, and find their L.C.M. (6) Multiply both numerator and denominator of J and j^, so that they may have the same denominator and still retain their present values. (7) If I = As and i = A, what is the L. CM. of J and g? What is the L.C.M. of $5 and $Q ? (8) Find the L.p.M. of 15, 1,V, ,-6»r- (9) Find the G.CM. of 2 J, 2^, U- (10) Reduce to lowest terms— |, |, |, -\\, \^, and hence find their sum. Exercise VII. (1) Find the H.CF. and the L.C.M. of 17,725;554, 1,054,872, and 2,406,090. (2) Bring i^Jli to its lowest terms. (3) Reduce ?, g, i?, and |§ to the same common numerator and hence point out the greatest fraction. (4) Reduce the product of ^f, AV) lo7» and f? to its lowest terms. (5) Divide the sum of f , |, A, V ^y the difference between i and I. (6) Divide 1 - (i + J + ^S) by 1 - (i X ^ X ,\). (7) Add together A, iu? ^"oVj ^Is- Express the fractions as decimals and find their sum. (8) What number multiplied by 35 J will be less by 5^| than the sum of 3g and 5-Hi ? :.F. is2; find and find their md hence find )54, 1,054,872, ion numerator : to its lowest mce between REVIEW QUESTIONS. jg s/a'L'^frsb'rt'^^he^nt tm'?^ to the difference between mw be 28 ? *^^ ^"^"^ '^ multiplied by \i the product no) Simplify ^^Jt3 , m -f- Hi ss by 5H tlis-^ ReTTlew QuestioM-ifisceUaneous Bxamples. Exercise VIII. (1) Divklo Ifl X 72 X J5 X 21 by 27 x a2 x 12 x 35 B:vMe2laxH,x,a0x2«by80x5.;3e 7.il?'^?"'^^"™"f •»'» and .0075 by th. differ^ce between (4) What is the product of :— -1 174^ 44| 40-iL aSi' 196|' n;V and 36^? by%»^^l^^f the^.oti^s in the following cases - -o ; 3-78 4- 200 ; .04735 1' ^0005 • m '• nn?^ t '^^ ' ^O'^O^ (6) If Europe has 3 8rtO o-. ' "^ "^^^ ' ^^^ ^ ^^'^OO. faits and /s'ia li'^'ifi^.t^i!;,-'- -^.205,803,9^^ inhabitants, which continentlit H. '^* ""'l' ^"^ 782,129,318 to the square mile, and hTw m^y ,noroT'^' ""'"^^ "^ ^«°1'^« bufhllt^;V^,,^7^o™?.v/""'' ('""' ^'^-' '^■"'• (10) P.nd the sum and diBeren™ ot 2,764A«r and 2,6334j. January, 1874. (1) By what must £157 19? ini,/ k^ j- -j j , quotient of 33J ? ^*"' ''^ divided to give a il 1. 18 BNTllANCE EXAMINATIONS. (3) How many minutes between 12 o'clock noon May 24th, and half-past nine in the forenoon of September 3rd ? and express the answer as a fraction of the year. ^ (4) Add (1-i of ^), (i of 1+1), (^). (5) A house and lot cost $3,600 ; the value of the lot is i that of the house. Find the value of each. (()) Subtract 2a S a sq. yd. from I of .^ of 3 ac. (7) Prove that multiplying the numerator of a fraction by any number produces the same effect as dividing the denominator by the same number. (8) Simplify -75 of IJ ^ 7-6 of A - (1 -875 - 1|) x 2 + 4 •875 4| (9) If § of I of an acre produce 41 bush, of potatoes, how many bushels will an acre produce ? (10) If a man working 9| hr. per day finishes a piece of work in 6 dy. ; in v'hat< time would he have finished it if he had worked 8 J hr. per day ? June, 1874. (1) The dividend is one billion two hundred and twenty- million two hundred and thirty thousand and ninety-two, tho quotient six thousand and eighty-four, and the remainder forty - eight hundred. Find the divisor. (2) Reduce 3 ac. 2 ro. 14 sq. pr. 4 sq. ft. 72 sq. in. to square inches; and 170,184 sq. ft. to acres. (3) 797 tons 19 cwt. 2 qr. 14 lb. is divided among a certain number of people, so that each receives 5 tons 3 cwt. 2 qr. 16 lb. How many people are there ? (4) Show which is the greatest and which the least of the fol- lowing fractions :— 1| of J, j^ of 3 J, J of 2§. (5) Reduce to its simplest form — (2i - § of If ] 6i 2i[ • 8| *of3i-|- 18 (6) What fraction of £58 bs. Gd. is ^ of £17 2s. Sd.? (7) A man invested ^ of his capital in bank stock, | of the remainder in real estate, and had still |fi,000 left. Find his capital. he lot is i that in. to square east of the fol- ENTRANCB EXAMINATION.S. 19 (8) Find the vahie of 43 cwf o ^^ oi ii. c^'t. (Qr. = 25 ib.^ ''^^- 2 qr. 21 lb. at £2 16*. 8«i. per (9) Find the difference between •48-ir:014-^0 ^"^ 7^-rij— of 4c'\•n^Krfti^sS^^^^^^ &A "r a year a tax ' ''*'^^- -^ '"^ ^'S income for a year. December. 1874. /q\ TT^,. ^^'^ fe""6 m li of a minute ^ (1) How manV Vnr/lt: ^^ r ^ake to cover a fl^oc;!- thlt if i'o ff 71^10,: 't U"; "''^«' ^i» ^'^ (5) After taking out of / "^ ^ ^^ ^'- ^ ^"- ^^^^ ? remainder was found to bo L')/ T^ '' ,1 l^f '^^'^^ents, § of the at hrst, and what part of £;3 is ilfat sum ? '""" ^'^ '^ "^'^*^''^ (6) Find the value of (8) A pint contains 34S cub in • ^^ W.II fill a cistern 4 ft. 4 in lom/'o^r^'^^'^ ^'«"°"« ^^ water "1- deep? "'• ^o»e:, 2 ft. 8 m. broad, and 1 ft i j (9) Reduce to a simple quantity 2-8 of 2-97 4.4 _ 9.0.; 1 idb 1 ) + 2-fi29 ^^25~' intoL'^t^'^^;",^^^ W and- ^- -7 . lintc"" i 1^"' ^^'""^ 1^ t-^ie lengtli of r fonn"'^i .^' ^^ *^ tJivided Imks, and ho«. ™uch ^„„,i itt;f,»|»» ^f^^^'^^ures 2,456 ill ■' nil il ;h ■ I i M r 1 20 ENTRANCE EXAMINATIONS. June, 1875. (1) Reduce to its lowest terms of3J + ig 2y ' § n (2) A merchant bought a number of barrels of flour for $4,000, and sold them for $5,200, thereby gaining 750. per barrel ; how many barrels did he buy, and what did it cost him jDer barrel? (3) A paid $60 per acre for his farm, v/hich was {; as much as B paid per acre for his farm of 150 ac. Find the entire cost of B's farm. (4) Find the sum of V- of £1 13.v. OJrf. + J of £1 bs. 8id. + A of £2 4.V. Sid. (5) A farmer having 17 cwt 2 qr. 19 lb. of pork, sold 4 cwt. 3 qr. 21 lb. of it, and the remainder he sold in barrels, each con- taining 2 cwt. 6 i lb. ; how many barrels did he sell ? (6) If it takes a man 1 hr. and 40 min. to cut J cord of wood, for how 'many days of 8 hr. each will he be occupied in cutting 18G cords 88 ft. ? (7) A man invests J his fortune in land, ^ in bank stocks, i in debentures, and loses the remainder, which was $8,000, in specu- lation ; how much was his fortune ? (8) The dividend is fifty-one million eight hundred and forty- six thousand seven hundred and thirty-four, the quotient is five hundred and eight thousand three hundred and one, and the remainder thirty-two ; find the divisai\ (9) Find the cost of 49-,3f yd. of cloth, when 7g yd. cost £7 18s. id. (10) A man paid $2,896,875 for land, and sold 56-25 ac. at $31 per acre ; the remainder then stood him at $20.05 per acre ; how many acres did he buj' ? December, 1815. (1) Find the amount of the following account :— Mr. Markham bought of Mr. Jones, Dec. 8, 1875, 12 yd. Scotch Tweed ^ $2. 85, 16 yd. of Silk @ $2. 12^,. 50 yd. Ticking @ UJc, 42 yd. Shirting @ 16^0., 12i yd. Flannel @ 50c., 20J yd. Scotch Plaid @ 60c. (2) I bought from A 97 ac. 2 rd. and 12 sq. rods of land ; from B, four times as much, less 7 ac. and 1 rd.; and from C, J as much .IS from A and B together. I then sold 120 ac 1 rd. and 29 sq. rods. How much had I left ? 21 )f £1 bs. Sid. + BNTRANCE EXAMINATIONS. (3) Reduce to its simplest form ^^^z^e^:!%i::^^i:^:::^^^^^ of flo.„. fo. for $1,97(5, which was $30 no vi f "^ '°^'^ ' ^^ ^^'« ''emaindor of barrels he boughT ^'''" "°''- ^'"^ the n„ml)er ^^^^!:VL:^lll^l^1 2^ 4 ,.rso.s. The first It is found that the first rece^vP^ ^'i'^.^^^ ^o'^'th the remainder. Find the sum received bv each '^ ^ "''''' ^^^^'^ *h« fourth. refiel^e S^^ ^^^.SIL^ ^f^^^ * ^^ ^^ -'-s, and mil liX EJiSh^Um t f ^^^ ^^ ^-^^^^ «^^^"-^«^ ^-v to^caVt^I^'^ili i:;^r27 Vn* ^^-/'^^i -hat will it cost (^) With carp^t^45 in wSe'tnf$lVp:i7ard' ?''''' ^^^ ^'^^^ ' I 7 1 yd. cost £7 June, 1876. W If a pipe discharge 2 hlid o-i „,, o . ? one hour, a how many hours wifl if J- ^^- ^ ^}- ""^ ^^^^^ in If Pt. the water flowi"„g ^JS tlie^sle'reLd?? ^ '''• "'^ '^'- (4) Add together, 16 ^3 and divide the result by ^§ o^ H of 7| 1 ^ y a „ J?. "^ "!f"'^ -'^"""^^ ''"come is ao.4no • /A >,- * ' . -pend per day so that after navin.7 ff ' * a i^^^' "^'^'^^ ^^e may |a.U.r o, i„c„n,e he m,. r^S ^el^^e^^-^sbs^dy"';"^ °" "'--^ IS of 3ft '':^' n ENTRANCE EXAMINATIONS. (6) A room is 36 ft. long and 24 ft. wide ; find the difference Sr yLdCd^th'"'^^^ with carpet k yard wide at $^40 per yard, and with carpet 27 in. wide at $1. 15 per yard. (7) If 162 gal of water wiU fill a cistern 4 ft 4 in Ion.? 9 tf for 2 d?";"thenTon: ' ^''^ ^" ' ^^ ' *^^^ "^^^ '<>^^'^-^' tlm fi^lrl In 7 1 i 07''^'" ''^^^^^ w°^"^. and the other 2 finish hPPni n .1 ^^-^ ^^V'""''' ^°"^ *he man who ceased work a field"yh!i?"°"'^'^^ "°^'^ ^-- '-^-- to mowtirwhol^ (9) A man sold two city lots for SSfiOn on^T, . ^„ 4.1. 1 December, 1876. 27'li ^r?"""?. T"^ J"""'"" ™ "lei-e in 8 ac. 2 ro. 27 pr fn3?;4i3,J,li'4,?in,'?-- ""' ""^ "■"">■ '-'■ -'•• ^'-i (2) A persons owns 3 of a shin and «p11o a r>f k- u i. •PI oan -wT-u J. • .1 ' " niiip, dim seas g or nis share for • il, JbU. What IS the value of the ship ? Iqi '^^l *^'^^^«"«e between the product of two numbers and ;kd h'^'^^'onrntT? "'"'?^ *^"^ ^""^^'^^ -^d thTtlousLKl SrtdtTsix.'^XVthe'X'^^''^^^'"^"^^ ^^^--^ *h- h""- (4) Show which is the least and which the greatest of the fol lo^^Mng fractions :-i of 9^, «-. of 9, and U of 8 2 (5) If telegraph posts are placed 80 vd. apart and a frpin CnTngT ^^^''^ ^°"^ --"d«' ^-- -any m7es' ^L'TsTt (6) A regiment marching 3J mi. an hour takes 110 steos in a minuta What is the length of the step ? ^ of ?roorooTfTri'9 ft r^* '' '" "^'^ "^" ^°^^^ *^« fl°°^ ENTRANCE KXAMINATIONS. (8) Simplify 83 - 1- of '2,% of U + 2 J -- A - 7. 23 (9) Find the sum of 6-27, 18-651, and 12'345, and the differ- ence between •34027 and -27. (10) If a room be 12 ft. square, what must its height be in order that the area of the walls may amount to GO sq. yd. ? July, 1877. (1) What is the least number that must be added to five mil- lions to make the sum exactly divisible by seven thousand and nineteen ? ( 2) Simplify 20 _ / 48i + 7:i - l.>3 ^^^ 21 Vl6i X 14i X 12J • 7F (3) Simplify ^^jl^-^- A^^ - X ^^^ ^^'- ^^'^^ m - n- 10.V. 9Jrf. (4) A man bought a quantity of hay at $15 for 20 cwt. He sold it at 85c. per cwt., gaining $22.25. How- many hundred- weight did he buy ? (5) 3S yd. of cloth cost $12.50 ; what will 23-i\ yd. cost? (6) A pers^on having an annual income of $1,400 spends a sum e(|ual to $625. 50 more than he saves. Find his daily expenditure (year = 365 dy . ) (7) A lady had in her purse just money enough to buy a cer- tain quantity of silk ; but she spent A of the money in flannel, I of the remainder in calico, and had then only enough money left tQ buy lOi yd. of silk. How many yards of silk could she liave bought at first ? (8) A room 15 ft. wide and 18 ft. long is covered with matting at a cost of $25; what would be the expense of covering, with the same quality of matting, a room a yard longer and a yard wider? (9) The average of four quantities is 18^89^^; the first is 26-207, the second 3-592, and the third is 38-06. Find the fourth. (10) A bankrupt owes to A $1,039.84. and to B $612.80 ; if A receives $357. 44 J, what will B receive ? i-i u ENTRANCE! I3X AMI.VAT/O.V.s. (1) H-v often is .; ,,,. o f, „„„.„„„, ,-„ 05 ,„,,o„g,? (•■{) SImj)llfy -■i ^ H Of 1:? - i} ■01 + 9 1 X -_ X 1 (4) Reduce 2 hr ''0 mm f« n i • . "' w - iir. _u mm. to tlio decimal of ^ wk the farm. ^ "- '' ''''^'' tiau.sactiou. Find the cost of (8) Find the amount of the following, bill of goods - m f-ords of wood (rr .?;;. r,o ,>er cord 16 y»„ the (4) OOi X OOi ^ 0001. EXntANCE EXAAil.NAnUNS. 9b rs? 1(1 sell it at whole. nd C. A Ipft; jind C. Find a rectan- e number i'^r ■•: the iciti, and le cost of !st coni- ctors of divisor Jr, plus an the (5) A cistern is g full ; one pii)e runs out and two run in. The first pipe can empty it in H hr., the second can fill it in 12 hr.. and tlie third can fill it in i<; hr. There is also a leak half as large as the second piiKJ, in how many hours will the cistern bo half full ? (6) T< ii men can do a piece of work in 12 dy. After they have worked 4 dy. ;j lioys join tlicm iu the work, by which means the whole is douo in 10 dy. What part of the work is done by 1 boy in 1 dy. ? (7) 1 buy a number of boxes of oranges for $(J00, of which 12 boxes arc unsaleable. I sell g of the remainder for i$-100, and gain on them $10. How many bo.xcs did I buy ? (8) Find the total cost of the following :— Cutting a pile of wood 80 ft. long, G ft. high, 4 ft. wide, at GOc. per cord ; digging a cellar 44 ft. long, JiO ft. wide, 8 ft. deep, at 18c. per cubic yard ; plastering a room 24 ft. long, 10 ft. wide, 10 ft. high, at 15c. per square yard ; sawing 6,800 shingles at 40c. per 1,000. Decetnber, 1878. (1) ((/) Delino abstract number, composite number, common nndtiple of two or more numbers ; and explain by an example tlie use of the numerator of a fraction. (/>) Express in figures four hundred billions, four millions, forty thousand and four units. (2) A man has 5 tons G cwt. of flour ; after selling 2.') barrels of 19() lb. each, how many sacks holding 150 lb. can be filled with the remaindor? (3) How many rails iu a straight fence 40 rods long, 5 rails high, each rail being 10 ft. long? (4) If it cost $57.(50 to car|)ot a room 20 ft. long with carpet 2S ft. wide at $1.20 per yard, find the width of the room. }l of ,7 of 2| - 1 -=- {\ + ?,) (d) Find the value of .•» ~J jT^ 1 --4of (i + iof _A_) (6) A pint contains 34§ cubic inches ; how many gallons of water will fill a cistern 4 ft. 4 in. long, 2 ft. 8 in. wide, and b ft. IJ in. deep? ' • (7) If 12 men earn S120 ia 12 dy. by workin- 10 lir. i>ev day, in how many days will 15 men earn $150 by working 8 hr per day ? " i- 26 ifi i m If RVTRAVCB EXAMINATIONS. :HSSS5SSfftt'i-s= in (2) Simplify 5 - (5) Eeduce 3f of J6iV-5{i- the fraction of 7cwf ^ ^^^ " ^^Ksrx^o) °^ '^^'^ ^^ '^ ton to (7) How manv biicL-« o„„t, to pave a walk a , '"'^'/^^^ covering 36' sq in ^;„ , field 10 rods 1 ^^\V'^^ around ti.e outside "^f" ^ ''^''""•eJ (8) A traj„ f ' ""^"''^' '^'^^^"^'^ ^ an acref °^ " rectangular W, and'passes^'m'J'l^s'er^f^^ ^ '"'^^ walking 3 mi ner the tram runnine? ''' ' ^'°^ '"^"'^ miles ^r hduJt ^ecetnber, t879. » (^) A man has 70^ q .(2) Find the price nf a-^ - Wide, and 6 ft, d'ir.t.'4«*'"5 " ."*"»■■ ^' "• 3 in. long ,. ft - ■ --^ -''^•' per cuuic yard ? "' ' BNTRAX* H EXASIINATION8. 27 (3) The foro wheel of a wacffon is lOA ft .•« «:„ * and turns 4 10 times more than'^Z iWn!'!) i/US" urft' m circumference; find tlio distanr-o travelled over in feoi ^ (4) __^^ - 1* of_i"o + 8 . .or, - -005 (5) Find the total cost of the foIlowinK : - " «fl7 u '''''''"* "*^ *'-0 I^r bushel. obT '« oats " .'JiV,. " 1,9.% '< barley '< GOc. '« ^,075 ft. of lumber " UlO per 1,000 ft. (' «'" parti/pttti^itlTnl^ ^'^^ -^ MeSuS^"' ^'"'"'^ ^°"^"°" ^^^^^"^^' ^"^^ G^reatest Common Find the G. C. M. of mn,on and 7,;)89.501,522. (•^) Shew that § = A. fcl Simplify j Hof Aof 73 25 + 155 12,iir - 92 "^ Qa Tj 3 0- ~ + -a-T- M« _ 12354 12,V - 2? 9| _ 3^3 1^ 10355- (4) A brick wall is to bo built 90 ft Inrin- 17 ff i • i j . s„„J4£f."^.?' w* "r- ^"'■^ «Vd., it u 3i"t. v,^ 28 '-■'if:, iii: !•!' in. ENTRANCi. EXAMINATIONS. (6) Divide 76 -391 QRf^ i, ' packing, etc ) Li . J"^^' ^o^en. AlIowiZVi, ^ ^'^ceived an barrel. ' *"""• ^0, find the number oi ell. 1 f""^"'^ P^o^* (^'') The di • packed in each . WJ A flagstaff ion f. i- ,. ^"veieu It was found fh„f "-io , '6'" was brokpn r>ff i ., December, 1880 .SSlhfo"c^fr^^^^^^^^ Hinu d -^"l^r^A-^^^^ ^-^'-- to the (4) P d f ^ ' ^°^ "^"^^^ "^'^y Vanow.d"^^f "^ *h^t there lOr . To L*^® amount of tho f .n ^'^ '''^^^ '»an per dav 5 10c. , 12}^ lb. poj.j^ g ot tiie foilowing bill .--ua jh T, / in all 45 lb 12 J^n^°^- ^^^^ @ li Sb . ^.^" ^" ^oj lb., ^, 1-^ oz., @ loc. per 2b, -P^' ^^'^ ' » geese, weighing ' (5) Simplify 5f_of ^\+3-So{2-n X.. n (6) What i. .^ ^ " '""^ £2o-mr8h ,^.V^- ^-dtr4$\f.^ ^k of stone 12 ft / , Jfi»d of stone ^ /. i • "; ^^ ^n- thick, when « M i " , ^°- ^^ns', :^vent3- tliousaaid 5ar8,.%'0 barrels' -"e received an i cost (including the entire profit packed in each I'e 50 in. by 30 ow many miles ?nt be covered the wind, and 'I yj times the I of a dpy, B ay. In what ii') -Minuend, hundred and 1 eighty.five sions to tlie 'e that there 'an per day? ib. beef @ ^35 J lb., @ B, weighing lid. Sfd. 8 f the *""'" in. 1ft. long, same 3 in. Us on the l,230,87| E>JTf{AX('K K.VAMtNATIONS. July, 1881. Sd (.')) How many minutes are there in Ji" nf ., ..o„,. /o-.- , , ••V of a week + ^-, of ^ dy. ? '^' ^ '' ^^''^ ('"'^^ ^i-) + KV ~ r- - , '-1 + l^Gl-vv - l«50Ji}l. 2 + i>i (0 Water in freezing expands about ^ in volume How mnn,. f.ta,'!:;Lf'nrr,sf™ '- -' -'-^-^ ^^ >o?r."oT December', 1881. (2) Divide the difference ot 13* -i- |ra» - 3,a 1 v 1 1 i j .lilaH4tta"°vo'Mi' Sle'^'-iTirvd" 'i" '°f'-^ ""-^ «'"*■'• lOA, 95 yd. Dutch stei@2% Vl s/vd ^™f '» ';"1»=' ® 5.v. willbeequalinlulkrlieib JeS? ™'^ ' °' "''"""'■" V6?b'. Sis' w''!fS„'",;:^,^e*" 'i*!?,!'' "' ">'" "=■""«• chain costin, ,s. e.„ :?th:'.:;:°c«Sg'5i'; G'r;::/ctt.'"^ r ;; Ml 80 Kl i- Hi '-' 111 1 !'! I I KNTIIANCE EXAJIIVATlOm m. Find ,, (^) By selling tweed af «o /jn 'hS,,tfX°Jt:rhU^.%'"„ '"T « "• wide, anCi Its thickness. ' * "' " '"• wide, and 6 ft. long. Pi! •llowmg that the morta,- increases tteb,* „&"," ^ l'' «"='^ wards he'increaS" i pie' SvS '" ',"• ?,"«''' '- »»■ After, much per cent, did he naaTe^ fKc^^t ^ *'' =°^ wh^cl^h^- g^^^^^^^^ state the prin.p. on' Find the G. C. M of Gb So I'ao T'^ ""^"^^'^ ^^^"ds. (2\ A A.i ^ . ot^^->90,142, and 85,054,059 f'md his gain on the whole lot ^^'^ '' ""' ^^'"^'^ Per 100 "t^ (3) Show that J = I, and that i - ^ = x| Simplify the following •— " ' . 263__ 113. 17i ^ + IJ - § of 12 f°H^jf°'i (4) Prove that 2-3 x -04= 090 4667.M04.'°''^"'^"»''--''^'"- -421, ■0001235,741-206, -03, and Beduce 76-0125 cwt. to ounces. 300*"^ F^'"1"» J«St\:,r;^Str? (M72 ..) in ., ,,„, ,0 „ .(^ of thickness. '"• ^^^S and 4 J ni. wide ; find its SSf ""■" -- ^" A^^icrn^trt? ^ijf'tit iZS III I ENTRANCE EXAMINATIONS. 31 (8) In a map of a countrv tlio sr'ilo i^ i „c • , mile (i.e., ,V of an inch rep/es ts a mi :) 'and TJown V'" •'^ 2,700 vote's'^ l^^e '4^^' if ^'•', for election in a constituency of as '>3 To l\ n,.^ R ' ^"?"^'^ ^^^ ^ ^^'«»'«' to those polled hy B as ..J to 2o, and B was elected bv a maioritv of 100 w ' many persons did not vote? "" " '"^•1°'^"^ of 100. How December, 1882. Jl) From 935 take 846, explaining clearly the reason for each w, is^^s- &thr ° £ ^^osrtiroxr 12c„ 15 lb. (i o. turkey « ISc.;* ,b. ij o^'l^^^^Gc "''"'^ ® thfi^(;l*'t^^?:„?^-,°Vo5i,."' -**• ^- "' «^' ^2. «M and (4) Prove that 3 of 1 = | of 3. Simplify ^—.^'i±_Z±p[.^ ^ ^_of^J + e of 5 9^-18 A+ ,Vof^{i-(g-offrrj) (5) Prove that 1-025 ^ -05 = oq-S •0703125"of lir"' '' ■'''' °'"^^''^^- -^-' -^en 1 lb. costs (6) Reduce 45,740,108 sq. in. to acres. a1^ "^l bottom of a cistern is 7 ft. G in bv 3 ft 9 in rx «K4hin'SrOOOrr ^''^ ">■ °' waLV "cu\;^e„?^ 4's speed to B\ ^ ^ '^ -^^^^ t^^® ^'^tio of (9) A does S of a piece of work in fi bv • n p^ n * , remains in 2 hr • and r fin.-Ii \i. .' , '^'^^ I ^^ what <;3J 32 I'll: ',„+ « -„ $70 more than h and twfc'-e fs iSxch as S '^ ^'^ ^"^^ (5) Divide the sum of f of 8i and 2^ of -)-• Iw f>,^ ,!•» between ^ of 3J and J of ^. of 2i. ^ " ^ ^^^ difference bv^'^Oo'tgy ^«f ?^.!f ^ "^^7 ^ 'l^^^' ^^^^ ^0 -S^' Multiply the sum (7) A farmer sold a load of hav at Slfi Ot ,v^,. *^„ .u i. , weight of the waggon and hay was 2 875lb th« w ' ^ '^^°^' was found to weieh 1 08'? Ih w!l ' i, i-!. ?® ^^a&gon alone for his hay ? ^ "'''''^ "^'^ *^® ^»^™er receive (8) ^ can run a mile in 5 min. , B can run it in 6 min Ti^^^ Ser^tr ^"""'^ ^ ""- ^ '" «^- - ™* s if ?1 ^i""^^ ""f" ''^^ '^'^ ^ '^^^^^i" '^^•ain in 8 dy. Thev work at (10) Find the interest on $275.80 for 91 dy. at 7% per annum. June, 1884. i\S^} T^® . ' . i« 24 hr. Reduce the d?^,^;;^^^'^";;-. «nd the „.ean solar day of a sidereal day. ^^"^rence between the two to the decimal (4) Simplify (a) f£l-rr) of 6 A , (6) -iVof^uinea^- -2- of a £ ... . 8a'. lOf^?. • (O) A grain dealer boii/)>if ai \ 16 In-., Li TlnA S taTs „™ ? '"■ ^ '' ""d S can do /t f„ ^pamtelyy '" '^ !>'• la what time canroh do i" (8) An armv, in its fiv«f r.-^^ wounded, andi 1 its seco m ,"r^"'"^«*^' ^ost 1 in 10 in killed and there were tliPn -j w^n "^^ <^"««^'ement 3 ia^S nf +l,J • . tate„^;:°„*:^et""" '"^" '*■ HowmaVme„teS"m"„tj !,££"**:, at'fgrpe' StVt-"n """'> -'«»-« (10) (a) rind the interest Z\IV°.^?^ •''"°"''«' '°' '"'-o. annum. '"^•'^ <•" «22o.40 for 10 ,,,0. at 8 7 „„r <'M Til Bin., and«?.rTjV? ViSteScSStE '°- December, 1884. (1) Of what number is 8 9rt7 v.«4.i, j- • (2) Find the greatest !!'^''^''''"^^"d quotient? (4) Simplify (a) 5J + 2J ^ 111 ^ ^^ ^ USM - (6) a x,^rx 05x0 -156)^1.^11 of§. i an solar day ) the decimal Entrance examinations. ? (including each. The em at 42Jc. >ne side for f the plate, an do it in each do it killed and emainder ; »t into the weighing or tare. 1 8 % per 37.20 for rate. t? >67 and issimere !?.'i7j(.., weed @ 36 wiS ^ti^i^tT'Za 'Tl^£- ^^ -^'^ -^-1-^ ^7 in. the room? ^<^^ J^rci, ,s $22.50. What is the width of (6) A boy can do a piece . r work in 48 dv o ^ the same in ? of the timp vrZ ? ^■' ^"^ ^ ^^^ can do wir?h?l60T»*X"inT*X"f'lT' '°.^- «>'^- »' brandy, only »3,60 per gaUon ? *'"" "'" ■"«""■<> "»y >» worth tn.'^rcriisraj'^Ftrn'j.f;'''' '™- '«* ^"'-- '««»■ MfficCLxixv" ™^^---17089G53-005904, $705-637, and (2) Simplify -,V (31 + 9\i)^ ,K of ^iO.9. 2d. 16.V. 2*:?. ^ ■ (3) Find the value of 17654 + 4-835 + 6-408 (4) Make out a bill of the following «oods - o^ ^a .. lie-, 13 yd. gingham (^ o;]c o.-^ "? ^ "'^^ -."-^.J yd. cotton® tweed @ $1,507 m yd. sera^® sT t'^ iu *Tf ^ ®,^7"- ^^^ ^d. ^f^^ A J 3 -y "• •■'ti ge (y? .sf 1 . < o, (, J y d . broadcloth ® $4 50 loj A merchant purchases suear at ^' ™ «" f"r 3 yr. 9 mo. at 7% per :imll'rnt:««?'™ "" ""y ="» of "-"ey double itself at 6% simple interest ? thl?^l''Zi ■rto'l^^ilSlt'IToV^'" ''"^°"^- ^ -" ^' - o. a It^ht^uilT/d'Sutlr'orih-: S™ iSr "-^ "•» ''-'■^ (10) A man having $720 spends n n«rf -f - ^ceived 7i times as much S he sLnt ^1 "i, ^"^ "^^^^rwards How much did he spend ? '^ ' ^® ^^^'^ ^^^ $1,305. It! III I! 'ii 36 ENTRANCE EXAMWatIONS. December, isSi't. (^) {a) Reduce to simplest form:-li'^!i ' " (oj A man who lost t nf T.- / --'""es r remainder the next year had Iwn wf 'V"" •™'"-. M'' f of the fortune at first. ^ • ""I »900 left. Pi„a th^ ^^^J^ °f «e ?ib]rt.?Sr'"^ ""=» '■■- '««f wli, make it exactly (7) Name the „„iW of ^2^"^^' f' ''"° »*' ^•'"-^-^ («) Pina .he .-.nple intero:'Z'o™ fTl ^7" they together fill the 5"tern ? '" '" ■"■■ '" ^^''at time wiii ■f'riy, ism. »S'\iStSfanrZt?!nt^ttf' '^''T"' ^'^ '-"d^ (2) Make out a bill of flin *^ii ® 68c., 35 yd. calico @ 15c ^3* d^^ ^^"«^f ^-28j yd. flannel 7 pairs of gloves @ 90c 12* vd )• ^^'.f °^ stockings @ $2 lo curtains @ $4.20. ' ^^ ^^- ^'"^'^ ® ^1- 12, 4 pairi of muslin 41 7t\tlVV:,i:f, 'o ^ence a lot 49 ft. front and 180 ft .exct^gL^^;?^^ ,3S each were , W A farmer sold «„ , ° ™'''* °' » «»»• ri™' fr'™8 »3,640 for"£tho"rtalui '"T' """^ »■"» •■?w at ,3, aua a calf at J12, find the nlfe,%tr " **"' ENTRANCE EXAMINATIONS. 37 nt^tL^Z^:',°lZ^r' '^''^ P-'- ^^"O interest i. (6) Divide $1,000 amonK^j B nnfl r -^ .1 ^ . $60 more than B, and t^^?e a's m'uch t^c "'' ^' ^""^ ^"^"^ work is completedluig dv W^.T°^^'' "^'"'' ""'^ ^^^^ ^'l^o'^ by the sixth manV ^^ "^^ ' ^^^^^ ^^^«^^«^^ «f tlie work is done how muoh doefs" in? ^° " "''■^''- "■'«*' »""■'"'« «ven. By December, 1886. an^d ^.0?r^' *^' P''^'^"^^ °^' -^^^ -^^ -0025 by the sum of -O, -02 lO^S. Y ^ '°''^ '' ' ''^' -^'^'^ ^°^^ '^^^y "^^ks of it will make a SLf wf fle^"^ft^\U'' whStiiVti'^r^-r^^^^ '^ $12.50 per thousand feet? ' ^'" ^^'^ ^°^^'^^ ^^^^.^^ at Thrill ter™L^£! ^ """^'^' °f ^°^««« ^"d «ows for $2,000. twice as much as rcow '"ir^'Tr^ ^°^*^^' ^"^ ^ ^^^'«« ««« cows did he buyT ^^'^ ^^^''^ '^"^^ ^^0' ^^^ »»any baS. ^?^e stnds'«5Sf '^ ^*'' ^-^^ ^'^^^ ^"'^ ^^^ ^^00 in the be all gone? ^ *^ ^'' ^'^"' ^^ ^'^** ^^^^^ ^i" his money (7) What will $1 amount to in 3 yr. 219 dy. at 7^°/ per annum? is 50c. on evei'y dollaJ boVJwedV ^'^ ^' ^^'^ *^^ ^^^^«<^ (9) A dealer sold an article for $8.10 and lost 10°/ • of v. * selling price would he have gained 10% ? ^ ' *^ '^*'** 88 ENTR AN(;k kx x m J N ATIONH. (11) If n, cow trives 1'' r.f i ■ f * .,. 8 oz. of butter can lo ; 1 f t, .^.-"''l'^ T'y '^"^^ ""'^ > 'Im- pound, of butter can bo ,,].'' vk^^'^^^^^ ? '"".^/ ^^^ --y . (12) Aman bought a quant v'ot'^'^^^^ ''' "''''' in packages of 1 li, e^ich fl \v?i t «"N>««ea to bo done up weighing them, howev'tr i't w.s fnn /h T' *° ^'^y ^'''» ? «>' 1 oz. too h-ght ; how n.:c>fsirh/ho"l;'ro:. uTe Vaf "^'^ ^'^^ (1) What multiple of o95 divided bv 'iO'i .,;,,„ 2) Find the L. C M of ^o 7- *, .-^'"^""^"^'"^t^^"* '^95? $100. • ^' ^- ''f ^5-' -^'^ «1, $o, §10, $20, $50, and (3) A man owns I of o nf 7 „f of his share he finds^ himkf worth TlOOw' tT^'l ?'' '^^"'"^' ^ IS the value of the whole inverment V " ''^^""^ ' ""'^'^^ (4) Change -A- of A i ^ ^ • , b ' ■' ""^ 3 + 3 ^-^ to a simple fraction. (5) What pnncii:)al will amount tn 9^m • k (6) If 1 lb. of thread ...Zs V, o V" \'7- f '»/«' »»y pounds wo„,., „.afe A^J,? ^/'ii^VlTd/ifdeT"'' ""'^ 4 atirroE f Zt'lo?'"''Srrht ' °" °"1 "^ ""'-* whole and how much '^ ^°' ^® •^*^*'^ ^^ ^ose on the I December, 1887. \ min^I^^rlt'oS'i^uTks ^7™^ " ^ ^'"'-^ "- lemons? ^""^^ ^^ ^ doz. oranges and 7 doz. (2) A man can run 100 vd in 10 q«o xx » steamboat go in SJ dy. at the same rate? """^ """"' ^»' of ScS,t'5% sir„»:::': '™» '">« i*"" »» .i-w to the 9th ENTIIANCK EXAMINATIONS. 89 (4) A person horrows money for (J yr. at 3J% nnd rcpavs at tlieenrtof tlic timo, as principal and interest, $847; how much aid he borrow ? « (5) A map is drawn to a scale of liulf an inch to a mile, liow many acres are represented by a s(nuire inch on the maj)? (6) One \yorknian cliarges $:] for a day's work of H In-., and another i^.,.yO for a day's work of 9 lir. , Which had 1 bettor employ and how much shall 1 have to j.ay him for work that h(> can do m a fortnight working G hr. i^v day ? ^\ ^""nnn '"" ^'T''}'^ expands 10/;. If a cubic foot of water weighs 1,000 ox., hnd the weight of a cubic foot of ice. (8) A merchant bought 1,000 yd. of carpet at 60c. per yard and sold B of it at a profit of 30%. A at a profit of 207 and the rest at a loss of 20%. How much did ho receive for the cari)et ? (9) A piece of land is surrounded by a stone wall 8 ft. high, and 2 ft. thick ; tae land inside the wall is 100 ft. long Tnd OU ft. wide ; how many cubic feet of stone does the wall contain? (10) A hou.se and lot are together worth $2,100; i of the va ue of the house is equal to J of the value of the lot ; find the value of each. wilHt htT^'l^'j/o^r' t" ^^- v"'^'' ^"'"' '"^^">^ gallons of water will It hold if 277 -2 < 4 cubic inches make a gallon? Jufi/, 1888. (1) Prove the rules for division (a) of vulgar fractions, (6) of decimals, using as examples '^ -h | and -012 -^ -6. (2) A produce merchant exchanged 48?. bush, of oats at 393c per bushel, and 13^ barrels of apples at .^3.85 j^er barrel, for butter at 37 Jc. per pound ; how many pounds of butter did he receive ? 4. -^^^ ,^Jn*''".^°'"^ -'? "'^- P®"" ^°"'' ^^""^'^^ at ^ o'clock p.m. on a trip of ^0 mi.; another going 37 mi. per hour starts for the same place at 12 min. past 4 o'clock p.m. ; when and where ^♦ill the former be overtaken ? (4) If in a certain town $3,093.75 was raised from a 3 7 tax what was the value of the property in the town ? * /o ' (5) By selling my clotl^ at ?1.2G per yard I gain lie. more n" o°n^ ^^ "^^^^"'^ '^ ""^ ^^•^'' P«^* yard ; what would T --"-'t hy selling 800 yd. at $1.40 per yard ? m If ■i III 40 ENTKANCK EXAMINATIONS. {^) A man havinir lost 00°/ ^r \ ■ mucli as another who has'j^4 Ja necr';^;*7 ^ '^ r^'^' '"'"'^^^^ «« secoml man's capital was ori« nt Iv* ) il/^ Vuu" '^f^'^**^ ' ^»'« man's capital ? '*,'«»]!> « J,000. What was tho first December, J888. $29.87 27. yn 19.9(i 23.19 17.84 12.09 |$31..17 30.05 29.70 32.73 31.19 2(5.07 ;$33.35 28.39 29.98 31.80 27.36 24.09 $35.00 34.83 36.10 37.91 35.55 31.87 Total '»tw;rt.:s*«..~^'''' "" »"-«"» «»'«• <"r«„ 64'U'^rd':^6\'„'r^^""-'««- *«nt throws is 10c. for e?ch Itl • '^'' ^T"' '"'' "-e mer- much change would yo.lZ^ ^iXl S' """""""■ "»" K.; iVj'"^,*^?.^«terest ou $387.56 fmm M„.I .«., , „ ■ I in \ ENTRANCK KXAMINATIONS. 41 (5) A bushel of potatoes weighs (50 lb. If u grocer bu^s a ton of potatoes for $15, luid sells them at luc. per ijeck, how much per cent, will ho gain ? (6) A barn 80 ft. long and (50 ft. wide is built on a plot of ground 30H ft. long and 204 ft. wide. The rest of tho plot is covered with cordwood to a depth of H ft. How many cords of wood are there? (7) Tlie interest on $870 for 4 yr. C^ mo. is $274,05; how much will $1,000 amount to in ;] mo. at the same rate? (8) A lot 11 rods long and 9 rods wide has a fence built round it. Outside the lot at a distance of 2 ft. from the fence a side- walk 4 ft. wide is built ; how many square yards of ground does the sidewalk cover ? July, 1889. (1) A bushel of wheat weighs GO lb, and a barrel of flour weighs 196 lb. If 3 lb. of wheat make 2 lb. of flour, how many barrels of flour can be made from 343 bushels of wheat? (2) Find the interest on $597.50 for 2 yr. 5 mo. 12 dy. at 87 per annum. ' '" (3) A and B start together and walk in the same direction, A at the rate of 4 mi. per hour, r. id B at the rate of 3 mi. per hour. At the end of 7 hours A turns and goes back. How many miles will B have ^one when he meets A? (4) The circumference of a wheel is Y of its diameter ; find the diameter of a w iggon wheel that makes 3G0 revolution.s in going a mile. (5) A town v^^hose population was 10,000 increased 10% every year for 3 yr.; what was its population at the end of that period ? (fi) The Map of Ontario recently issued by the Crown Lands Department is drawn on a scale of 8 miles to an inch. On this map the Township of Scott measures 1 A in. in length and IJ in. in width ; how many acres does it contain ? (7) If for $7 I can havs the u.se of $35 for 3 yr. 4 nio., how much a month shall I have to pay for the use of $8,750? 1 1 IBNTRANCB EXAMINATI0V8, 4t%,^tt^^^^^^^^ a quarter of a .ile M I'nes of scantling 4 "n souam V'"^^°'*^'* ^^ three continuous per thousand feet ? ^"^'^ ' ."^^^^ ^^" the lumber co"t at $1? , prove the correctness of thrw^.r^ ^ '" ^°'-'"^^"tally, and *■ ^^ adding your results ;— 1st. 2nd. 3rd. 4th. 5th. 6th. *lli^n*-l'J-ii-^^.^^o; TOTAL. 23.871 30.03 16.99 27.09' 29.13 33.79! 18.47 32 29,' 19.02 27.06 29.38 28.77 30.81J 26.73 29.04 33.84 30.16 39.17 34.45 29.89 27.97 $47.81 26.77 48.77 24.95 43.07 28.47 50.05 28.88 54.39 29.51 61.93 No wot' yo marks will be allowed for th 'k ts correctly done. ^ " is question unless all the ■December, i889. oniltiV:TLT^^^ 'Sr;' ^-V «-<• each «,ai„ is W An orchard is 24, L """ '""' '"'°*^'- cto. per cnbic foot wha/^u I'^J ."",*. "^i rods wide. At U 9 in. wide and 4 ft d«p ' °°* '° '"s » ditch around it 8 ft' iJ^im 2 j" .'?™ J°' *S ^ »■"' s™ed '2J-/. B ,„,. j. .. „ "' '^'•■■- How n,„ch did the'lot colt A} '" fiNTRANCH EXAMINATIONS. 4d f a ipilfi in continuous cos^ at $17 six weeks' itally, and Its .— TOTAL. if all the f $144 ; cts. per lim per 888, to 9.) rain is in 17 other ? At IJ t 3 ft. : to C (6) In a room 2(1 ft. 6 in. long-, 16 ft. 8 in. wide, and 12 ft -T* ^^r ®^'® ^^'® *^^'®^ windows each 5J ft. high and 3 ft wide and two doors eaclx 7 ft. high and 3^ ft. wide. The base" board 13 9 in. wide. How much paper, | of a yard wide will be required to cover the walls and ceiling ? ' (7) A farmer sells to a merchant 3,015 lb. of hay at $1G per ton, and takes in payment 6 lb. of tea ® 80c. per lb 2')* lb of coffee @ 2(3C. j^^r lb 33 lb. of sugar @ 12 lb. for"'a ddlari npr b ! ",^'^!•^«^^l«i«• P«r lb 14 lb. 13 oz. of bacon at lOc! per lb., and the balance in cash. How much cash does the larmer receive ? (8) Brown purchased /^ of a mill property for $4,0G4..'S.5 and bmith purchased /,- of tlie same property at a rate of 57 higher What did Smith's part cost him, and what fraction oAhe pro- perty remains unsold ? ^ (9) jfy farm contains exactly 184 ac. 76 sq. rd. 24^ sq. yd ' Jrnn^ T ^ "" ^r '" ?^'^"" ''^"'^ ^^^^^^^•^' ^™ ac. of grL crop, 76-9 ac of gram, 23-(;08 ac. of meadow, 34 ac, of pasture, and the remainder is uncleared bush. What ner cknt of my farm is uncleared ? v imi, per cent.. (10) Write down the following statement of .^ix weeks' cash receipts; add tlie amounts vertically and horizontally, and and prove the correctness of the work by adding your results •- 1st. 2nd. 3rd. 4th. r)th. (>th. Totals. MON. TUES. $95. Of) $89.24 71.58; 6.5.41 58.47: 69.29 4.5.81 63.42 Wet). 57.99 80.07 93.56 77.68 !5«J.79 67.24 50.60 91.87 82.54 79.18 Thur. ^78.04 62.49 71.08 93.74 57.96 86.60 Fri. Sat. TOTAL. $59. ,37;$ 98. 16 67.02 82.91 63.36 72.12 87.31 51.42 76.89; ^0.21! 67.96; 82.75 July, 1890. (1) Write down the following statement of six weeks' cash receipts ; add the amounts vertically and horizontally and prove the correctness of the work by adding your results •-- 44 ENTHAKCB fiXAMIKATIONS. Ist. 2nd, 3rd. 4th. 5th. 6th. 96b. 9b 58.71 47.58 29.69 81.45| 42.63 $24.89;$79.79$40.78 41.65' 24.67, 94.26 SO.fiO 87.9r 54.82 81.79 99.57, 70.80 56.93' 68.77 80.71 74.93 96.57 60.86 TOTAL. $89.61 . 42.5l|... 89.761 21.90'.. 96.671.... 75.82 .. ■j^ _i ^ • • I 1 it i^itttSn;;:s£^si^^ "r ^'^^^^^'^^ ^^ - years (3) Some Atlantic Tinpr. ^ ^ '""' "^"- ^°^ ^^ is he ? They average 8 da's out and 8"br^' '? ^^'"^ ^^ ^^-^ P^^ day. carry a supply for 4 days extra K^. ^" '^'^" ^^ ^^^^'^^"ts the^ hold of such a steamer wm 4 occu^Z ""^7 ""^'^ ^^^^^^ ^^ the trip If each ton is 33 cuSc fjet ? ^ ^'"^ ^°^^ ^^'^ ^^r round (4) In a factorv 10 mo.^ ia At the eml „t a ^<«k Z; ,lr.r«3l''n if" ''f'" "" ^■"P^^- TOch as two women »,fj »830.00. A man is naid a« What fa the shSTeach ? ''°'""'' "' ""■"'' ■" 'hrerboys! thiltear?^ fowSfp'™^:nf ,-' *'''''' --^ ™ " fo^ra..way ho„,., .„d .j for^cL^TSte'* go^TrS J' 30lh! °m.'"'wf^iStif'^^ »'«■•>"■ '» •» -'-ned April then pay ? " ""''«' at ej per cent, what amount must I aris> Ch:js:,r.'lis'';^r•,^t^•f/11 r- '- ™^- at 66 cents, per acre more tha^ W^ ' V^'^ ^^^'^ ^^^'^ 2 bush., - ^ -as apart, ana the Crai^SSstZS,- eel^^^oit ' wij Ir'-""- S-t^ts a^r f ?f -™ '- <» m^'kn -„ -* «^^ "' "» >"te oTfj^^ ""^"f »°'- 't H mi. o„ ENTRANCE EXAMINATIONS. *45 December, 1890, recLVntr^'illthT ^^^ ff»o^".^g statement of six weeks' o f Jf i^ ' . % amounts vertically and horizontally, and nr the correctness of the work by adding your results •- ash ove 1st. 2nd. ;Jrd. 4 th. 5th. 6th. Total. $84.56 $74.68 73.55 91.32 64.39 57.95 78.19 65.43 47.62 54.98 49.17 63.58 157.92 $78.81 81.47 90.54 ";.41 42.86 5'2.29 86.57 64.93 71.46 92.78 63.69 $51.27 74.23 83.57 54.39 67.44 96.08 : Sat. TOTAL. $73.28 36.19 75.64 46.37 85.16 79.31 ■Mowed Jor this question unless all the work No marks w> is correctly don^ ./^l"^ .T^°" "^"^'^ ^.^ °^ ^'^ ^^^'^' -fi i of the remainder C ^ $60"ir atr Xd"th;'"' r 7' ^'^ ^ "^^^ heTadTeft'^a't «)Du per acre, h ind the number of acres he had at first. (3) A grocer bought 6 cwt. of sugar for $52. 10 : he used 65 \h himself and sold the rest so as to make Uc per ^ound profit on the whole quantity. How much per pound did he sell it for ' ■15 mi ^a't*'U nf'^"" ^1"^'*°" *? T*^ ^"^ Belleville, a distance of 50 mi., at 3i m . per hour, and B starts from BeUeville 3 hr ^U% k' f^ "V;- ^^' ^°"^- ^^^^^^-^ do they meet, a^id ho^v far will B be from Kingston when .1 arrives at Belleville ^ (o) A note for $162.50, with interest at 5i°/, was given on January 14, 1889, and paid on November 28, 18°90 Whit was the amount paid ? , ^"^^v/. wnat was .x.^Vv^ T^^'^- ^^\^^ ^^- ^°"S is to be carpeted. It is found that by stretching the carpet lengthwise, any Vne of fouj nieces width respectively % yd., 1 yd., U yd., ^nd IJ yd. wHl exactlv carlt' NiliT^'^^"' '^^"'"^ ""^^^"^^ ^^-"^ ^he 'wTd h of tt Iw .," the narrowest piece, worth $1.10 per yard, be chosen what will It cost to carpet the hall ? i^ ^ ", w cnosen, J^U ^°"^^* ^ ^.i'^^ ^,''':™' ^^^ ^^'^^ ^ong by 96 rods wide at $12.50 per acre. / paid .^14.75 per acre for clearing a n7$l 35 perrodforencosing^the whole farm with wire fenoS^ Taking mto account that I sold the wood for $1,160 and ash^ fof 117.20, how much has the improved farm cost me per acre? I; % I % 46' ENTRANCE EXAMINATIONS. (8) A loaned S $120 for 1 yr. and 8 mo. and received a', mv ment in full at the end of tliat time .«^130 05 ww ^ cent, interest did. pay? ^i-iU.Jo. What rate per (9) A farmer sells a merchant 30 bush, of wheat at 00c nor 5 y^orl'dcSh ^ttro ''^^^ '• ''r "^^^-^^^-^ sells U.etm'^ yard and 4? v^ 1^ at $,J.OO per yard. 16 yd. of calico at 8c. per how mucl/" ' ^^'"' '^" "^^^'^ ^y *^« transaction and Julij, J 891. r-JlK^'''^^iAV' *^^ following statement of six weeks' cash TOTAL. 1st. 2nd. .'}rd. 4th. 5th. 6th. $75.59 $62.68 $59.63 82.61 j 79.81 48.79 49.83; 89.64 75.16 1 46.98 ^34. 75 77.63 81.14 67.19 56.95 i 91.04 i 68.17! 47.80 ! 7 UX T $62.78 92.13 47.85 39.67 85.94 49.85 $1)7.36 '$91.34 81.78 78.81 59.76 93.19 48.77 87.17 79.68 95.79 86.97 98.99 (2) A note of $360, drawn April 20, 1890, is paid JuJv 9 1«oi wath interest at 7^% per annum. Fi;.d the' Tm^ount pafd ' ' (3) Brooms are bought wholesale at $20 per o-ross • wbnf r,... cent, profit wiU bo made by selling them at 20c.Ch? ^' ini^^ ^T?nff5%^'^'"°'' °^.^" ^"^^' t^^« sum of the follow- S^flK/nllfeolstX"' ^ ^^ *'^ «^ ^^«^ 1^0 s,. rods; an^d and ^-07 bv ?h" ^'^ l^^t""^ ^H?''''^ ^y '''''^"''' -105 by disease 2?0swtf^^MnJH^""l^^ '^-'"f- "'^^'^^ -mainedfandX^. ^ov sneep lett. H md the number in his original flock. (6) A legacy of $9,500 is to be divided amone A n .r.A r that ^ will ,et A of the whole, and S wiCt^ ^s ^^ch a^' ? jtfmd the eh res of each. fe-t 5 as mucn as t . id as pay- t rate per t 90c. per ;he farmer at 8c. per makes a ction and eks' cash md prove rOTAL. 'he XL'orK- 2, 189L ^hat per follow- ts ; and Jiserase, iiid has dC, so 1 as C. ENTRANCE EXAMINATIONS. 47 valine Jf^wif r??' ^"" ^^^S^ ^f *^« «hests of tea is 25 lb. ; the oTtlt'ealh chesT? '°""' ^^ ''''■''■ ^^^ ^"^ P^-d: (8) Find cost of digging a cellar 48 ft. long 30 ft wirlp „„^ 'i^L^si .r;v- r^ar • "-^ «-'-' -^^^ ^M^y, 1892. (1) Make out the following account, neatlv and accurat^lv 'n y>ro/>er/orm: -Nicholas Nickleby bought the eoorlffrn^n,' (a) What was the price per cord "> (6) At «4 per cord what would the load be worth ? (cJ) How much will it cost to paint the outside and both floors of a two-storey cottage, 36 ft. long, 33 ft. wide and 18 ft wi a 10c. per square yard. The wafc to be THiA thick and nA allowance to be made for cornices, openings or partSs? drlwn^eb'eTsqo* ^'l t ^^^ ^"^^ *' ^^^^ on a note of $ ({); Whrft IS the smallest sum of money with which von ran buy chickens at 25c., or ffee^o nf f^n^ /,. T I ^"^^" ^P" can lamb) A can give B 10 yd. start, and C 21 yd. in a race of 120 yd. ; B can give C IJ seconds' start over the same course. Find the number of seconds in which each of them can run a mile at the same rates. (7) A person invested one portion of $1,000 in 3§% stock at 80, and the rest of it in 5% stock at 112, and his joint income from both was $44.06^. Find the amount invested in each kind of stock. (8) The central part of a room 24 ft. long and 18 ft. wide is covered with carpet 2 ft. wide at 4s. 3d. per yard. There is a painted margin all round the room 3 ft. wide, and the total cost is £8 lis.; what is the cost per square foot for painting the margin ? (9) In a quadrilateral field ABCD, AB = 159 yd., BC = 105 yd., CD = 90 yd., DA = KU yd., BO perp. on AC = 84 yd. Find the area of the field in acres correct to three places' of decimals. (10) If an iron ball 7 in. in diameter weighs 10 lb., find the weight of one whose diameter is 10 in. P. MANITOBA teachers' EXAMINATION. (1) A person has $15,566.G0 invested in G% mortgages; he Lves eacli year + of his income and adds it trs his ^ anifal ■"/>..=* saves each year + of his income and adds it will be his income for the fourth year ? ) his capital. PVBhia SCHOOL MSA VI NO RXAMIVATIOff. fift «oSf^ '^*''''.' '""''^fl" ^-'"•^^ '" t'"' f'«-^l'as., of 3l> horses nava «JHO for carnuKes «7;-. fo,- „tublin^^ a„,l l A 7 for i,ls m nS' ^ H« 10H.,H one horse which the insurance company mZ ioo^' with (4) Three contractors huild a road for $10,000. A has '>') mAn a work for Hi cly. a„d .'JO men for in dy. B has 40 mcTn'tor iS leceives $200 for superintendhig the work To hovv nnu 1 J. each contractor entitled ? **" vvoik. io now much is (5) A note of $f!,000, dated May " Oti pavH>,le in 4 mo after date, IS discounted on July 21st at f?°/ • v o-:,;; u 90 dv nf wl,;,.i. +1,^ 7 , /o •' '■•'^ 'K another note at on the investment will a purchaser realise? ' ^ (8) A niiner finds a ^old nugget weighing 24 lb 10 oz Avoir- dupois which proves to l,e 18 carats fine. If standard gold 'o t^nugg::." """' '"'-'-^ ^'' '^-^^ -"-' find theTalIfe;-f (9) A railway train runs over IISJ mi. in 4* hr It ston<» 10 min. at one station, 2.f min. at each of 12 other stations and runs through a tunnel 2J mi. long at 16 mi. per h^ur Exclusive oltSKftunlY? ^^ *'^ ^™^^ ^^^' ^- ^- ^'^^ doiis^s'^tTrVf; 'r^' ''i'- ^ '■"• ^'''^«' 11 f^' '"•^^'' ^-« two aoors « ft. high, .J ft. 4 m. wide; two windows 8 ft. 4 in hiL'h 4 ft. wide ; and a fire-place 4 ft. 2 in. square. How man"v roll^ c^f^paper 8 yd. long and 1 yd. wide will V required to pantile i' ill > ilk G. (1) Simplify ^ X I - § of I|_I_M X -064743589. wa^ai'^o r- I f;i\i^, ^|- f.^ ^^^ 1«- per cwt. for pound. Whatdolpay inmon;y! atdtt"manVprnds^of^^^^^^ i' :i 56 PirBLIC SCHOOL LEA VINO KXAMINATIOK. (3) At what time after 3.30 o'clock will the two hands meet for the first time? ( 1) A person i)cvforms § of a piece of work in 11 dy., he then nets help from a man and tliey finish it in 4 dy. more. In what time could each do it bv himself? '■" ^ (5) Simplify :l^^^^^L::J^, and A± 'O^lfi ^ ^ " -00481340 ' ^025~' (G) If brass be composed of 03 parts of copper and 31 parts of zinc, what quantity of brass contains 4 lb. moi'e copper than of zinc ? (7) Two acres of land are contained in a field whose width is 2 chains 80 links. What is the length of the field ? (8) A man left g of his property to his eldest son, f of the remainder to his younger son, and the rest to his wife. Upon dividing it was was found that the eldest son had $750 more than the younger. Find the share of each. , (9) What sum must I lend for 10 mo. at 6^ % per annum, so that I may receive interest to the amount of $237.50 ? (10) If 500 men excavate a harbor basin 800 yd. long, 500 yd. wide and 40 yd. deep in 4 mo. ; how many men will be required to excavate a basin 1,000 j^d. long, 400 yd. wide and 50 yd. deep in 5 mo. ? fi. • (1) A grain dealer bought 1,300 bush, of wheat and sold ^ of it at a profit of 5%, J of it at a profit of 8%, and the rest at 12% profit. Had he sold all at a profit of.10% his gain would have been I16.68J more. Find the cost price of the wheat. (2) The gross annual receipts of a railroad are distributed as follows :— 40% for working expenses, 54% to pay a dividend of H°/o to stock holders and $28,350 placed in the reserve fund. Find the amount of the railroad stock. (3) A's present age is f JB's, but 34 ^ r. ago it was ^ B's. Find their present ages. (4) A boatman rows 5 mi. with ihe tide in the time he would row 3 mi. against it. But if the current ran J mi. per hour more, he would row twice as fast with the tide as against it. Find his rate in miles per hour in still water. (5) A and B have e..^h $4,000.- A invests in U. S. 5 per cents at 104, and B in 3J% English Consols at 91. At the end of a year A sells out at 109 and B at 98, Give the year's income of each and also his capxial after selling out. PUBLJU JrCHOOL LEAVING EXAMINATION. 57 nnum, so (6) If I buy a horso for 680 and am allowed 9 months' credit, and I forthwith sell hiin for tHe same sum giving 3 months' credit, find my gala per cent., money being wortli 8% per annum. (7) A property of $2,000, consisting of three fanns of unequal vaJue, IS to be divided equally among three sons. They agree each to take a farm and balance the accounts by money pay- ments. The three farms are valued as 11, 8 and 6; find the payments that require to be made. (8) The sides of a triangle are 10, 12 and 16 ft.; find the len' di of the perpendicular on the short side from the opposite angle/ (9) The diagonal of a square is 4 chains ; find the area. (10) If the radius of a sphere is equal to the side of a cube the solid contents of the sphere are ,i x Ui the solidity of the ^^^^- -^(^^hio ^oot of iron weighs 450 lb. ; find the diai^jter of a bo lb. cannon ball. K. (1) What quantity must added to the difference between 5Z be 98 ? ^° '^ *^^ ^^™ ^ multiplied by 4^ the product may (2) Select the greatest and the least of the fractions TiHif -jiss^, ^/rs' (3) The preas of three squares are as 1 : 9 : 16, and the second is known to contain 944,784 sq. in. ; find the lengths of the sides of the first and the third in yards. (4) A mother and two children stiirt on a long voyage At '^^I^'^^ n-® ^T °? *^^"' ^Ses is 35 yr., and are in the ratios of d5b : J9 : 2o. At the end of the voyage the mother's age is to that of the eldest child as 728 : 94. Taking 12 mo. = 1 yr. find the time of the voyage in months. ' (5) What is the least number of years for which the simple interest on $145.37^ at 4% wiU be an exact number of dollars? (6) Find the difference between the simple and the compound interest on $9,902§ for 2i yr. at 3 J% per annum ? ^V ^^ ^i^^r}^ invested at 5% per annum, and at the end of each year $120 is deducted for expenses ; how much of the capital will be left at the beginning of the seventh year? (8) Jones started from Halifax to Winnipeg and at the same time Urown from Winnipeg to Halifax. Jones reaches W. in lb hr., and Brown arrives at H. 36 hr. after thev met on the road. Assuming uniform rates, find the number of hours each wan was on the road. -siU, ^! . >'l HI 58 PUBLIC SCHOOL LEAVING EXAMINATION. ■ (9) If 3% stock sells at 99, what should be the present worth of $150 due in 9 mo. from date? (10) If a cubic foot of iron weighs 441 lb., find the weight of a 13-inch, cannon ball, the metal being 2 in thick, (tc = V-) m\ |!ir t til! iiii - I and J + J + Ans. i%\. •01342 by -005©. SECOND PREVIOUS EXAMINATION, CAMBRIDGE. (1) Find the quotient obtained by dividing the product of the seven whole numbers next in order after 30 by the product of the first seven whole numbers. Ans. 10,295,472. (2) The circumferences of the large and small wheels oi a bicycle are 176 in. and 48 in. respectively. Hqw many more turns will the latter have made than the former if the machine goes a distance of 15 mi.? Ans. 14,400. (3) Express the difference between 1 - J + ^ i 4- i as a vulgar fraction in its lowest terms. (4) Multiply -01019 by 23-04 and divide Ans. -234777(5; 2-44. (5) Expre&s the quotient of -21 divided by -Oil as a decimal. Ans. 19-09. (6) Find the cost of 2 tons 3 lb. 5 oz. at Ss. Ad. per pound (long ton), Ans. £747 46'. 4^d. (7) A level tract of land 20 mi. long and | of a mile broad is flooded to a depth of 5 ft. Given that a cubic foot of water weighs 62 lb. find in tons the weight of water on tlie land (long ton). Ans. 57,872, 571f. (8) A sovereign is worth $4.07 in America, and 25 francs 2 centimes in French money. How many cents will a man lose who changes £15 at the rate of 25 francs for £1 ? (A franc = 100 centimes ; a dollar = K'O cents.) Ans. 4?^?. (9) Two men, ^l and 13, working alone can finish a piece of work in 7 and 8 hr. respectively. If they work at it for an hour alternately, A beginning, in how many hours will the work bo finished? Ans. 72. (10) Find the amount of £400 in 24 yr., reckoning compound interest at 4%. Ans. £441 5*-. 10-272d. (11) A man buys 5% foreign stock at 40 and sells out at the end of the year when the stock has fallen to 38. What does hp jgain per cent, on the transaction ? An8. 7J%. 'm ■'}! PUBLIC SCHOOL LEAVING EXAMINATION. 69 (12) The excess of the present value of a sum due in 1 vr ;;S°"S^ T^y^-^ fn ^%' °^^^- t^e present value when interest i^ reckoned at 6% is 10*. Find the sum. Ans. £55 13s. M. (1) There is a rectangle whose length is IJ times its width, and which may be planked with boards of lengths 5 8 or 9 ft all running parallel to any (the same) side. What is the leasi size of the rectangle ? & if"l J^ an ounce of pure gold is worth £3 18s. ; and in a guinea j of the weight IS pure gold, and the remainder an alloy 50 times less valuable; what is the weight of the pure gold in a guinea ? (3) How much money must be invested in stock at 97i which pays an annual dividend of 6% to realise an income of $600 per annum r ^ a) A person invests $4,500 in purchasing stock at 90 (par value 100). In 3 mo. he sells 30 shares at 95, and in 3 mo. thereafter the remainder at 87. If his money be worth 8 7. what does he gain or lose by the transaction, no dividend having been paid on the stock in the interval ? (5) Show that the foUowing is approximately a correct method of calculatmg interest at 6% for a given number of days:- Divide the number of days by 6 ; multiply the quotient by the number of dollars on which the interest is required ; and the result IS the interest expressed in mills." (6) A bill due 4 mo. hence is discounted at 7°/ per annum varue?'^*"" ^^'"^^ '^ ''^'^'''^^ ^°'' ^*- W^aUs its face ^^l ^^ ^h^.''^}.'' ^"^ *^^"*- wi" ^100 in 3 yr. amount to as much as $120 in 2 yr. at 7% ? (8) A mortgage which is redeemed, principal and interest, by three equal annual payments of $250 each, is to be sold. What should justly be paid for it now, a year before the first payment: interest 7% per annum? ^ ' (9) A grocer has teas at bs. and 3s. 6d. per pound. He mi.xes ' them in equal quantities, and sells the mixture at such a price that he gams as much per cent, on one kind as he loses per cent, on the other. What was the selling price, and what does he gain or lose per cent. ? (10) The volume of a solid whose faces are rectangles is 786 f^-lxL ', , Its edges are as the numbers 1, 2, 3. Find the length of these edges, ^ I t. 60 PUBLIC SCHOOL LEAVING EXAMINATION. N. ■ Kin ti ^>m I ! (1) Simplify 4 + i + I X if of 7fj, and 1 + 1+- 2i 3J 4J Reduce 8 oz. 6 dwt. 3-iV gr. to the fraction of a pound Troy. (2) Divide, to 6 decimal places, nine million eight hundred and forty thousand and eighteen lO-miUionths, by one hundred and hfty-nme thousand nine hundred and eighty-two 100-millionths. (3) What wiU it cost to purchase bricks for a wall 150 ft long, b ft. high, and 18 in. thick, bricks being worth $6.25 per thousand and each brick being (including mortar) 9 in. lone 4 J m. wide, and 3 in. thick? ^ **' nav Vp°Ji"^nK^°' ^' 1^^^;-^°^ val"e received I promise to pay A. B. 31,500 one year after date, with interest at eight per ^l^t ^.^.^^^""'- ^^'^ "°t® ^s endorsed as follows :-Jan 23 1877 $400 ; Aug. 20, 1877, $500. Find the amount required to pay the note when 5.ue (no days of grace). (5) Explain the termsi-Stocks, Shares, Dividends. When is stock at par ? At a premium ? At a discount ? A man having $25,000 Dominion Bank Stock paying 87 per annum, sells out at 120 and invests in Bank of Commerce hislnc^e '^ ** ^^^' ^""^ ^^^^ ^*^°' ■^"''^ *^® alteration in (6) How much sugar at 8c., 9c., lOc, 13c., and 14c. per pound, must be taken to form a mixture of 400 lb., worth l^o per pound? ' ' • S ^. ^°^" ^^°f weight is HH of an ounce contains 37 parts m 40 of gold and the rest is silver ; gold being worth $17 per ounce, and silver worth $1.10 per ounce, find the value of the coin* (8) If at Toronto sterling exchange is quoted at lOj, and at Liverpool exchange on Paris is 26 francs 85 centimes per £1, find what a Toronto merchant, remitting through Liverpool, must pay to discharge a debt of 12,000 francs (brokerage included in the above quotations). in?n 1^^ *J^^fJ"«t«f.of a 20c. piece be to that of a 25c. piece as 10 to 11, find the ratio of their thickness. (10) Two trains respectively 99 yd. and 132 yd. lonff and moving on parallel rails, pass each other in 6| seconds when running in opposite directions : whfin mnvipo- in t>e -"m-^ d-rec tion the one passes the other in 47i seconds. Find thej rates : t I TYPE SOLUTIONS. The following solected problems are solved in full as types of the questions likely to appear in the public examination papers m Ontano and elsewhere. A careful study of these questions and a thorough mastery of them by frequent reproduction wiU go far towards training the student in the art of writing out solutions m a limited time. A few written out daily on the blackboard and formally demonstrated will prove an. efficient tome, and wi 1 give the confidence and celerity necessary to suc- cess. Several problems here given are more difficult than those usually set for the Primary Examination; but the student requires to attack at his leisure more difficult work than he can do under tlie rigid time limit of an examination. A stiitable test ^^ easdy given by having a number of these problems written out on sh^s of paper and then distributing these slips at random to he different members of the class, who then solve them on the l.lackboard or on paper without any reference to the book The pupils should do all the work, both problems and solutions :- d/'\tterbotrw 1"^'^ ^^r.^'^ Tf'y «• «^'^k ^f ^^ter in 16 for" 9 d V rT' ^A ^"^ i''"^'"S: 6 dy., the woman alone drank lor y dy. more, and then there were 4 gal. remaining and sh« calt^first"''^''^" '^ ^''- ^^"'^ *^« -™^r oTg'Ut S SOLUTION.-She drinks in 15 dy. 3| gal., or J gal. per day; ■; „ }y "^ " and leaves 3 J gal n 16 Cask holds 10 gal. dd TYPE SOLUTIONS. f'llll (2) A and B start to run a race ; '.heir speeds are as 17 to 18. A runs 2i mi. in 16 min. 48 sec. B finishes the course in .34 min. Find the length of the course. Solution.— ^pee(/.9 are as 17 to 18 ; therefore the timea are as 18 to 17 ; hence B runs 2J mi. in \i of 16 min. 48 tec. ; or B rans 2J mi. in 17 x fj<> sec. orB " 5 " 34 x 56 " orB «' -s^ " 34 sec. or B " ^V X 60 mi. in 34 min. = 5.V mi. (3) Find a number which lea\e.3 remainders 1, 2, and 3 respec- tively when divided by 7, 8, ar.d 9 j and the sum of tho ths ea quotients »= 570, Solution.— f of the n-imiv r .= 1st ( aotient + | 4 " ' - 2nd " + I i " ■' -3rd " +f .-. (I + i + ^1 of Rnrabsr = 570 + (f + = + 3) ^^^^r±^ of number = 570 + '^1jL1'-^±1^ 504 ) 504 .-. 191 times member = 570 x 504 + 366 = 287,646, .'. number = 287,046 -^ 191 = 1,506. (4) The average of ten results was 17-5 ; that of the first three \v;»-i^« ^as i? of cost price R.tf ,^, ^ "^ yholesale price = ] f wholesale price. ^ mo at?/^. "^ ^'''^ ''^' '^^' P^'^^^"* worth of ^;-.10.51 for 3 Or,mysellingpricewasHof$510.5] = $10.01 x ',0 - ^oOO 50 ••• my selling price ^ |? wholesale price = .S500 50 " . . wholesale price = ^ of S500. 50 = .S 1 58. 79 1. ' (19) In 1850 the population of a town was 7 600 • in 1870 it- was found to hp, ^ 1Q« je ) to oav^oK S"^ ^^-^ the interest at the end if each fl^Tj. '^ to pay $200 of the principal each ye.nr together with - '■TOO (H) = l.UOO X 101,051 J- 100,000 = 1,610.51. Solution No. 2.— Mn tin"- f-osftMo n'.i«t, j • • -n. 5^^ and counting compound 'in::'^'^^',::^^::]^ the foil, vmg statement beginning .yith the last^p^ment :- I 'I i \ M TYPK 80LimO!J8. Payment. 5th 4th 3rd 2nd 1st 1»T Mode 1,100 100 (H) 100(H)' 100(H)' 100(H)* liND MOUK. 220 240 (H) 260(H)* 280 (ii)' 300(H)* But $154 + 193.60 + 239.58 + 292.82 - $880 same. Difference. 880 in favor of 2nd mode. 154 " 1st mode. 193.60 '♦ «« 239.58 •' " 292.82 " «• They are the (21) The gross rec< pts of a railway company in a certain year aro apportioned thus:— 40% to pay the working expenses, 54% to give the shareholders a dividend of 3J% on their shares ; and the remfuiider, $42,525, is reserved. What was the paid-up capital of the company ? Solution. -40% + 54% = 94% ; 6% receipts - $42, 525 reserve. .-. 54% receipts = $42,52o x 9 = 3J% capital. Hence y^ljf capital = $12,525 x 9 ; .-. capital = 6,075 x 9 x 200 = $10,935,000, (22) I have two debts, one of $400 due in 2 yr., the other of 12,100 due in 8 yr., botH without interest. I'wish to give a mortgage without interest for the whole $2,500. For what length of time should the instrument be drawn, supposing money is worth 5% per annum simple interest? Solution. —Interest ==. j^o principal = -^a principal. .'. discount = -jj^f principal. Thus the discount on $2,100 for a year = $100 ; and the interest on $400 f(jr a year = $20. Now the interest must be so arranged as to cancel the discount. Hence we see by inspection that one way of accomplishing this end is to pay the $2,100 a year fee/ore it is due, and $400 5 yr. after it is due. And this arrangement will exactly coincide with the whole time, viz. 8 yr. Hence the mortgage may be drawn for $2, 500 and allowed to run 7 yr. without interest. (23) A race in opposite directions round the sides of a right- angled triangle, starting from C, the right angle. The boys run 13 yd. and 11 yd. respectively in a given time, and meet first at D, the middle of AB, the hyp., 2nd at E, a point 30 yd. from C. Find the area of the field. Solution.— In every 24 yd. covered by both together, the faster runner gains 2 yd. = -^^^ of whole distance run. .-. 30 yd. = iV perimeter ; . . perimeter = 360 yd. Now the triangle is right-angled with rational sides, and we see that 36 = 9 + 12 + 15, which are the sides of a right-angled triangle, «nc« V -r X- = J.U , ncuut; s/ut; siues are w. izu, iou : ana tne area = 60 x 90 = 5,400 sq. yd. TYPE SOLUTIONS. 68 of ^,f ILfn'^'^p^® f '""^ °' *'^^^°« *^« ^'^"^^ quantity to both term. SoLUTlox -Book work. A proper fraction is increasorl in value by adding the same quantity to both terms '"^'^^'"'^ '" 48.3 519 -" 519' Ist ca8e;-"*^i^ = 483 483 - 6(\ 519 - 86 "483" —619 2nd case .-^JB < ^ ' '^l +J7 , 3731 + «7 3798 ''' ^^'' -^ ^^ "^^^^ +"^0* ''*• ^ 4628' '*'"^*' *^^ fraction is increased in value by decreas- ing the denominator. S if tbf^r*''' '^n ^. T'^ '" ^ ^^® ^'"^« B requires, B can do it in rt of the tune C takes. AH working together do it in 18 II How long would each take separate!/? ''^ ' Solution. -A's time : B's time = * • 1 ^ i B's " :C's " =1:1 = 2 . . A's : B's : C's = 1 ; 2 : 3 Therefore their rates of work are :— A's rate : B : C's = 1 : J : J = 6 . •■• ^ does A of Vb = sV per day. ; 2 3 3:2 '1 "- ^tf Ans. 33, 66 and 99 dy Therefore actual rate must have been = 2 mi. per hour 2nd case : Decrease of rate would have been 4 mron a rate Xo?!' ^r' ' ;,• ^'f ^"^^ °^ «P^d - i actual r^;^ * '*'" road ?\ actll '.^^ = * ^?"^^ ^^*^ ' •• ^"^^'^^^^^ time on the .-. actual time = 7* hr. at 2 mi. per hour: .'• distance travelled = 15 mi. 70 TYPE SOLUTIONS. (27) An hour after starting a train breaks down, and spends another hour on repairs. Afterwards it runs at g of its former rate and arrives i) hr. behind time. The conductor observes that if the mishap had occurred 50 mi. nearer the terminus, he would have got his train in 1 hr. and 20 min. sooner. Find the length of the trip. Solution.— Decreased rate = i regular rate; ,-. increased time = I regular time ; that is the time lost = § regular time = f hr. on 50 mi. ; .'. schedule time = 2 hr. on 50 mi. ; i.e. schedule rate = 25 mi. per hour; consequently distance run before accident happened = 25 mi. After tJie accident— T^oss of time = § regular time = 2 hr. ; .-.regular time = 3 hr. ; and regular rate = 25 mi. per hour. .'. distance after mishap = 75 mi. .-. whole trip = 25 + 75 mi. = 1 00 mi. Remark.— These solutions illustrate the application of the important principle of Inverse licit io. For any given distance, every increase of speed pitoduces a decrease of time; and the fractions expressing the rate and the time are mutually reciprocal, and so on for a large number of practical applications of this principle. (28) What price must I pay for bank stock 3 mo. before the dividend is due, so as to make 9% on my money, the half-yearly dividend being 8% on the par value? Solution. -Considering 8% half-y arly = 16% per annum, the price of the stock, without reyard /-> the cmning dividend, would be 100 x V = 1777. B^^t ^jj^ ^^,^,3^. ^^ entitled to * of the half-yearly dividend, viz., $4 due in 3 mo. The P. W. "of this at 9% = 4 X iU = 3-912, which must be added to the price of the stock, .-. total price of stock = 177 5 -f 3 -91 2 = ,$181-689. N.B.-Eight por c»;nt. half-j-early is = 16 per cent, per annnni + interest on $8 for 6 mo., so that the first as3Uin])tii)n is only commercially accurate. (29) A and B enter into partnership for 3 yr. A putis in $20,000 and B $5,000. B is to manage the business, and the profits are co be equally divided ; but at the end of the first year A increases his stock to $36,000. How shall they divide a gain of $28,500 at the end of three years? Solution.— It is evident that B's services are considered equal to $15,000 capital. Thus A has $20,000 invested for 1 vr., and spou,wu lui- > ^r. = $rf2,000 for 1 yr. ; ana iS has the equivalent TYPE SOLUTIONS. 71 of $20,000 for 3 yr. Hence their stocks are as 92 : 60, or as m X ioOO -Vl7'o.?o1 *^ of 28i thousands = Jf x A^ x 1000 = i^ perimeter ifp. AgS, „ s»Sl'"IhZrJtJ" ° '^""J'' *"""• ""•' '"' « = '"ghest rate of inUrT.-./S.rsSUlitS-£^^^^^^^^ iJ^Tt, ™."'«"™ 'he KULE : To fi„!l the time of' meeting, sub- For four travellers we should similarly obtain ExAMPLK If^ = 17 a = 20 6 = 13, c = 6; thenfc = 7, and and C 141 mi "^^"^^ ^"^''"^ ^^ ^ ^^ = ^«^ "^'•' » 31f mi., ThfbLl''rt«fvi"q^^'*°'^l'^''' employed men, women and boys. The bovs worls b. P'' Y'''^^^ ^^'"^^ 4^-' ^"d the men 6c. ine boys work 8 hr. per day, the women 9 hr., and the men l'> hr The boys received $5 as often as the women receivS «10^ Slmar:Te7b""^'!/' ^^ l'''^ ^' there;^rived $2?: now many of each were tliere, the whole number being 59 v each^riTor^^'l'i,^"^^.?' ^^'- ^' ^^y' «^h woman 36c., and each man 72c., . . their daily earnings are as 2 : 3 : 6. And the total amounts received by each class are as 5 : 10 • 24 Hencp their numbers must be as | : \^- • At Dividin,* f\Q i^Tw .^' wfi finrl 1 f=i Krt^.c on T « . * ' ^^viaing £>9 in this ratio, we nna lo boys, 20 women and 24 men. (34) Two partners, A and B, gained $700 in trade. A's money was o mo. m trade and his gain was $300 less than his Ttock A's s^ocT' ""^^ ^'^^ ^°'' '^^" ^'^' ^^« ^° 5 ™° ^M Solution.— Let x = A's stock. ' x + 250 - "R'q Ar,^ +i,« profit, are to be divided in ratio ,^ x' 3^^^ (xTsFof x 6. He^^ we have the equation .-^^,„^„ x 700 = » - 300. a? = 8a? + 1250 Whence Type solutions. 1& (35) Find a decimal multiplier that will convert Troy ounces per inch into tons per mile. ""noes TTRH)- X sTf^ \ _ converted into a decimal. (36) If a person spends | of his money and $20 more then i- of .tsstV"' '">• ^"^ -- ''' ''''' hot „,Ai'?"h::f Solution. -If he spends ? + 20, he has f - 20 left " " i of this - 20, he has | + 20 left : .-. i (f - 20) + 20 = 28, • or /a sum = 12^, or sum = $98. .t^T^T''''' ^A- ■*■ ^^ = -^' §«^ = 8, or a, = 36, what he had left after first expenditure. .". f a; - 20 = 3G, | a; 1 98, as before (37) A commission merchant sold a consignment of goods on n£ '^^''^'^o'o/^"^ ^^^ instructed to invest the proceeds in other goods on 2% commission, both commissions being deducted in advance and amounting to $265. Find the procSds of the consignment and the value of the goods. Solution.— proceeds = commission + goods Now 1st com. = 3% of proceeds = 3% com. + 3% goods 2ndcom. . 2°;Joods «.e. Whole commission = ,37 mm ^\°r..:^A add 2% com. to each of these equals, afe wThave''^ ^°°'' . l4''°"'' " ^° '?"'■ "^ '^°/° ^'''''^^ ^ "'"/^ proceeds, '• *' i06 °^ *^*^^ " iOO °^ proceeds. Multiply both sides by 20 „_j 102 X 265 „^ — Too — ^ 20 = proceeds = $5,406 .'. goods = 5,406 - 265 = $5,141. (38) By selling out £4,500 in the India 5% stock at 112* and investing the proceeds in Egyptian 7% stocl, a person finds his income increased by £168 15.,. Wh^°t is th^ ^Z of the latter Solution.— First income = 45 x 5 Second income = ^^ ^ ^^^^ x 7 price Hence 45^J12iiil_ 45^.^ price * add 45 X 5 t<) both the equals, and 'W im 1 1 mi ml 1i tyPB SOLt/TlOKS, Divide both numerators by 45 x 7, and we get — T— = -. price 4 450 = 5 price .'. price = 90. Multiply both sides by 4 pric« is ^^'\I'!l^T:C::.':^l7Z *"° «^^- -^ - rectangular field of the diagonal ' ^'^^ '" °"" ^«^«- ^^"d the length These are aU the i nte^alf actors o7 ^fiO J.t ^^^ = ^^ ^ mo- difier by 6 ; ,. the sS are 16 anS 10 ' and h^ Y ^'","'°"^ square root of 16^ + 10^ = 18 8679623 rods ^^°°^^ '' = in/erlit'87 I^^Sm 1f.^^ \^^> ^^0 dy. and bearing at 6%. Finf the procS ' ^"''"'^ "* *^^ ^^"^ °^ ^"1^ ^^d ^Sr^XrlSrilth^^^^^^^^^^ - ^"-- m«^^ ; ^-^ dy. Interest on $876 for 9.^ d v — «i 7 .«f;c - 46 dy" Tie 759 ' ^"'°"''* ^ ^^^^"^^^ Proceeds = $893-856 - $6'-759 = $887.09. of working the road te4 55% otth\' ioi'^eiitsf ° '"'"""^ SOLUTION.-Mortgsige = «800,000 ; stock =. «I 20O 000 ^^Intorest on mortgage + int. on stock = U0,l^^7s,m . .'. 45% receipts = $88,000 in 52 wk • .-. weekly receipts = (88,000 x 100)"i (45 x 52) = $3 760 69 for $100 worth of th« mir'-^f?-- ^^ ''°''' ^^^ ^^^ "material vi jii_ _i^..i,,x«.vtuicu uxcicie now cost him ? tn»fl soLtrriONs. ie iZlt ^^ '^ =«* '^^^^^ + ^ material. Vf ir ?^^^®^ + § material. (A) *)■ "/material, /. mateSl ff J Vo x t - '1^^' "TV?"'''' reduced cost is - f of S80 - seCS. " ^ * - »*"'. and this at eat^up^ 10 a^omrpa?turtt"9°' ^ ^/^ ' -^- ^^^ ^1 oxen eat up 24 ac/in il wP Ls" 6 ' ^"^ ^^°- ^."^ o-en will Newton, 1704.) ^- (^^oposed by Sir Isaac by^^^oToSo^roTn^i-j^^^^^ --,^s ' -'- -n^^ ^* -' *^- in 18 wk., will eat UD 10 ..' °'^^'' '" ^ ^^^ o^ 8 oxen not grow.' But si„:^ by';;;s:nTSf "owJlf' .''? ^^^"^^ ^^^ oxen in 9 wk can p/f ,7^ ?. i .A S:i'owth of the grass 21 grass in 10 ac for the ast'^S wlf ^Mil'"' '^" ^^°^'^^ ^^^ ^he sufficient to feed he excess of oT A '''" ^' ^' "^'^'^ ^« ^^^^^ be for 9 wk., or what 1=f^h? . ^1 oxen above IG, that is 5 oxen And in 14 wk the e'^cess ofTs^b.'"^^ '^^ ^ °^^^ ^°^ 1« ^k. grass, by analogy! wTirLsucU^^^^^ ^^^t. 4' the increase of for 18 wk., for it ils wk • U ,!i f sufficient to feed 7 oxen fore add th^se 7 oxen wb f.i, 1 " ' ^,,'^''^1' ' ^ °^«"- Where- suffice to feed! o the 8 whTch b! "^'""^'^ °^ ^^"^^ ^^°"« ^'°"ld wk. feed, and tL sum^i 1 b« ?-^''''' "^^^^^i^ ^^°^th ^^ter 4 suffice to' feed 5 oxen S wk tL '^'''"' '^^'^' ^^^t^^' ^^ !» ««• suffice 36 oxen for the same time ' " ''°'°''"'^' '' ^°- ^^^^^ S0L„y A. Martin, M. A., editor Matkematical Magazine, Ene, Pa.-In the first case one ox eats i of ^ or ^ ,, ,, ,,,^ roxtt:'fo'f!nj\t^^,f -- ^^ ' T^- "i- the second case 1 ac. in 1 wl^'Ce t ox ea^T' '"^ *' °^ ^^^^ ^^°^« °" 1 wk. in each ca rthereU M '^' same ^qt.antity of grass in 1 ac. during 1 wk is l,^ _ • t * t^^ = p «r of the growth of acres, 1 ox will eatTn 18* Vi/ sI t ^^^"s'f °' ^Tn " Quantitv of r>rocc> ;„ „„ x. i '^* "t, U 2 x J4 x 18) = 60 = ana bO ^ f .^ 36, the number of oxen required to eat it. ' a r ' I u m' Typb solutions. (44) In a meadow 20 ac. of grass grows uniformly, and 13.^ oxen in 13 dy. can consume it, or 28 oxen can eat up 5 ac. of it m 1<> dy. How many oxen could eat up 4 ac. of it in 14 dy. ? COLENSO'8 Solution.— 13.0 oxen to 20 ac. is 26^ oxen to 4 ac. 28 " 5 " 22I " 4 " .-. 22-4 oxen : 26-6 oxen = 13 dy. : 15 iV dy. i.e. 3 days' growth is eaten by 22-4 oxen in -,V dy. .;. A dy. : 16 dy. = 3 days' growth : 85J days' growth. «.«. original grass = 85J - 16 = 69J days' growth. .-. (IG + 69J) : (14 + 69J) = 22-4 : 25. Ans. 25 oxen. (45) The interest already due on a mortgage, together with what acrues during the time, will board 28 people 4| mo., or 19 2oiV mo. How many people may be supported on this interest and what accrues during the next 12 mo. ? Solution :— 4i mo. boards 28 people for 4 J 1 man for 1 19 19 people for 25iV 1 man for 476 Interest due + int. for ft Also, (B-A); + + + (1 n mo. (I u il i( 1 1 1 1 1 (( 367 72M 46^ 205M (A) (B) (C) (D) (E) (F) " Ans. u (( 4i 25tV 25tV 20?i 1 H .*. (D - A) ; Interest due boards And, (C) ; Interest for 12 mo. boards . .'. (E + F) Int. due + int. for 12 mo. boards 21 men 12 •• /j '7fSt^ ^^ ^^ ^^' °^ ^^^^^ pasture 40 horses for 50 dy., and 60 ac. 70 horses for 80 dy., how long will 90 ac. support 100 horses the grass growing uniformly all the time ? Ans. 100 dy. (47) With the interest already due on a certain mortgage and that which will ariso while the work proceeds I can exactly pav the wages of 15 men ;'or 1 1 mo. , or 31 men for 5 mo. , wages being uniform per man thioughout. Find how long I could engage 9 men on the same plan. Ans. 20 mo. (48) Two measures from a vessel A and one measure from B produce a mixture of 56 wine and 79 water ; but two measures from Band one from A produce 58 wine and 77 water. Find proportion of wine and water in each vessel. Solution. —Add the two proportions and we have 3 from A and 3 from B give 1 14 wine +156 water in ^70 • .*. 1 •' A " 1 " B " 38 " + 52 " 90- But, 2 " A " 1 " B <' 56 " + 79 «' 135 J .;. 1 "A alone gives 18 " + 27 : i.e. 2:3 oimiiarly 1 from IJ '• 20 " + 25" •* 4:5 TYPE SOLUTIONS. 77 (49) A father left $16,395 to be so ^irriA^A ,.. , sons, aged respectively 15 17 and o^ w®^ ,^"'°'IS his three the two younger put out at' s mpL ln?e;e J at'^V " '^' '^^''' ^^ they come of age, each woukl tCn v. ^^ »/^ Per annum till that if one of these shades had been nurouTaTfT^ ^"^°"'^^' ^"^^ the time since the eldest came ofTe it 1, id ' '^""^ '^'^ ^°^ share. Find each share. ^ °"^*^ amount to his havrrhrij.?Ty?tld" therrr^ ^^^^ ^°""^- -" -i" the P. W. of $1 for 6 yr at 57 '''" fo°""^'"? ^^°"^d get no^ should get the P. W. of SI for 4 4""- gV. ^"^ '^ T°"^ s°» the amount of $1 for 4 vr - S9 uZ \V *"*^ ^^^®s*^ gets alaliW. ' ^"^ ^ '''■ «^' "^ '^^""at ^a^J^^SrSta^l short arm : long arm = u ^.64 •■• 64 sKrm=J^"^r«^^ ;< short arm; and tions and divide this by long arm y ^ w' ^"^^^Pj^ ^^^^se equa- 64 X 49 = (true wei^hj)^! tr'e weight' ^Tx^J^e'^'^ altifge\h^e"Si,^oSrf t:^^ .^T ^^^ -P^' ^^^^-^ proportion of 11 gold o 1 coDoer twfr""'. ^,^ ^''' ^"^ the and there were 288 oz. coppeS ' The fi/J n '''^^'^' '^ ' ^^PP^^' ' rate of £3 1 7.s-. 10 W per oun Jp f >.o i ''"^^' '^ ^^^^^^ at the and the whole su^tC rnedt%T?4l lH^'f' ^.^-T^^' number of ounces of each metal ' '**' ^'^' ^^^^ ^^e Solution.— 20,300 - 288 - 20 019 «, ■ ^ £3 17* lOA^ - v&-'3 \~ i'.^ °^- corned. ^ 2nd alloy = 20,012 oz. - +f gold Hen^ IM X H gold + f^ ^20,012 - ff gold) - 5 ^4fi« e.e. Agold X 579 = 221,869 - 220,132 ff 737 ' ^ V Vr gold = 1 oz. ; gold=lloz. ' '^"^^ . . Jt suver = 20,012 - 12 — 90 nnn .1 .r» - Gold + ^ver = 18,6,1 ; ''; ^op^^l'i^fc "''* °" ( , ^!i I sijr If 78 TYPE SOLUTIONS. (52) A and B run a race which lasts 6 min. At the end of the 4th minute A is f\xs oi the course ahead ; at the end of the oth minute B increases his pace by 20 yd. per minute and wins by 2 yd. Find the length of the course. Solution. — A gains in 4 min. the i\s of the course .'. 20 yd. - n°«o course = 2 yd. .". course = 3 mi. (o.'>) A, B, C and D run a race over a course of 1 mi. First A and B race, and A beats B by 20 yd. Next C and D race, and C wins by 60 yd. If A and C now race, which will win and by how much, sui)posing that D could beat B by 40 yd. if they were to run the race ? Solution.— D goes 1,7(50 while B goes 1,720 .•. D " 1.700 '• B .-. C " 1,760 " B ButB " 1,740 " A .". B " 1,<)61A " A .'. C beats A by 79|f yd. It 11 1,661A 1,661tV 1,760 l,680if (54) A and B race to a post and back again. In returning A meets B 90 yd. from the post and reaches the starting point i) min. before him. Had he then returned ho would have met B at a distance from the starting point equal to I of the distance between the posts. Find A's time in winning the race. Solution.— Suppose A had met B the second time, he would then have traversed the course between the post 2^ times and B 1| times ; A's rate : B's rate = 13 : 11 ; i.e. B loses 2 yd. for every 11 yd. that he goes. But when A met him he had lost 180 yd. and must have gone 990 yd., and he was 90 yd. from the turning post ; .■. distance of course = 990 + 90 = 1,080 yd,, and therefore A ran altogether 2,160 yd. and gained -i\ of 2,160 yd. But B took 3 min. to run this ; .-. B's rate = ^3- of 720 yd. per rain. A's rate was therefore \} of -,^3- of 720 yd. per min. = ,2,- of 720 yd. A therefore required 2, 160 -4- (A of 720) = 16i min. to double the course and win the race. (55) In a race between two boats a spectator, walking at the rate of 5 mi. per hour, is J of a mile ahead of the first boat at starting. When it passes him he observes that the interval between the boats, which was 30 yd. at starting, is reduced to 20 yd. At IJ mi. from the starting point, the first boat is over- taken by the second. Find the distance traversed bv the F.nef- tator after the first boat passed him until the end of the race. TYPE SOLUTF^NS. 79 he IS llfi) = Sii'oc?. SOLDTION. -First, A loses 30 yd. in rowing 2,200 vd " 10 yd. " 733* vd DassedCr'^^' f"' 733|^-220 = 513J yd. before passed by A Now 5 mi. per hour = ^^ yd. per min. • • Sgoes513Jyd. inaimin. V f "., . " " =-4?M'cl. permin. .. A goes li mi. m 2,200 -=- A,Y = loj min. :_S goes lOJ - 3J = 7 min. at H^ = 1,0263 yd. altogether. £-^(i 10. A 'TiA \ ^' ?' ""^«^t°oJ^ ^ piece of work for A n icT^"^ ''^i ^"'^^ '"^ ^y ^^""self in 4 mo., B in 6, C in !) £ and'n^^ ^^\ -^"^ ^ ^^f"" ^°^^ ^ certain.time after' A, ami . i a certain time after B. A received £13 3.s. UHd Sow n'" 5' i^"^'^ ^ ^V^^ '-^^^^^^^ ^«t^««" them £8 1.. 7 vl." ?e?oTe c\n;^ n^l."^"'^ ^'^r ^. ^^^^^ ' ^^^ 1°"^ did B wo k befoie C and D began ; what did each person receive for his work ; and how long was tlie work in finishing ^ £2'^12r'2S7^ '^'^'''^'^ * ^^^^ ^*' ^-^^-^ " ^^^'^ ^' .: A rec'eived (£2 12.9. 2,\) + (£13 3*. llfi) = £15 16. . . Time of C and D = £26^ ^ (£2 12*. 2,%!) xi^n mo • g ^««e!^ed £26* X (12 - -n) = £1 19.9: aid. :. B received £8 1.9. l^r^d. - £1 19.9. UM. = £6 2s UM .;. Bs time = (£2(>^ ^ £G 2.9. 0^.) x G = ufmo ^^ * .. As time before B began = 2U - 1J| = 1 mo. , /. a s time before C and D began = IfJ _ 3 j ^ i j^^^ A worked the full time, .-. work was completed in 2\\ mo. (o7) A and B agree to carry 292 lb. a distance of 3 mi. for 2*. ^„n? 'f r' "^'^ *M ,^°^d suspended from a 6 ft. pole at a dis- Af^^r "It?- '''•/vf°"' f' '^°^^^^^^' ^"d ^^^'-y it thus 6 furlongs. whpn tbfln "l 1'^ change places and carry it IJ mi. farther. Zl^\.ll •? 'I'P' ^^°"^' *K^ P°^^ *^ -'O i^- fro"^ B's shoulder, in which position It was carried to its destination. Neglecting the Zh. ? l^^ P°^ ^^''^J^ ^^^ "^°"^J^ f^^i^^y between them in i)ro- portion to the work performed. G f ur'^X?- r^* ^:;'- /°' ^¥- = 1^- P«r furlong. At the end of lVvno-1 «7 'Changed places, hence at the end of 12 fur. each had I'd . ^""^ ?' *¥ °'^"' 4 ^"^-^ before they rested the weight was 32 m. from A and 40 in. from B. • the Ad. for this part of the journey should be divided as 40 : 32, i.e. A should get n of nf 87, '" i' ^^'l.B^should get U oiAd. = \^. In the last stage tj S S^'^^J^^'.V^/^ i"- ^'°"^ ^"d ^0 in. from B, .-. the m. should be divided as 30 : 42. .e. A should ^^t ii^ -f ««r = ^rf., and B Hotjid. = Yrf. Thus A gets altogether 6 + ^ + BiiSS ^1 li i l:J I If, ! ; f i ?■ 80 TYPE SOLUTIONS. difference = j'o (68) Two cisterns of equal size are full. The tap of one would empty It mo hr.. the tap of the otlier in 4 hr. Both taps are opened; when will one cistern have twice as water in if as the other then contains ? Solution.— 1st empties i, 2nd i in an hour per hour. Suppose a third cistern which empties A per hour more than he second, the level of the water in the second cistern will then keep half-way between that in the first and third. Therefore when the third is empty, viz. in 3^ hr., the first will have twice as much water in it as the second has in it. (59) At what time after 3 o'clock are the hands first equally distant from the figure III. ? ^ j Solution.— Suppose the hour hand to move backward at the same rate that it really moves forward. When the hands meet they will be equally distant from III. But the hour hand is now as far above III. as it would in fact have been below III. had it simply moved forward as usual. Hence the time required to meet is the required time. \ Now, in 12 min. they arproach each other 13 min. spaces, Ans. 13|i min. past ?- o'clock. (60) Pure gold is wortli $20. 62 J per ounce; 18 lb. of a mix- ture of gold and silver ib %v'.rch $3,473.25, but if the silver were §? 07Q Tr.^ ^^° ? T^® ^'^^®'' '" *^^^ mixture, it would be worth «i,J/».75. Fmd the weight of the silver in the mixture and its value. Ans. 51 oz. silver at .$1.37* per ounce = $70. 12^. lii! liiii I: EXAMINATION PAPERS. FOR CANDIDATES FOR TH1HD-CLA88 CERTIFICATES. 1811. (1) Write in figures and express in words the numbers seven hundred and one units in the 6th period, fourteen in the 5th, one hundred and twenty in the 3rd, fourteen in the 2nd, and nine in the 1st. (2) Show that the corresponding operation in the simple and the compound rules, are based on the same principles. How many years, months, days, hours and minutes from 20 minutes past 4 o'clock p.m., July 15, 1862, to 25 minutes past 11 o'clock, (.3) State the principles on which is based the rule for finding the G. C. M. of two numbers. Apply them to find that of 3,621 and 1,581. ' (4) The driving wheels of a locomotive are 17J ft. in circum- ference, and the trucks 10|, what distance must the train move to bnng wheel and truck into same relative position as at starting ? (5) State the general principles on which the rules of fractions depend ; and find the simplest form of (7| 4- 5J) of { (4J x J) + li } X (3J - T^r). (6) From the sum of 2H ac, § of 3 J ac, ^ roods, and -ft- of ItV per., take 4 ac. 25 per. 12 sq. yd. 25# ^"^^o"^ "^^^ divided a farm among three sons ; to the first he gavi3 80 ac, to the second i of the whole, and to the third " as much as to both the others. How many acres did the faim contain ? I IMAGE EVALUATION TEST TARGET (MT-3) /> % 1.0 1.1 ■ 50 US tii Ui Itt u 123 136 i25 i 1.4 1^ ■ 2.2 ■ 2.0 1.8 I 1.6 150mm /APPLIED J IIVMGE . Inc ^^ 1653 cjsl Main Street .^gag -w Rochester, NY 14609 USA 4^=-^ Phone: 716/482-0300 .2='.^= Fax: 716/288-5989 1993. Applied Image. Inc . All Rights Reserved %^ l\ ^\ ^\ ' V ^<\ ^% '^\ «♦_ '^ «2 fiXAMLNATION' PAPBR8 FOR (8) Find the sum, difference and product of Ml of, and -425 •-. ic ilf tn*"^"'' °' J"^^"^^ according as the unU is £> 5.v.,' or o ac. 2 rd. 10 per., or 6 oz. 10 dwt. 16 gr. (10) Sold 20,900 ft. of lumhpr fnr «'V>i roi • • , . I78.37i Wlmt had it cost jl^r C. ^r ' "*' ^"'"'"^ ^^^^^^^ Krin«i'«r2 °i'.V''« sovereign is worth ^o, and in Sc^or^urten'l: ^^"^^'"^ *=-^^-'«-^« Ontario .nrrency into Nova (12) (a) Received S4,100 from my agent, who had dedurto,! toinviSf'?^"''*^'^**'^^^' '"«l"^inK commission, to my agent 8?on? ""' '" commission of 5% ; what was hisTommTs- J872. (1) The demand of 10 hoUrs' nav for 9 Imnr-a ,..«>i, • lent to a demand of what increasfp'^rcent.'Tn wages ? '" ''""" (2) What number divided by (,^ + .3) ^ (3 - J) x (| + i) will give -,3^ of p of ;i.' of 247 ? ^yk 11? 436 fi^^h^l?*^ ^""-^"0 J °^ following account :-448 lb. butter o-x^ 13 c^^Moregg^^^rGs! ^'l.V""' ? ^^^^^ ^'^^^""^ Uot^' lb. ham I lofc. ^ ' ^''"'^' ''^'* '^ ^^-'^O, and 481H «3,^3Vc%t?JrO T$/ro"t-'°" ^^ follows :-^«o,500, B what does Lchcld?to*rCive?" ^"^'''' " "°^^^ ^^^'^^O; (6) A lumber merchant boucht lOfi Of^n ff ^* 1 u *. » per M and ^tailed it a. U.llVc.-rl', ht gat^^ " ""« «9^?n ^°''' "'n''^ '''^*®'" '^"«' be mixed with 600 ea.1 winA of •i.oO per gallon, in ord«»r tn moL-^ *i, "'y" """ B*^. wine, at gallon? ^ ^''^ mixture worth |2 per (9) If $120 gain «5.84 in 196 ^y find th- ~-s r — - -,j., uiiu tile jjaui in ODU dy. i.i:' CANDIDATES toil TIURD-CLA8S CERTIFICATES. 83 (10) A merchant bought 500 barrels of flour at $6.25 ner worth l'>7i>'"°" '""^^ ^'' ""^^ '^'^ ^*'"' '"°"^^ ^'"K ^^^l^^^"^^ fraction and fully explain the terms Numerator and Denominator. Simplify a of 3 «i~- 5.1. V. Jfl^r''^^ * °/i ^* '',°''^' °^ ''■'^"^^^ ^"'' ^ °^ S Of 830; what were 2 cords worth at the same rate? (.]) Show how to convert pure circulating decimals and mixed circulating decimals to vulgar fractions. Find the sum of -m, -321, -32, .785fi4, 5, and -4326, and the product of 3-45(> by -425. 1 ^Vv^T^.T'Y ^*^L°' ^"•"^'' ^'" ^' required to inclose a Ztlfu^'- ^°!;'^' ^^^ ^-^- ^^''^^' -- ^^- '''^''>' '^"^l«-«h side of he roof 24. \ ft allowing oo-^ f^. f^, .j^e gables, and making no deductions for doors and windows? n'S S"^ ^^^ ?i^ •'''"«-? .''^■^^^•'^•«n the true and the bank discount o^ ?2,o00, payable m 90 dy. at 7°/. ,ol^}/'"'^/°f<;^f Postering the walls of a room 30 J ft. long, 18s ft. Wide 12 ft high, at 18c. per square yard (no allowanS for openings) ; find also the cost of carjjeting such a room with carpet 27 in. wide, and costing $1.80 jter yard. (]l '^^"l^f cent, of an army was slain on the field of battle h^fj- ?f ^'J^f '"^i'V^er were mortally wounded ; the difference bet\\ een the killed and mortally wounded was 1, 100. How manv men went into battle ? ^ (8) Having received a stock dividend of 87, I find I am now tlie owner of 297 shares; how many shares ^d I own aUimy (9) Given, that pure water is composed of oxygon and hydro- gen in the proportion, by weight, of l.". to 2, find the weight of each in a cubic foot of water. ^^^1^°^"^ many railway shares (lOO each) at 40% discount must be sold m order that the proceeds invested in bank stock, which IS 4 / j)elow par, and pays a dividend of 7%, may yield an mcome of $1,(J80? ^° ^ ^ (11) A railw.ay company pays $24.75 per acre for a portion of road 100 mi. long and 94 J ft. wide; find the whole amount paid. 84 EXAMINATION PAPEK8 FOR i li (12) An insurance company took a risk at 2J%, and reinsured i Of the risk at 2% ; the premium received exceeded the premium paid by $42 ; find the amount of the risk. (1) Simplify A + H of A iS74. "i X ,\ + m,r'^ -Tlr ''^-^' (2) Water js composed of two frnsos, oxy^yen and hydrogen, in the proportion of SSJ) to HI ; what wi^l.t is there of each in a cubic yard of wati'r (cubic foot of wattM' woiKhs J. 000 oz.) ? n) The Slim of .«1,41G is to be divide.] ,,monR ir, men, 20 women and JO children, in such u i.winnor that a man rrd a child shall together receive as much as two women, and rA the women shall together receive ?1S0 ; find the amount received by each man, woman and chikl, respectively. (4) A bankrupt who is paying Hl^c. in the dollar, divides among his creditors 8()..'}00 : what do his debts amount to? (5) It costs 96.25 to carpet a room 22 ft. fi in. long, with carijet 27 m. wide ani SI.?', per yard; find the width of the room. (0) If 3 men or 5 boys can do a piece of work in 17 dv in how many days will 5 men and 3 boys do a piece o' ork \hree times as great ? r ic^ /^^ ^Jli? ofe o°^* °^ ^^ ^'^- ' •!»'• ^ »a"« of cloth when 3-75 yd. cost $J*o2o ? (8) A man invests h his fortune in land, J uf it in Bank Stock, fl m provincial debentures, and loses the remainder C$8 000) in speculation ; what was his fortune at Hist ? (9) Bought 9 000 bush, of wheat at $1,12^ per bushel, payable 111 b mo.; I. sold It immediately for $1.06 per bushel cash, and put the money at interest at 10%. At the end of six months I how much? '^ ' ^^'" °'* ^°''° ^^ *^® transaction, and Mnl ^" "i" e^^'»'"5,tion, Arithmetic and Grammar are valued at 200 marks each ; Education, Geography and History at 150 marks each A candidate obtains 70°/ in Arithmetic, 65°/ in Grammar, 60 % m Education, 50 % in History, and 40°/ in Geography; find his average rate ner cent, (;,p. rntA nor rgn* obtained of the aggregate marks). ' ^ CAKDIDATEH FOR THIRD-CLA8« CBRTinCATHK. «5 /x'r,. (1) Simplifv ^ « - 1 m « " 1 a ^ lU - 2r X 10,»3 - 7i } (2) A wine merchant pays $175 for a lio«>l"ena of wine «n.l .0 es.t off into an o,u,,l nu.nbor of .,m.h. ,.in and I alf-ni^ 1.0 to,, how many dozen of c,„h has ho. and at w at musr • sell It im- dozen to gain A of his outlay ? (3) m.'it must be the face of a note so thnt when discounted at a bank for 4 mo. au.l dy. at f) ^ it will ^ive i?o40."'°""*^'* \ i^ndfnf"?! ^- '''Y'"*^ '^•lual .Shams of a ship, .sHl respectively ■\, i, and *. of their shares to A who dies and leaves lis share XthV)"So wr;'^f^"r^ '"^ ""^'-^^^ - theshirbenow wortn «Ji,.JOO, what is the value of ^'s share '•> forSlVrJT '/'r "?^ '''^?'- ^^ ^^^'^^^^ >'o can .sell it at once ioftl 1 •' 1 ''''^^'J'^''""'"«'t for .six months at a cost of 820 paid m advance, ho can realize S1.30 per bushel. He adopu the former course ; money l,ein^^ worth P ' per annum determ ne how much he has Rained or lost by so doin^. "etermme (6) Exjiress the value of -8:] of S.v. + -o^ of 2 g.n-neas + 1 -8 of 5.9 hfi i,ld 90^^''"';^ ^°'!^'^^, f ."'""^^' °f ^^'•'•^l^ «f flo"'- for $1,800; w„« « of ■''"''■" ''"'^ "°^'^ ^ "^ *'»« remainder for 81.568, which was 8224 more than cost. How many barrels .lid he buy ^ 81C?S"ckf '" '"'^'^ "' '■''*' "^''^^ '^ ^''« ^-'-i ^-'- of » .3. > d , ,s o be exchanged for part of a strip of land of tho same Si'ut^lenTX'^^^''''^ '^ "" ''' '^ ^^- *^'"^ ^^- ^-^'th of the^ bn^^il ^ merchant in New York wishes to^emit to London « bill of exchange for £293 l.v. Od. ; what is the cost of this biU when exchange is at 9^^ premium '•» 1876. (I) Find what quantity must be added to fiionj^f i3of u , i^|of68\ of2§ nofmHiitw ( 3J 3Jk to make it equal to (2. of 3| of 3| of 1? x f) HI f'S M EXAMIXATION PAPERS FOR (2) Reduce to its simplest form (•075)» + (026)' (•07o)» - (075) (-025)'+ (-025)- ' '^"'^ *^'^'''^*' 9-17045 by 3-36, giving the result to the end of the first period. (3) Express A of 12.v. Gd. + A of 3 guineas + A of £4 - J, of 2Jrf., us a fraction of £5. i i^ *•« , « rount of 5/, and stdl make a profit of 157. Find the marked pnce of broadcloth that cost him §;J.80 per 5W (5) At an election in a constituency in wliich the number of ratroiTt'c'r' ')Vr' '""1 '/'''' candidates r^hMl^! rat o of ( to 5, and tiio successful candidate was elected bv u majority of 240. Find the number who d.d not vote (fi) A rectangular plot of ground is GO ft. long and 50 ft wide- one pathway 13 made surrounding the plot on the outside, and tv^o others intersectmg at right angles in the middle of the .)lot • find Sirem^Cr '' '\ "^'^ ""' ^°^^ ''''' ^' ^^"^^ ^•-^'' •T^-L"^./"'? ^ engaged in business, the former contributinc w A HOO^'n^'f '<'".% ''^'' ^'r ^'^^«'P*« '°r the first year were $2,800, of which 5% was paid for ins.irance, and Ur/ for other expenses ; of the f^alan.e, B received a certain sum or managing the business, and the remainder was divhled Tn,. o- portion to the capital invested. A's share was «1,250 ; find y^'s allowance as manager. ^ ,* v , y, s 01^^3/0^ '^t'\'''f ^r ^''"^- ^^''" «1'520 amount to 81,733.75 in -i jr.r* iind also m what time $33.40 will double itself at <»S/^ per annum? « i.t^n ai ni^nU a^'?!?' '"""^''^ ^^^ ^''^? ^* '^ ^e^t'^^" P'-ice per head. He sold § of them at a gain of 2oV, vV of them at a gain of 157 HowlV7T?t" "' %^"-'\°^ ^^%' ^'^'"'"S ^» the whole $2/7: How much did ho pay for the 400 sheep ? (10) If 3 horses are worth 7 cows, and 5 cows cost as much as 30 sheep, and 16 sheep cost $165, find the value of 12 ho^^es i877. (1) If 69 German Thaler.s, of which 9 parts in 10 are fine silver, weigh 41 oz., what i. the value of a Thaler in English money when standard silver, of which 37 narfo ^ ^q " «£ ^ worth 6*. lid. per ounce? " " ""®' '^ CANDIDATES VOU TillKD-CLASS Cl.KTIKIi ATliS, $7 (2) A, n and C c«n ilo ji piece of work in 2 dy., A and C in in what time can B do it alone ? (3) A certain kind of brass is niado l.v fusini? toc^ether old brass refined copper and zinc, in the proportion 'of 33 65, and 21 ; how mucli of each must be taken to produce 170 lb of brass after allowing 2fi % for waste? ^'^' (4) March 21 1877: sterling exchange is quoted at 92 for demand bdln; wliat must l.e paid for a demand bill for £18 r.l ' ut ^^"/^i^rJw • ^ *^® 7f ^^ hisnvluir a ship worth $48,G28i Tf fi/°\ ^ "? ''*^"' °^ ^"'" '''« ^^^'''^'^ »"'>• recover the value of the ship, and the amount paid for insurance ? (G) The numerator of a certain fraction is ) as much atrain as . s denommator and the sum of the numerator and denoSt^r IS ooj. a' ind the fraction. width lake^nsi'v? ^f^^' '\ I- f'-' '^"^ ^«"«^'^ li times its width, takes 17by yd. of paper 1 ft. 9 in. wide to cover its walls- ^sti Js 7^.^'/" ' l?' ''" "'"'■ "'^^ ^^'-'"^ 27 in. wide ad costing $1. /o per yard ? G r^ M 'iJ'.i ?ft7^' °^ *'7 "u"""*^''^ '" W4,93S.i)44,494, ami their other. ^""^ ^ numbers is 81,, 044,059; lind the (9) The difference between the interest and tlie discount of a sum of money for 1 yr. and 9 mo., at 8X, is S9.S0 ; find the sum! (10) A rectangular field whoso length is three times its breadth contains G ac. 900 yd. ; find its length and breadtT ' 1878. L^lv:^Z:tM,C""' """'* «°— M""'PK and (2) Prove that 23 -f ? is equal to 2^ x 5. Simplify lL±lk ^ ^^- + ^^ ^ ^H n-i-r h^^ "" 2ri- **» EXAMINATION' l»APi:ilS VOH (3) Divide to decimal places nine million eight hundred and forty thousand and eighteen ten-millionths by one hundred and fifty-nino thousand nine hundred and eighty-two hundred- niillionths. (4) Define ratio and proportion. Show that when four quan- titus are in proportion, the product of the extremes is equal to tlie product of the means. Find a fonrtli jiroportiomil to 7(17 ac. 9 chains 279 yd 4 ft 208 sq. mi. IHl no. 9.') yd. 4 ft.. !?I.:{17. ' ' '' ('>) Find the ratio of thn simple interest to the true di.scount on a sum of money for a >riven time and rate. The interest on a sum of money is 8110, and the discount for the same time and rate is !?SH ; find the sum. (<\) How many bricks. in. long, 4 J in. broad, and 4 in. thick, will ho required for a wall CO ft. long, 17 ft. high, and 4 ft. thick, allowing that the mortar increases the bulk of each brick 6^°/. (T) "What is the Square of a Number? The Square Root ? ini oo'l^'^.T^^® ^^ ^^'^-^ '^ 102,596,641, find the square of 101,2J.» without going through the operation of squaring. Extract the square ro.it of -OIT'llO -f 1 : 004 76. (8) A man rows 3 mi. down stream in 40 min. ; without the aid of the stream it would take liim an hour ; how long would It take him to return against the stream? (9) A grocer bouglit a qufintity of tea of a certain quality, and t as much of an inferior kind, the cost of the latter per pound being only 80% of that of the former ; he mixes them, and sells the mixture at an advance of 10% on the cost im- pound of the finer quality ; find his entire gain ixjr cent. (10) A man invests a certain sum of money in railway stock sdling at 80 and paying 5% dividends, and 50% more than that sum in Bank of Commerce stock selling at 120 and paying 8% ; his income from both investments is 8520. Find the amount invested in each kind of stock. J879. (1) Show that H = ,83 and that jj = 5 4- 9. Simplify |2J X4-75 ^ Jof (4J - 3H) + Of (3M A ^ -9) of £5 16*. 8d. 1-75^ 4Ax2tV H 21 -5 X 13J 4= -25 } CANDIDATES FOR THIRD-CLASS CERTIFICATBS. 89 numbeS"^'*'" '^' '"'" '"^ "P°'"^'"ff" i« division of decimal 10 mS j ^ ""^ *' «°"^»-««ted methods, otherwise plices.^''^''^'* *^" '''"'"■° '''°* °^ -097199881 to six decimal Simplify (^-64 - 2.{ ,a •0000390625) 4- (r^'-16 + ^.0-2). (4) A rectangular courtyard, ISO ft. lou" and IV^ ft w;,i. (o) The amount, at simple iuto.-e.st, of a sum of n.onov at a jr., nnd the prmcipal and the rate i>er cent. " BO^%tjZ"ooZZ\'r^'''''^\''^ ^^''"^' ^^'«»-t>^ respectively the mixnire at « W ' u ''i"'' ^ P^^^-ortion that hy selling ine mixture at «2.80 per gallon he made a profit of 107 • find the proportion m which the wines were mixed '^ ' t„ K ! ;1 1'l"' ^ f°'',";.? P'rtncrship, ^'s capital being to S'» as S to K ; a tlie en.l of (ij mo. ,1 widulraws 20" of his cacital ami — -"vv. ^i i07 per -r ind the amount for which the note was 80 ■XAMINATIUX I'APEKS FOB 1880. (1) Examine the statement " Division is a short method of Subtraction." Apply your nnswer to ilhistrnto the following examples:— ( ,/. (3) What is the Square of a Number ? The Square Root ? Explain why, in extrat-ting the square root of a number. you mark off tlie number into " [)erlod.s of two figures each." Simplify (3,/32 - 2/28) h- (v/32 - y 28). (4) Define Ratio, Propottion, and Mean Proportional. The quantity of saline matter in sea-water is -03(5 of the whole weight, and of this weight -Ofii is magnesia. Find the number of grains of magnesia in a cubic foot of sea-water, sup- posing 32 cub. ft. of it weigh 2,000 lb. (5) Show that "Bank" discount exceeds "True" discount by the simple interest on the True discount. If $G be allowed as true discount on a bill of SI 50, having a certain time to run, what would be the discount if the bill had twice as long to run ? (6) A and D form a partnership, A supplying 25% more capital than B. At the end of the year A withdraws G07 of his capital ^rl.i^,^'''*-^^''''''''' '^^°^- °^ ^''^ ' '-'^ ^^'^ ^"'^ °^ - y^'- there is a gain of $.3,383.50 to be divided. How much does each receive ? (7) A merchant bought 350 yd. of silk and 1,470 yd. of lustre the price per yard of the bistre laing 30% that of the silk ; he sold the sdk at a gain of 35%, and the lustre at a loss of 334°/ and lost on the whole 839.20. Find the cost price of the silk per yard. (8) An agent sold a consignment of floHr for $4,800, and invested the proceeds (less his commission on both transactions) in the purchase of tea, receiving on the latter purchase 4% on the amount invested. His coninii.^sio,. on both transactions being $300, find his rate of commission on the sale of the flour. !l ill CANDIDATES *'0R TlllUl>CLAWi CKBTIPICATES. H ft olfi""^ ^.°!'? ^"^'"""^ P^**^" *^® '^^*^*8« °' 2j, a'37, 3006, u, ***'• r, and 3'ol6. (10) There is a garden-plot in the form of a tra™»zn!H ii.»,«u« two parallel sides are 40 yd. and 60 yj res^^ctivd^ the oJh^r sides bemgresi^ctively yO yd. and 24 yd. Sio rtlmt the r^ pendicular distance between the parallel sides is vV 1 1881. (1) Find the L. C. M. of 545, 26,487, 1.853, 11,421. One kind of brick is 4 J in. long and 2| in. thick- another of w«M T ":'t \^ •"• *^'^^- ^^^^^ •« the si^o of tirei;as? piece :ih?r^i;i;;^'S?Urck ? "'-^ ^^ ^^"^•*^' ^^^^^^ -" »- constructs yo!?dSS;;^r;^:n:n ^rr^rs ^ t ^jr ' ^"' ^^°"' (3) Simplify C'^ °L^'i_+ .V of 7? „ ^ \ . 4 of 6} - 2i ... u ''*'-"^'* ' "'^ " 25— iWi- 26 sec.ttndTo^2 d^.°' ' "'• ' '^* '' "^^ ' * ^^ ^^ ^^- -^^ -- (4) Describe briefly the Metric System of Measures. IT-eoyVnin;'"'"' '°'"^''' -'^ '"^- '■"•' ^"'i a £R8 FOR (9) A mortgage for $1,000 payinj? 77 per annum, payable yearly, has 2 yr. to run ; what should a lonn Hociety give for the mortgage ihnt it may receive H'V on its invcHtment, it being assumed that all money received by the society can be lent out at 0^. 1882. (1) The fore end hind wheels of a carriage are 9 and 12 ft in circumfei-ence respectively. There are two jioints. one in each circumference, at present in contact with the ground. Show that as the carnage moves on these points ran never at the same time be the highest points of each wheel. (2) Reduce (^L-J^l?^ _ 5 tons. 2 of 4i + -jij 859 \ , _ IO85) °' ^ lb. to the fraction of (3) Prove that -48732 is equal to ^?^ 99900' (4) Find the present value of $320, due 2 yr. hence, at 87 ner annum, compound interest. ^^ * (5) Find approximately in how many years a given sum of money will double itself at 15% per annum, compound interest. • /rL^**'^ '"^^^ *" ^'" °^ exchange on Paris can be bought for » 1,500 currency, exchange being at the rate of $1 for 5-25 francs and gold being at a premium of 8J%. Mi?i?*1'^"]^r^®^'' * ^''l"''^'' iad and B had «10 less than C had. thfn i fhen ? ^ *° ^' ^°^ ^^^^^ dollars had C more I A -I ill 96 EXAMINATION PAPERS FOR (2) One-quarter of the time which a man spent on a journey from M to T he travelled by steamboat at an average rate of 14 mi. per hour ; % of tlie time he travelled by railway-train at an average rate of 25 mi. per hour ; and the remaining hour of the time ho rode the remaining 7 mi. of his journey. Find the dis- tance from M to T. (3) At what time between 4 and 5 p.m. is the minute-hand exactly two minute-spaces ahead of the hour hand of a watch marking correct time? (4) A man, assisted part of the time by a boy, completed a job in 15 hr. The man received g of the pay and the boy received i, but the man was paid at double the rate the boy was, in pro- portion to the amount of work each did. How long would the man unassisted have taken to accomplish the job? (5) How much water must be added to a mixture of 15 gal. of vinegar costing 52c. per gallon and 13 gal. costing 40c. per gal- lon, that $5 may be gained by selling the whole at 15c. per quart? (6) A total of 250 marks is to be allowed to a paper of 10 questions. To the first 7 questions the average is given. Divide the remaining mai'ks so as to allow 7 marks to the tenth question and 5 marks to the ninth for every 3 marks allowed to the eighth. (7) A bookseller charges on certain tooks 35c. on the shilling of the published price and gives a discount of 35%. What is the actual rate he charges on the shilling ? (8) A bill for $253.03, dated 7th October, and payable at London in 3 mo, from date, was discounted in Toronto on 20th October, the discount being at the rate of 9% per annum and 45c. being charged for exchange. Find the proceeds of the bill. (9) A cubic foot of water weighs 62*426 lb. and a gallon of water weighs 10 lb. How many gallons will a cylindrical cis- tern of 5 ft. diameter by 4 ft. deep hold ? 1887. (1) Prove the rule for the multiplication of two fractions. Simplify ^^i - -^^) xJ4i - (2 | - If.) } (U + 3^) .=- (IJ - 94 X V'r) ' (2) A, B, C, rent a pasture for $92 ; A puts in 6 horses for 8 wk., JJ 12 oxen for 10 wk., C 50 cows for 12 wk. If 5 cows are reckoned as S oxen, and 4 oxen as 3 horses, what shall each pay? i i Mil CANDIDATES FOR THIRD-CLASS CERTIFICATES. 97 (8) A does a work in 10 dy., B in 9 dy , C in 1^ dv • all hAonn ; 1ST? completion. In what time was tlie work done^ (4) Prove the rule for the division of decimal T>.Vi,l« f« o,-^ decimal places, -OOlSbDd by -OO^Hei ^^'''"'''^'' •"'^^'^^ t° ^ix (5) On March 23rd a bank gives me S845 for a note of $8(10 When is the note due, interest 8% ? ^^°' nf ^!?l/''''^-*^'^''°'^ '"^ ""^^^^'^^'S, oi 184 tons 17 cwt. 3 or. 14 lb °on ^(^r/=oribV°^'^°'°"^ '"'''''''' ^' ^^7 17.. ni per veils soK?.'o?''' V4 ''°?\^* I'?' ^"'^ ^f^^r ^ """^ber of years sola out at 9o, and found that I had made 747 ner annum snnple mterest. How long did I hold the stock p"^ ^ ' (8) There is a mixture of vinegar and water in the proportion aLed'sTth^ro-f ^ parts water ; how much watefmust be water? P^'*' ^^ '^^ "'^^^"^^ ^^^^« '^^^^ be 2 parts (9) I invested $10,000, but sold out at 20°/ discount How J^^ ^^S^e5s:^;nftii^s^ya^d^^-- -^^ 3o»F lo^^o^P^! *!"\P^^^ture of a cube of zinc is raised from t\iJJ^ : f."^^ dmiension is thereby increased -3°/. Find the percentage of increase in the bulk. ^° a i,-S i7f *^' ^"^^^^'^^S at the rate of 10 mi. per hour through qfi^l? T 'if J^.^'^eter nto a rectangular reservoir 187 yd. by 96 yd. In what time wiU the surface be raised 1 in ? (1) Simplify (a) i888. i of ^of Hj-2k of 3§_of Vy /MTxn , 4J-(3J + 4f)+-3J + ^- H sec.^?^ '°'' °^ ^^°* ^y- ^" ^^^ ^^'' S hr- 52 min. (2) yl can do a work in J the time that B requires S can do iVSv^ ° How V"' ''^\f • ^^^^^• ^" -orkingXSef do ?ttn 18 dy. How long would it take each one separately ? (o) A man cot n 90 div^' ««*'> '-^-r "»•• ^r'A r-^ i • i . i him •»l,200 cJsh lust tVrW;;r'Cy^eVrfl"dt"nlJ fJl ill 98 BXAMINATION PAPERS FOR I ■ (4) Bought 78 ac. 3 rd. 15 per. 7 yd. 1 ft. 9 in. of land at $80 per acre ; sold ^ of it at $120 per acre, and the rest at $-005 per square foot. Find gain. (5) A number of men and women earned $93 i)er dav, each man getting $2.25 and each woman $1.50. Had there been 6 more men and 7 more women the whole number of women would have earned the same as the whole number of men. Find the actual number of each. (6) A commission merchant receives 125 barrels of flour from A, 150 barrels from .0, 225 barrels from C; he finds on inspec- tion that ^'s is 10% better than B% and C's is S-^^ % better than ^'s. He sells the whole lot at §7 per barrel, charging 47 com- mission. What sum must he remit to each ? ° (7) A compound of tin and lead weighs 10-43 times as much as an equal bulk of water, while tin weighs 7-44 times, and lead 1 1 -35 times, as much as equal bulks of water. Find the number of pounds of each metal in 7G5 lb. of the compound. (8) A bankrupt had goods worth $7,950, which, if sold at their full value, would give his creditors 81 J % of their claims. But I of them were sold at 17J% below their value, and the remainder at 23|% below their value. How many cents on the dollar did his creditors realize ? (9) A begins business with a capital of $3,200 ; after 3 mo. B is admitted as partner with $2,400 ; after 3 mo. more C is admitted with $1,600. What fraction of the year's gain should each have ? (10) If it cost $11.20 for paper for a room 25 ft. 3 in. long, 19 ft. 9 in. wide, and 12 ft. high, when the paper is | yd. wide,' find cost of the paper per linear yard. (No allowance fry doors and windows. ) (11) What is the cost of polishing a cylindrical marble pillar, 2 ft. 6 in. in diameter and 12 ft. long, at $1.25 per square foot ? (12) A square field, containing 16 ac. 401 sq. yd., has a walk around it outside 12 ft. in width. Fipd the area of the walk in yards. 1889. (1) (a) Simplify io fractional form.) •5 X -006 Aof|x(i)' 16 X -625 ' (Answer CANDIDATES FOR THIRD-CLASS CERTIFICATES. 0d 101 4 £? ^a"^^ ^® ^^erage, correct to four places of decimals, of 12H, 21, 7|, -034, 3-125, 0, 24-58 and 12 A. (2) In what time will $30,441 gain $2,210.10 if, at the Jo"^l/oo®^ ^^'^^ °" $24,944.10 for 1 yr. and 15 dy is $2,596.92? What is the rate per cent, per annum (365 dy. to a (3) A hou.=o that cost $15,500 rents for $155 per month It IS insured for $10 850 at r/, yearly ; the taxes are 15 mills on an assessment of $12, 4oO, and $346.45 is spent each year on repairs Wiiat rate of mterest does the investment pay ? (4) A rectangular field, whose width is | of its length, con- tains h) ac. 123 per. In going from one corner to the opposite how much shorter is it to take the diagonal than to go around the two sides ? (5) A note of $2,450, dated Halifax, June 1, 1886. for 4 mo bearing interest at 6%, is discounted at a bank on Aug. 15th ai o/^. Find the proceeds. (6) A farm cost 3| times as much as a house : by selling tho house at 10/ /as-.5 and the farm at 7|% gain, $3,993.30 is received. Fmd cost of each. /o j* » . (7) Bought 64 yd. of cloth at $5. 70 per yard. If it shrank 57 m length, fand the selling price per yard to gain 20/^. (8)^ and B are partners, A's capital being i of JS's. At the end of 5 mo. A withdraws 4 of his capital, and at the end of 9 ?Ao^T.i . .r' *,°^^V'- ^°'^ ^^""^'^ t^^y ^i^'de a gain of $4,222.33 at the end of the year ? ^ (9) A man sold his 5 per cents at 78 and invested the proceeds in b per cents at 104. His change in income being $385. find how much 5% stock he had. ' ./IS^ ^ *^f^^®^ shipped 400 bush, wheat at $1.40, 800 bush at . S . ''^^? ^"^^- ^^ ^^•-^' t° h's agent, who sold the first at 20/^ gam, the second at 15% gain, and the third at 4^/ loss, ihe agent s commission was 3%, and other charges were $83 44 • nnd the dealer's gain per cent. * ' (11) What is the cost of boards, at $1 for 50 sq. ft., to make a closed box 7 ft. 10 in. lonp:, 3 ft. 8 in. wide, 2 ft. 6 in. high (outside dimensions), the boards being 1 in. thick? (12) Reckoning a pint to be .00 cub. in. ; if 469 gal. are takea out of a cylindrical cistern 7 ft. in diameter, how many inches will the surface of the water be lowered ? {n =, 8|.) 9 i F! 100 EXAMINATION PAPERS FOR K 1890. (1) (a) Show how to find the L. C. M. of two or more numbers. (6) Find the L. C. M. of 24, 105, 180, 96, 336, 84, and of (c) 4410, 7350, 7875. » . » . , (9) (a) Prove the rule for finding the product of two fractions. (6) Simplify HH -^ U)£ + ii-Zi-^l* of -95 of 5.V. + 11. of 3-3 + . -012 iV -d. (3) If the Avoirdupois pound is equal to 7,000 grains Troy, and if 6,144 sovereigns weigh 133 lb. 4 oz. Troy, how many sovereigns will weigh an ounce Avoirdupois? (-1 ) A man engages a sufficient number of men to do a piece of work in 84 dy., if each man does an average day's work. It turns out tliat 3 of tlie men do respectively i, |, and \ less than an average day's work, and 2 others i and iV more; and in order to complete the work in the 84 dy., he procures the help of 1 • additional men for the 84th day. How much less or more than an average day's work on the part of these 17 men is required? (5) How many bricks, 9 in. long, 4 J in. broad and 4 in. thick, will be required to build a wall 45 ft. long, 17 ft. high and 4 ft. thick, supposing the mortar to increase the volume of each brick ■iS^"^ A circular race-course is 22 yd. wide and has an area of 12 ac. Find the diameter of the inner circle. (7) The area of each of the longer walls of a room is 330 sq. ft • the area of each of the other walls is 220 sq. ft. ; the area of the floor is 384 sq. ft. Allowing ^5- of area of walls for doors and windows, how many yards of paper, 18 in. wide, are required to cover the walls ? (8) The pressure of compressed air varies inversely as its vol- ume. If the pressure on the inner surface of a cylinder fitted with a piston be 20 lb. on the square inch, and when the piston IS forced in 2 in., the pressure becomes 30 lb. on the square inch : what is the length of the cylinder ? (9) A man has $20,000 Bank Stock which is at 170 and pays *. .no ^^^/^^ dividend of 5% ; he sells out and invests in Stocks at 108, which pays 3J% half-yearly. Find the change in his half-yearly income. ^ (10) Bought goods at $5.70 on 4 months' credit and sold them immediately at $6. 12 on such a term of credit as made my imme- diate gam 6a°/. Reckoning interest at 4% per annum, how long crecut did I give ? . " " CANDIDATES FOR THIRD-CLASS CERTIFICATES. 101 (11) A merchant in Montreal drew on Hamburg for 10 000 pilders at $-415 ; how much more would he have received if lie had ordered remittance through London to aAIontreal, exchanLro at Hamburg on London being 11 J guilders for £1, and at London LonST ^°' ^'°^^'^S^ ^^^"^' ^i% ^^'' remittance from (12) (a) What is meant by averaging accounts ? (b) Find the equated time for the payment of the follow- ing account : — ^''- John Smith. Cr. _____ June 10 Jidy 15 Aug. 20 Sept. 1 To mdse, I 1SS8 @ 30 days .$9.)0 July 10 "45 " -JOO Aug. 15 " fiO " 250 Sept. 5 "oO •' i.-)o; By Cash $4.-)0 200 jl J89I. (1) (a) Show that -O-ir) = -y^y • (6) Show that -412 = -^W-. (c) Add, without reducing to vulgar fractions, -312, 9-4 and -23. ' (d) Make a drawing that will show the number of square yards in a square rod. (2) Find the premium paid to ensure a house worth $7,500 for 8 of Its value for 3 yr., the rate being 1% of the policy for each year. (3) A tax of $24,750 is levied on a town, the assessed valua- tion bemg l-o mills on the dollar ; what tax does a man pay on an income of $1, 100, of which $400 is exempted ? (4) From the list price of a line of goods a purchaser is allowed a trade discount of 20% ; a further discount of 10% off the trade •'^.'^^.^oj.t^ki^g a quantity, and a still further discount of 5°/ off ins bill for cash. Find his gain per cent, by selling at 107 less than the list price. " ^ /o (5) A man invest $12,000 in 3% stock at 75; he sells out at 80 and invests ^ of the proceeds in 3^% stock at 96 and the remainder- at 5% par. Find the change in his income. (6) A man puts $350 in a Savina's Bank each year, making his first deposit Dec. 31, 1890. How much will there be to his credit Jan. 1, 1895, the Bank adding 4% per annum? ^ liil mi 102 EXAMINATION PAPERS FOR .'li\ (7) A owes B $400 duo in 1 yr., $300 due in 2 yr., $200 due in 3 yr. What sum paid now would cancel the debt, money being worth 5% per annum compound interest? (8) The sides of a trianj-lo are 13, 14 and 15 ft. ; find its area, and the length of the three perpendiculars from the angles on tlie opposite sides. (9) The external dimensions of a rectangular covered box, made of inch stuff, are 7, 8 and 9 ft. ; find the capacity of the box and the quantity of lumber in it, (10) A well 7 ft. in diameter and 28 ft. deep is to have a lining of special bricks, fitting close together without mortar, 7 in. thicli ; find in tons the weight of tlio bricks, supposing 1 cub. in. of brick to weigh § of an ounce, and 1 cwt. = 112 lb. (tt = ^). (11) yl shipped to 2? 1,000 sheep, the buying price of which was $4.50. ii pays a freight ciiargo of 17Jc. per head and the cost of feed and yard is 2|c. eacli per day. His first sale is made at the end of 2 dy. which consists of a lot of 2r)0 head at $5.25. At the end of the third day he sells a second lot of 525 at $6, and at the same time 5 sheep are killed by an accident. The balance aro disposed of at $5 per head at the end of tlie fifth day. B takes 10% of the profits for his commission and remits the balance to A. Make out JB's Account Sales to .1. (12) A has 8 bottles and B 2 bottles of wine. At odd times a common friend, C, joins them and the three share equally. To recoup .4 and B, C hands over $10. How should A and B settle between them. (13) Add vertically and horizontally the following statement : 1 ' ' 1 i ii $1,169.84 909.58 575.72 2,678.28 312.83 1,052.47 339.11 1,732.50 1,237.50 113.56 3,661.00 1,139.67 $3,650.12 866.78 742.49 1,180.66 1,638.24 342.65 687.23 514.02 3,839.25 1,291.98 973.03 670.22, $139.10 914.19 1,654.70 119.25 2,016.72 108.00 215.17 557.60 777.60 112.50 311.20 1,201.641 $97.22 239.49 196.17 8,418.60 1,542.24 349.95 1,020.00 600.00, 136.70 1,850.14 636.99 7,3o7.51| $26.55 297.02 859.69 2,223.42 5,300.20 136.97 1,124.50 475.00 4,656.65 738.75 243.44 252.47i $851.02 ' 312.60' 1,477.421 568.35 116.02: 1,214.03 1,732.25 138.50" 1,097.47,1 1.204.74'i 142.91 i 694.62 ' ii T. ' 1 T. i-.J*C CANDIDATES FOIl TllIKD-CLASH CERTIFICATES. 103 T. 1892. (1) («) Define and k'ivo examples of Q\iantity, Unit, Concrete Number, Abstract Number. {h) When can concrete numbers be added, multiplied ani divided ? (f) Explain the basis of our system of numeration. (d) Show that a square numVjcr never ends in 2, .'), 7 or 8. (2) (a) Find the value of to 8 places of decimals 1 ^ r. 3 1 ^ :5.4 1 1 ' fo^ 1.2" io« 3.1.5 1 3^4.5.6 1.2.3 ■ 10» 172.3.4 10 0" / (ft) Express as the product of powers of prime factors 11. 12. 13. 14. 1.5 38. .m 40 V 93 3:, 10 = (3) A regiment of 1,000 men, 4 abreast, and marching 3 ft. apart, passes over a bridge 3 mi. 44 yd. long in 56 min. 10 sec. If each man takes 9(5 steps per minute, determine the length of each step. (4) A dealer shipped 200 barrels of apples to Liverpool ; the average cost of the apples was $3,75 per barrel ; for what sum must he have the apples insured at ^% premium to guard against all loss, in case of shipwreck, his other expenses being $75? (5) A and B are two railway companies that pay respectively 4J% and 1§% per annum on their $100 shares. When the price of a share in A is 101^ and in A 32|, what is the amount of money which, when invested in one rather than in the other, would give rise to a difference of income of $31.50 ? (6) On January 1, 1890, a person borrowed $2,417.50 at 6|7 simple interest, promising to return it as soon as it amounted to $2,582.50. On what day did the loan expire? (365 dy. = 1 yr.) (7) Distinguish between Simple and Compound Interest, and between Interest and Discount. A teacher's salary of $1,000 is paid in four quarterly pay- ments at the end of each quarter. What sum at the beginning of the year is equivalent to these payments, reckoning compound interest at 2% per quarter ? ■irf 104 EXAMINATION PAPERS FOR has he left if £1 = $4 80 ? "^ ^^'' ^°^ "^"^^» Canadian money fJ6 ft. respectively. V^V -f"^ '^'*® ^'*^®'^ °^ * triangle are 25, 39, a ind Its area. ' ANSWERS AND SKELETON SOLDTIONS. ExFRCiSB I. (Page 7). (1) 161,416. (3) 132,329. (4) 98,127. (5) 4,192. (6) 1,766. (7) 12,481,875. (8) Total = 1,937,271 ; average = 193,727 nearly. (9) 1,511,194. (10) «3,316.17. Exorcise II. (Page 8). (1) 3,996. (2) 1,541. (3) (6) $3.20. (6) Total $9, 994.. 5 49-995045. (4) $5.90. M. (7) $749,902.43. (8) £9,410 U. Od. (9) 24,156. Exercise III. (Page IQ). (1) 350,790. (2) 5,555,657; 3,086,521; 5,334,678,204,562. (3) Remainder = 270. (4)1,485. " " (6) 60,768,396. (7) 2,231. (9) 374; Rem. 446. (5) 52,479Hi. (7) 2,231. (8) 37,217. (10) '27,869,764,561,776,892. Exercise IV. (Page 11). (1) 1,634. (2) 3,415,956. (3) 3,522,178. (6) 121,932,631,112,635,269. (6) 40, 166, 302, 248, 305, 278, 754, 132. (7) 1,630,188,053,103,649,203,285. (9) 4,222,404. (10) 87,860,370. (11) 3,876. (12) 624. Exercise V. (Page 12). (14) $80,040,769,503. i \ I m t '^1 106 ANSWERS AND fiKEI FTOy 80H/TI0NS. Exercise VI. (Paob 18). (1) 9; 9 X 16 X 17. (0)9 n\ 1 AAa ,, ^ ?5)'H877. (7)8. [ij.. [?>Jjt««- ^^f_^ Exercise VII. (Page 14.) (1) 882; 1,314,385,280,208. (0)37 ... . ,.. (8)i (9)ih: (fSii^j,. ^^)^< i^^j ^ 826.19-ji^. Av« (10) 2,t^r.^, u 2.633iJ ^ 5.387V^; difference - 120Hf is AH8WEB8 AjrO SKBLETOH BOLUTIOMt. m 2. Batest. 09. )Z. 912. nin. January, 1374 (Paob 17). (1) Sum + No. = 33J ; .-. No, sum 4- 33). No. = £157 12*. 10 Jd. X nV = £4 14*. U?d. Ans. (2) } oz. = y^iiff bush. No. bush. = 4,810 X V X TThv = 29-,3aV bush. Ans. (8) 102 dy., from 12 o'clock May 24th to 12 o'clock Sept. 3rd - 102 X 1,440 = 14G,8HO min. Subtract 150 min. to get the time to 9.:}0 o'clock. Ans. 14(),730 min. Second part— 146,730 -f (3fi5 x 1,440) = V^V yr. Ans. (*) 1 + 1 + I, If = 23 3. Ans. (6) House + lot = house + i house = J house = 13,600. Ans. House, $3,000 ; lot, $G00. (6) 2,420 sq. yd. - 2tU sq. yd. = 2,417 J J8 sq. yd. Ans. (7) Public School Arithmetic, pages 121, 122, 125. (8) 2 .- J + 1 = 2J. Ans. (9) } ac. yields 41 bush. Ans. 143 J bush. (10) 9J : 8J = 78 : G5 = 6 : 5. The days have been shortened by i, hence their number must be increased by i to give the same amount of work ; 6 x f = 7i dy. Ans. price ore : June, 1874 (Paob 18). , ^) .i'vJ'^^^A?^- - *'^°° = 1,220,225,292. If this number is divided by 6,084, we have divisor = 200,563. Ans. (2) 1 ac. = 4,840 yd. ; 1 rood = 1,210 yd. ; 1 per. = 30i yd • 4 sq. ft. 72 in. = J sq. yd. Thus the field = 14,520 + 2,420 + 423i + i = 17,364 x 9 x 144 sq. in. = 22,503,744 sq. in. Ans 2nd part— 3 ac. 3 roods 25 per. 3 yd. ft. 108 sq. in. Ans. a (3) 797 tons 19 cwt. 2 qr. 14 lb. -^ 5 tons 3 cwt. 2 qr. 16 lb. = 153 and the fraction mi, or nearly 154 shares. (4) f = -285 ; i = -883 ; | = -875, and they are in order of magnitude. (5) (Hf + I) X I = Wr^ = im. Ans. (6) The sums are 13,S8GcZ. and 4,107c;. (36 X 4.107^ -i- ^37 x l.%98fi^ = * Avq (7) I of I. capital « $6,000 ; capital - $40,000. 1 1 ti fti I 108 (8) ANSWERS AND SKELETON SOLUTIONS. Sum X 43 = £121 16*. 8d. That sum x i a 18 4 XtV» 6 8 XiV= 5 8 H It This sum x -jV = price of 43 cwt. " 2 qr. 101b. 101b. lib. whole. 9^ f( £123 16Al0i - (9) 6 - 2 = 3. Ans. (10) i^^V income = $7,200 ; income = $7,500. December, 1874 (Page 19). (1) Product = 10,010,010 + 476 = 10,010,486 which- 21,028 = 476^^?.. Ans. ' ' (2) Time = 44 sec. at 1,000 ft. per sec. Ans. 44,000 ft (3) 1 02. = 480gr. ; 4,320 + 408 + 22 = 4,750 gr. 2nd pari- Ans. 26 ac. 2 rd. 30 per. 8 yd. 8 ft. 115 in (4) Dimensions are 235 in. by 225 in. and 25 in. by 36 in' Number yards required = (235 x 225) 4- (25 x 36) = " 58 yd. 2 ft. 3 in. Ans. j • k^'^ ^ oo; _ l?^ tr'^r ^^'' ^^^' ' """" = *1 ^3*- '^i^- Fraction = ffi (6)Vx0^x^^x|xix-x,|,xA=W = 4H. Ins. A^s 26f ft " *'^* ' ''*' "" ^'■^*^*^ = 46 X 9 sq. ft. (8) 1 gal = 8 X -LJA cub. in. ; cistern = 62 x 32 x V cub in (Tl : V It ^"'- '"^ ^^'^ ^ '' ^ ^) = 8i\li.°"li°: nm o iJi "". ^'^ X V X V = 51 4- 3? = 9. Ans. (10) 2,456 links = 24 '56 x 22 vd =540>q9 vA o,«/.^ i -i, • 22 yd., 640-32 yd. at $8.86 =:$4787~2352 Ans. ^^'" ^ June, 1876 (Page 20). (1) (1 - *) X I - 1. Ans. (2) No. bbls. =600-1 = 800; 4,600-800 = $5. 75 per bbl. Ax. (3) Price = I of $60 x 150 = $16,200. Ans (4) (2*. 9^.) + (8.,. ew + (3.. SUd.) = 15.. OHd. Axs. 5 Rem. = 1 2731b.,. 1,273 - 206^ = 6 bbls. and361b. Ans. H^SrS'in'TsVj mt. " ''' ""' ' ''' ^^"^^^ ^ ^^'^00 min. ; i^o. days = 37,337i -^ (8 x 60) = 77^ dy. Ans ANSWERS AND SKELETON SOLUTIONS. 109 (7) Eemainder = ^ fortune - «8,000. Ans. $60,000. (8) (51,846,734 - 32) ^ 508,301 = 102. Ans. (^) ^?f ^®' '^ shillings = (49-i5f H- 71) X 158i == £ol 35. lU^d. Ans. (10) Price of rem. =$2,896,875 -($56.25 x 31) =$2,895,131 25 Acres m rem. = $2,895,131.25 - $20.05 = 144,395|^^ ac." Add 56i ac. sold ; total = 144,451+^1 ac. Ans. December, 1875 (Page 20). (1) 34.20 + 34.00 + 7.25 + 6.93 + 6.25 +12.16 = $100. 78. Ans. ac, r. per. (2) ^'sland = 97 2 12\ = 383 8 } = 720 ac. 3 rd. 30 per. B's /ov^' " =240 1 10jRem7="60b'ac:Frriper. Ans. (3)H + .\-H + 5J = 5iU. Ans. (4) (a) See Public School Arithmetic, pages 137. 138 (6) Example :—'^\- ^ j ' ' I*t Ti^f + ^ = quotient required .-. fr = quotient x ^ See P. S. Arith., page 29. 112. (( 5 = quotient x fx 11. or 5 X 9 = quotient x 4 x 11 ^ X 9 ^. ^ , „ = quotient = tV x ?. <{ t.e 11 X 4 (5) i remainder cost $1,672 ; remainder cost $2,090 • :. 20 barrels cost $110 ; cost per barrel = $5.50.' Number barrels = 400. Ans. (6) Remainder = U 5 .-. i,V sum = $700 ; sum = $6,000 ; and the shares are-$2,000, $1,500, $1,200, $1,300. Ans. (7) 7*. 6d. = £§ ; one guinea = £H •■• <^ >«.^i) + (§.x i X f X f*) = H + M = £W. required fraction = J x jVV = A- Ans. (8) 7,494 per. cost $370.70 .-. 11,220 per. cost 370. 70 x 11,220 + 7,494 » $555.01iVW. Ans. (9) 1-3749 shillings buy 1-875 lb. 1-875 X 308 .-. 308 ^ 1875 X 3080 13749 (( 1-3749 625 X 3080 4583 lb. 420VK^lb. Ans. (6) Cost = $1.20 X (45 X llj) + (3 x Y) = 156.26. Ans. n -*! Lf'! At u ^H ^^^H !| i 110 ANSWERS AND SKELETON SOLUTIONS. June, 1876 (Page 21). (1) Tho prices are in cents 64 x |, 20 x |, 100 x 4, hence 64 X I X V = «20.80 ^ ' 20 X 4 X V = 5. 58 J \ = $53. 88 J. Ans. 100 X ^ X Y = 27 ,80 ^ ,58J I = ,50 j (2) f + 21 453 18 + fi = 2 shillings, 8 fraction = 25 x 20 x -1 = 4,000 ^ 453 = 8-83002 +. Ans. (3) 1 hhd^ = 54 gal. ; .-. 1,053 gal. are discharged in 1 hr. and 4,953? gal. are discharged in 4,9531 ^ 1,053 hr = 24,768 -h 5,265 = 4 hr. 42 min. 15-i«3 sec. Ans. (4) 16 X 15 X 11 X 35 . 13 7 X 30 X 11 11 X 2 1 X 15 X 1 _ 2 _ X 2 X 63" "~7 362 X 24 3x4 A-i-B = 27 X 11 48 _ 55 119 "24 " X 119 X 9 X 10 X 11 .^, --^39x5=^^«- 82 119 9 X 4577 25tSV,'^ 3 !• 4577 24 X 119' Ans. (A) (B) (5) $1 - -0275 = 9725 [(2,400 X -9725) - 582] 4- 365 = $4.80. Ans. (6) 27 in. = I yd. 2nd cost = 12 X 8 X I X 1.15 = 96 x 1.53i 1st cost = 12 X 8 X 1.40 = 96 X 1.40 .-x . , a , Difference = 96 x •13J = $12.80. Ans. (7) 1 gal. = 8 pt. .-. 162 X 8 pt. = 52 X 32 X 27 cub. In. ••• 1 pt. = -Lfi = 34§ cub. in. (S) A, B, C do i in 1 dy. ; or J in 2 dy. . . B, C do S in the other 7 dy. .-. B, C do Ti\- in 1 dy. ; or f in 6 dy. ; .-. A did Hn 6 dy. ; or | in 2 dy. ; 14 dy. Ans. (9) Lot A cost i of 600 ; lot B cost | of 600 • .. total cost = $1,280 ; loss = $80. Ans. (10) 3,655 -4-43 = 85 = number sold. 680 j- 85 = $8 = gain per head, . . cost per head = $35. iiS^^ ^J^ Z'^r^ = *°^^^ ^°' bought, .-. 40 head remain. 400 -^ 40 = $10 ; $35 + $10 = $4.5, pric« at which r8= malnder must be sold. Ans. ANSWERS AND SKELETON SOLUTIONS. Ill December, 1876 (Page 22). «i^) ^ ^t =.^'^'^:2o^'l- y*^- ' 2 ^^- = 2,420 sq. yd. ; 27 per. =. 816 sq. yd. 6 ft. 108 sq. in. -^ ^ i i^ ?I y^- = 27 yd. ; 7 sq. ft. 23 sq. in. The sum of these is = 17,781 sq. yd. 4 ft. Vil in. = 23,048,771 sq. in. An.S. 2nd part— Ans. 18 tons 17 cwt. 3 qr. 18 lb. 11 oz. (2) i ship = $1,260. Ans. $5,040. (3) (300,303,003 + 2,431) -^ 20,306 = 14,789. Ans. go go (*) gT ' 1^ ' ^- '^^^y ^^^ ^^ o^<^6r of magnitude. (5) Train goes 20 yd. per minute ; miles per hour = (20 X 60 X 60) -M,760 = 40^. (6) Length of step = (5,280 x I) -^ (60 x 1 10) = 2 ft. 9' in. Ans. (7) No. yards = (\s^ x 19 x 144) ^ (15 x 36) = 114 yd. Ans. (8) 83 - 4i + 11§ - 7 = 76 + 6+| = 82ii. Ans. (9) 6-2777777 + 18-6516516 + 12-3454545 = 37-2748839. •34027 - '27777 = -0625. (10) Length of walls = 48 ft. ; height x 48 = 60 x 9. Ans. 11 ft. 3 in. m July, 1877 (Page 23). (1) 5,000,000 ^ 7,019 = 712, and remainder 2,472; .-. to give quotient 713 and no remainder, we must add to the dividend 7,019 - 2,472 = 4,547. Ans. (2) Expression within the brackets = 473 2 3 4 7 37 2 X — X — . X _ X y 12 33 43 49 37 5 ~ 105 ■ 20 _ 2 _ 14 . 2l 105 "15 ^^' (3) Expression = (£14H ^ £6^) x (£10H -^ £m) - 30 ^ 253 480 575 209 "^ IT ^ 259 = T4- ^ ^*^'^^ = **^ ^*- ^^- '^^«- (4) 20 cwt. cost $15 ; , . 1 cwt. cost 75c. gain = 10c. per cwt. ; 2,225 -»■ 10 = 222J cwt. bought. Ans. £m. 48 ).!f 112 , ANSWERS AND SKELETON SOLUTIONS. (5) 3J yd. cost 812J ; 1 yd. cost !? x i - f 4 2 25 23,- yd. cost $4x^^2=37? = $93.75. lb 4 (6) Savings + expenditure = $1,400 Savings + (savings + H{r2o.bO) = 1 400 :. 2 savings = 1,400 - ()25.50 = 774 50 •■•. «^^i"?s = .S387.25; expenditure = 1,012.75 which ^ 365 gives daily expenditure = $2. 77?i. Ans. Ji-?^fV^^^^^ 'P""' ^ °^*^^^ remainder; ^ remainder •■• ^'^ "'^"^y buys lOj yd. ; money buys 37* yd. Ans (8) Area = 5 X 6 = 30 yd. ; proposed area - 6 x 7 = 42 vd ••• cost = -H of $25 = .$35. Ans. « x ' - 4^ yd. (9) 18^ = 18 -117845 18-il7845 X 4 = 72-471386 = sum of all the numbers. 26-207070V 3-592592ri 38-06666fi(i 67-8663299 = sum of three of the numbers 72-4713804 67-8663299 4 -6050505 = 4 -605 = 4th number. (10) $1,039.84 is discharged by $357-445 .-. $612.80 is discharged by ?^445 x 612.80 ^- .^ .^ ^ 1039.84 = «210.65. Ans. December, 1877 (Page 24). (1) 6 yd. 2 ft. = 6§ yd. = 20 ft. ,- 25 fur. = ^^ x 5,280 ft. ••: quotient =^ x 5,280 - 20 == 25 x 33 = 825 times. foi 3 bush'°' ' ""'' = ^'''' ''' ' ^"«^- ' 10- per gaUon = $2.40 Seiiing price - $1.60 + 2.40 for 3 buah. = $4. 118 AKSWmtS AND 8KBLBT0N SOLUTIONS. (3) let Nr. = ^5 . i^t Den. = L^ ; ist fraction - 275 2nd fraction = 3 3rd Nr. = lU ; 3rd Den. = IP ; 3rd fraction = ^^^ ^ ^^ 63 600 ' Whole expression = rZ2 x 3 x ^^^ ^ ^^ = 312U 28 600 ^^' (4) 2J hr. -^ (3J x 168) hr. = Hiv (5) A gets i sum ; 3 left ; . . B's share = ? x _ - $20 3 5 B gets I sum - $20; C's share = "2 x f = _:, sum C gets T^ sum 11 10 * ■ ^^^ = jQ - ^20 ; -iV sum = $20 ; sum = $200. (6) 2 ac. = 320 sq. rods ; 320 ^ 40 = 8 rods, the width of field .-. perimeter = 2 (40 + 8) = 96 rods number trees = 96 rods -^ 12 ft, = 132. (7) 20 ac. at $60 = f cost of farm ; .-. cost = $3,000. (8) $1.20 per bush. = 2c. per lb. ; .-. 25 lb. cost 50c. $12.50 per M. = $1.25 per 100. 30c. per cwt. = $6 per ton. $65.62J + 18.00 + 14.90 + 17.50 + 393.60 = $509,624. ■|* ! !, P M July, 1878 (Page 24). (1) (a) See Public School Arithmetic, pages 93, 104, 96. (6) 1,260 = 90x14 = 10x9x7 x2 = 5x 2x3x3x7x2 .-. the prime factors are 2^ x 3- x 5 x 7. (2) Dividend = divisor x quotient + remainder Divisor + quotient + remainder + 45 = 561 Divisor — ki x remainder ; Quotient = 6 x divisor . . quotient = 36 x remainder, from C and D. .-. 6R + 36R + R + 45 = 561, from B. ;. 43R = 561 - 45 = 516 ; R = 12 .-. divisor = 72 ; quotient = 432 .-. from A, dividend = 72 x 432 + 12 - 31,116. Ans. ! it I i 114 ANSWERS Aim SKELETON SOLtJTIONS. (3) Cost + I cost = f cost « $80 ; .-. 12A tons cost 870 • . gam on loj x 20 cwt. = $10 ' " 25 X 20 cwt. = $20 " 25 cwt. = $1 ; gain on 1 cwt. - 4c Ans 1x1 (4) -001 X 001 •OOOi 100 = -01. Ans. n) 2 1 1 ^ '' 3 ~ 2 ^ 6 "^ amount to be run out. -Ul+1-1_ 1 8 12 16 24 ~ 48 ^ amount that runs out each hour ^hen aU the pipes are at work and the leak also .fi^ * • ^ - ^ = No. hours required to reduce to i full. Ans ^^ la "®'!.'" ^? ^y- ^° *^« ^hole work 10 «• 6 '' t^°^^• f^orkleft.- Sboysin 6 '. f^:;k'^-* = *-orkIeft. 1 boy in 1 dy. does i - 18 = H^- Ans. (7) §(No. _ 12) cost $360; .. No. - 12 cost $540 . lou hut No. '« $600 (S^ t, IZ'ir' ^''' ■• """ = «0« -^ 5 = 120 boxes. ANS. (8) $9 + $70.40 + $64 + $2. 72 = $146. 12. Ans. Dbcbmbeb, 1878 (Page 25). (3) Number cf raUs = (40 x 16*) - 10 x 5 - 830 (4) Width X 20 ^, „, — g-^j- X $1.20 = $57.60. .-. width = 5760 X 3 X 2J _ 2 X 120 ^^ ^'• (5)Num..22 10^12.^^_^^_3 ^2^69 ' ^ 7 140 3 70 Whole expression « ^^ ^ 70 ., T '^ 69 ~ ^- 870; Ans. IS out each ■ull. Ans. ft. tea. Ans. 116, 117. ANSWEBS AND SKBLBTOM 80LUTI0NB. 115 (6) No. gal. = 1» .x_i|,-|jii^8 ^ ,3 ^ 3 _ ^^^^^ (7) 12 men earn $120 in 120 hr. .-. 1 man earns $10 in 120 hr. 15 men earn $150 in 120 hr. = 15 dy. of 8 hr. each. (8) J A's share = | B's ; .-. 7A's = SB's ; A's = f B's. .-. B's share + I- B's share = 210 ac. = V B's ; or B's share = 98 ac. which cost $1,470, .-. B's land cost $15 per acre ; selling price = $35 per acre. July, 1879 (Page 26). (1) See Public School Arithmetic, pages 8, 93, 104, 126. (2) Fraction = 6 ^ (5 - ■^\) = 1^. Ans. (3) -101 - -100999 = 000001 Multiply by -0101 Product 0000000101. Ans. (4) (8 X 4 X 12) cub. ft. weigh (12 x 2,000 x 16) oz. 1,000 oz. .-. 1 cub. ft. weighs 1-2 xJOOO X 16 8 X 4 X 12 (5) 1st fraction = - ; 2nd=^^; 3rd=-L of a ton = JLofacwt. 6 13 200 10 Required fraction = ^x^xi-=ii. Ans. 6 13 10 195 ,(,. 60 X 40 x 30i X I o„ -,- „_, (6) -" .„*--* X 80c. = S4.').37 J. Ans. 16 X 60 (7) J ac. = 80 sq. rods ; 80 -h 10 = 8 rods = length of side Rectangle is 10 rods by 8 rods = IGo ft. by 132 ft. Length of walk = 177 + 177 + 132 + 132 = 618 ft. Number bricks required = 618 x 6 x 1,728 -f 36 = 177,984 bricks. Ans. (8) 40 rods = J mi. ; 12 sec. = jU hr. . . combined rate = J mi. x 300 » 37J mi. per hour ; /, rate of train mST^ -B mBi^ mi. per hour, Ans, ! : ilii I! nISlEi I'i- F 116 ▲MSWBR8 AND SKBLBTON SOLUTIOM*. December, 1879 (Page 26). (1) Remainder = 684 ac. 1 rd. 32 per. 12 sq. yd. 1 share = 45 ac. 2 rd. 20 per. 25 sq. yd. Now as the number of persons is integral we can find it by inspection, for we see that 45 is contained in 68'.' a little over 15 times, so that the number is probably 15 or perhaps 14. Trv 16 shares thus:— ^ f j ac. rd. per. yd 675 7 2 . . . . - 30 rd. 1 3 20 . . = 300 per. ... . 12 12 = 375 yd. 684 1 32 12 which is the precise quantity given. Ans. 15. /ox 411 X 24 X 6 rt^ ^,, ^ ' — ^— 27 X 20 = $44. Ans. (3) L. C. M. of 10 J and lis = 105 .-. fore wheel turns 10 times whUe hind turn 9 times, x. A *-®- °^^ revolution more for every 10 that it makes, and it has done this 440 times .-. distance = lOJ x 10 x 440 = 46,200, as before. (4) 1st Nr. = 11 J _ H = W 2nd Nr. = yUi^ ; 2nd Dr. = ^ ; 2nd fraction L Jl .•.expression = ^M2xAxl^? = ^^0=8,WA Ans 60 11 121 9 11979 '""^' ■^^®- (5) $54.90 + $8.92J + $24.20 + $6.60 + $26.75 = $121.37i. Ans. (6) 4 lb. bread cost 10c. when wheat is at 90c. • . \ lb. bread = Vff bush, of wheat. .-. when wheat is at 135c., 3 lb. bread cost iV of I35c. = lljc. Ans. (7) I marked price = f cost = ^ x 240 ,•. max'ked price » f x t >< 240 ». $3,60. Ans. find it by le over 15 , Try 16 fiber shares nount to bf nes, !S, and it V. Ans. J. Ans. b. bread Ic Ans. ANSWERS AND SKELETON SOLUTIONS. June, 1880 (Page 27). 117 (1) The partial products are shifted to the left because the relative value of each figure of the multiplier depends on its dis- tancMBfrom the decimal point. Thus in the multiplier G00,417 the figure 1 represents one "ten," and we really multiply by 10 units ; and the G is really GOO thousand. Ans. 104,803,155,405,621. (2) See Public School Arithmetic, page 96. G. C. M. = 13. (3) See Public School Arithmetic, page 125. 1st fraction = 2 ; 2nd fraction = U ••• 2V3 -mn = H^im. ans. (4) (90 X 17 X 4 X 1, 728) -^ (9 x4ix2J) = 104,448 bricks. Ans. (6) 12 X 48 X GM. = 3,024 o' 15 X 60 X (>kd. = :68 9 20 X 56 X 4id. = 443 4 14 X 40 X Ib^d. = 723 4 3 J 4,659 5 1,553 X 73 = $1,133.69 5 X H = .IOjV N.B.— l.s. = Vc. 3s. = 73c. Id. = He Ans. $1,133.79-A. (6) 76-391955 ^ -0000020385 = 763919550000 -^ 920385 = 830,000. Ans. (7) Profit per dozen = -1485 - -135 = -0135 Total profit -r -0135 = 79002000 -f 135 = 585,200 doz. sold. 585,200 -^ 8,360 = 70 doz. in each barrel. (8) No. miles = 50 x 3 2 x 24000 x GO ^ ^ 5280 X 70 X 144 ^' ' ^^^' (9) -i% longer part = ^s x ^^ shorter part ; .-. i longer = J shorter ; . . longer = f shorter ; .-. both = « shorter = 120 ft. 45 ft., 75 ft. Ans. (10) A and B do i of work in 1 dy. B C C " A " .-. 2(A,B,C) " -fH orA,B, C,"|H .-. tinae required = |J| of a day. II I 1^ n ni Ans. 118 ANSWERS AND SKELETON SOLUTIONS. December, 1880 (Page 28). (1) See Public School Arithmetic, pages 1, 8. The word dumber is used to mean a collection of units or even a sinele unit. See pages 9, 16. (2) 68,590,142 85,044,059 1 2,774,474 16,453,917 5 192,927 2,581,547 13 652,277 45,935 73,496 1 18,374 27,561 1 000 9,187 1 Ans. 9,187. (3) 17 X 7 X 73 = 8,687 rations required. 48 tons = 96,000 lb. 4 cwt. = 400 lb. 2 qr. = 50 lb. 20 lb. = 201b,; total = 96, 470 lb. 9 oz. = 1,543,529 oz. 1,543,529 ^ 8,687 = 177|t^^ oz. Ans. (4) 1.47J + 1.182 + 4.431 + 1.89g + 4.57J .. $13,561. Ans. (5) 1st Nr. = § + 6§ - IJ = 5*. 1st Dr. = iV X 2A X 2 4 1 2 1 2nd fraction = 1^039 20003 35 Expression = x 6 17 ^ 11 19039 _ 4-5'' 20003 ^^■^**^^^^- Ans. (6) Required weight ^ijl^_l_** X 1,875 = 53,625 lb. Ans. «ij X OJ X If (7) $1 - -0155 = $-9845. («3-375 X 365) + $1230-875 = $2,462.75. And $2,462.75 -^ -9845 = $2501-523 + i July, 1881 (Page 29). (1) (a) See Public School Arithmetic, pages 16, 22, 28 and 93 ib) 2,000,000,018,760,681 -^63,245:553 = 31; 622, 77? Ans! (2) See Public School Arithmetic, page 94 (6) 132,288 = 20 X 3 X 13 X 53 * 107,328 = 20 X 3 X 13 X 43 .-. L. C. M. = 28 X 3 X 13 X 43 X 53 « 107,328 X 63 = 5,688,384. Ans. ANSWERS AND SKELBTOM SOLUTIONS. Hd (8) 72,000 + 640 + l,OrjO = 73,590 min. Ans. (4) 1st fraction = .'\ = 2nd fraction. 117 3rd fraction = 1,761/3^ 4th " = 1,650H^ Difference = llO-.Vj" = llO^Vtf- An'S. (5) Insurance, etc. . . . ^ $12.'). 00 Loss of 8c. per bush, on 2,090 bush. ---■ 167.20 Gain to be realized on the whole ^ 522.50 Extra profit required on 3,135 bush. ^ $M14.70 ; or •25Ii^^ per bushel. .-. selling price must be $1.05 + -25^^ = $1.30gi?. Ans. (G) (a) -9840018 4- -00159982 = 98400180 -=- 159982 = 615-070321 nearly. Ans. (6) "QQ^^^O ^ 285 ^ ' 9999990 407 N.B.-G. C. M. = 24,570. (7) 9 cub. ft. of water produce 10 cub. ft. of ice. .. iV " " " 1 " " A of 445 X 100 X 175 = 7,008,750 cub. ft. of water. Ans. December, 1881 (Page 29). (1) 314-159 ^ -0000008937 - 3141590000000 -^ 8937 ; 8937 = 9 x 3 x 331 Divide by 9 and by 3 and we have left 116355185185-185 ~- .331 = 351526239 ^G^It- (2) 1st fraction == ~ ; 2nd fraction = ^^^ ■ difference = 96 o 3 3rd fraction' = _ ; 96 -f ^ = 252. 21' 21 Ans. (3) 115 at 70d. ; 95 at 3ld. ; 84 at 43rf. ; 72 at 32d. ; 10 at 66rf. = 17,571 pence; Id. = {^c. 17,571 X U = $356.30 A. Ans. (d) 10 volumes of lead weigh as much as 114 volumes of water 10 " platinum " '« 210 " " .-. platinum is __ = times as heavy as lead 114 19 .-. same volume of platinum weighs 56 x _ = 103-^^ lb. ANS. 19 120 AN8WBIU) AND 8KBLETOM SOI-tmoVS. (5) Chain weighs 7G x 2 = 152 cwt. at 15*.v. = 2.866# Ropo - 18x6 = 108 - 23J«. = 2,638': Difference = 182*. ■. £9 2ii. An8. (6) Selling price - 1^ cost price =. «2.60 ; , cost - «1.60 Required price = l.GO x Li = S-^ 72 A vs. 10 ■ (7) Solidity of plate = GG x 36 x J = G6 x 27 cub. in. " sheet = thickness x 54 x 27 cub. in. .-. thickness ^ (GG x 27) -=- (54 x 72) - 4 J linear in. Ans. (8) One brick and mortar == II x ? x *! x 1 = ^L cub ft 16 4 8 ,'{ 512 ' ' Solidity of wall = 60 x 17 x 4 cub ft 40,9G0 bricks. Ans. (9) Gain = 20% ; i.e. he sells 100 lb. for cost of 120 lb. or 10 lb. for the cost of 12 lb. Second case:— He sells 9 lb. for the ccst of 12 lb Second gain = 3 lb. on every 9 lb. = J = :i3^y. Ans July, 1882 (Page 30). (1) The G. C. M. of two or more numbers is their greatest common factor. Usually the name is restricted to integral factors. Every measure of two or more numbers will also measmre the sum or the difference of any multiples of these 4 4 7 10 1 1 68,590,142 2,734,474 451,550 52,043 1,743 199 48 85,054,059 16,463,917 57,073 5,030 1,544 151 7 1 6 1 2 7 3 Now 48 and 7 are prime to each other, .-. the given num- bers have no G. C. M. ''•"Tir'iloSt.'^^lIfi^aillfou^^ai^^ '^^^ subtraction. INiiWERSi AXD .SKELETON SOLUTIOMI. (2) Gain per M. - 14.30 - 10.50 - .80 ISl a :. gain per foot = — - 1000 8 Total gain -= 9,870 x 8 x •987 - 8 X 8 - $63. 16f 10000 8_ 10000 " (3) See Public School Arithmetic, page 121. X = 26A-1H -24Hx63 1512 + 51 \:>r,:] D 24 U-^x^xkxl^- lix63 6 23 6 35 63 + 28 91 .•. Expression 1563 ^ 11 ^ J3 91 2 X 521 182 rA\ 23 ^ 4 92 . ^'^ lo " 100 = 100-0- '''''• 5462-9911235. No. of Ounces -= 7, 501 J x 16 - 120,020. (5) In -V min. goes 6,072 ft. .-. " 1 " 6,072 X jOj ft. or " 1 hour goes (6,072 x A x 60) + 6,280, mUes - 18. (6) 122,496 X 1 X 1 X thickness = 36 x 16jx 14* 12 24 i.e. thickness - 36x33x29x24x12 2x2x9x9x 122496 = 4ft. »3 in. (7) £1 = 24 francs = $1.14 x 4 .-. £250 lO*. = $1.14 X 4 X 250i = $1.14 X 1,002 = 1,140 + 2.28 = $1,142.28. (8) If iV represents 1 mi., and -,V represents 5 mi. = one side of square township. . . Number of acres = 5' x 640 = 16,000. (9) In 1 dy. 8 men + 4 boys do J + -^V = J. .-. time = 3 dy. (10) In every 48 votes, 23 were for A, 25 for B. /25 23 \ 1 .'• ( TB - — ) total votes given = 100 = _ total voti*s o-;ven /. total votes cast = 2,400. Aks. 300,. 122 AK8WERS AND SKELETON SOLUTIONS. December, 1G82 (Page 31). viy If itZ"''- '^^ "*"''" '^'°°^ ^"^^"^^^^ ^-« -^ -P- See H. Smith's Arithmetic, Canadian Edition, page 13 (6) Product = 70,300,000 + 8i>,,610 = 70,382,610 Required factor = 70,382,(310 -^ 9,402 = 7,485-^^. (2) $5.84 + 2.32| + .93 + 2.76| + .74 = S12.60J. (3) L. C. M. = L. C. M. of 22, 56, 42 81 = 11x8x7x81=49,896. A ^i^^ ff :,^^^.= 5 X 9 X 17 X 53 ; of which factors only 9 and 17 will divide 124,083, .'. G. CM. = 153. ^ ExlUseXLYl.""''"^' ^'' ^^^^^° ^'^°°^ Arithmetic, page 121, (6) 1st fraction = -f ; 2nd fraction = 1 ; whole expression = 4. Case IL^ ^°°^ '^°'^' ^^ ^"^^^^ ®°^°°^ Arithmetic, page 157, (6) 1 lb. costs 16s. X -0703125 112 lb. cost 16 X 112 X -0703125 iV of 112 cost 112 X -0703125 = 7*. lOK (6) Ans. 7 ac. 1 rood 6 per. 21 sq. yd. 7 sq. ft. 20 sq. in. (7) 3,750 lb. = 60,000 oz. ; .-. = 60 cub. ft. /. depth x7jx3J= 60; depth =60 ^7^4- 3^ = 2 ft. 6^ in. (8) 22 yd. = 1 mi. ; .-. in 2nd case A goes |^ while B goes 79 g^ mi. ; .-. in 1st case A goes | of |? while B goes !?. Rates 60 : 79. Ans. ^^ (9) A does work in 1 hr. ; B doesl : C 1 in 1 hr A, B and C do ^^ work per hour. Time = 2^^ hr. (10) 20% = I o Cost - ^ cost = 60c. = I cost ; .'. cost = 75c selling price = Z cost = 2 x 75 = 5 90o, ANSWERS AND 8KELE)T0N SOLUTIONS. 1S8 June, 1883 (Page 32). (1) (a) Book work. (6) (Dividend - Remainder) ^ Divisor = Quotient (c) 108,419,716,001 - 18,748,005 = 5,783f^HMirF. ''' ^^^SK^^1?;S^ "^-V^«outnines,»rem.is|. It should be 7. .-. The product is incorrect. (6) Weight = 4 lb. 2 oz. x 500,000 = 2,062,500 lb. ^""^ TtS.' "^ ^°^'^°° = $3,300,000. £ s. d. £ s. d. (3) 375 tons @ 8 15 6 = 3,290 12 6 107J " ©11 14 = 1,257 15 10 '< @ 10 10 = 105 17 «' @ 15 10 = 263 10 48 " @ 18 7 6 = 882 15 «' @11 10= 165 15 Amount of invoice £5,904 12 6 = 24Jc. x 119,292J = «29,027.84i. (4) Distance round the field = (63 -5 + 27 -75^ x 2 .'. Cost = $1.75 x 182-5 = $319-375. (5) (a) = 182-5 rods. 362880 - 60480 + 15120 - 4392 + 1385 314513 302880 (6) = t^JiBVVj^ = !^^ 441 W Vi- 3760" /CN « ^ f Nitre 15 arts in 20 (t)) Gunpowder ■[ Charcoal 3 "20 (Sulphur 2 "20 362880* y or J of powder. iV !!^ or tV weight'I^lToX'."'- = °'^'^^^^' 2° ^-*- X ^ - 133J cwt. is Nitre = I of 133J = 100 cwt. Sulphur - iV of 133 J = 13 J cwt. 124 ▲VSWERS AND SKBLBTON SOLUTIONS. (7) Cost of wine $2.60 x 360 = $ 936.00 carriage = 17.20 duties = 83.50 Total cost = $1,039.70 gain = 50.00 Selling price = $1,089.70 He must sell rem. which is iJ of 360 = 306 gal. for $1,089.70. .•. He sells 1 gal. for $1,089.70 -f 306 = $3.56^. (8) From January 3rd to April 6th = 93 dy. Interest = 257.81 x ^^g x t*t = $5.25HH-. (9) Seconds' pendulum = 39-37079 in. 1 metre = |i yd. = H x 36 in. = 39 -375 (t Difference = -00421 in. (10) (a) Min. hand in going 12 min. gains 11 min. on hour hand .'. as it has to gain 20 min. it must go \j x 20 = 21^ min. .'. they are coincident at 21 A min. after 4 o'clock. (6) To be at right angles there must be 15 min. spaces oetween minute and hour hands. As there are 20 min. spaces between them at 3 o'clock the minute hand must gain 5 min. It gains 5 min. in if x 5 = b^[ min. .*. 5-iSf min. after 4 they are at right angles. December, 1883 (Page 33). (1) Indicating the work first, we have the expression (59,404 + 47,675) (.59,404 - 47,675) -h 7 x 13 x 19, = (107,079 X 11,729) -i- 7 x 13 x 19, = (15,297 X 11,729) ^ 13 x 19, = 179,418,513 -r 13 X 19, 13| 179,418,513 , 19) 13,801,42 4—1, 726,390 —14, .•. Quotient = 726,390, and remainder - 1281. (2) Sold 5 for lie, or 5 doz. for 132c. Bought 5 doz. for 50c. Gain on 6 doz. ^ 82r.. " 20 '» ' = 328c. >< U boxes -136.08^ (1 7 X L.( ANSWERS AND SKELETON' SOLUTIONa. (3) Cost of fence = $1J x 2(40 + 25) = $a X 65 = $195 Cost of land ^^^ x $300 = «l,875, which is less than ten times the cost of the fence. (4) If C gets 1 share A gets 2 shares, B 2 shares - $70, . . 5 shares - $<0 = $1,200 ' 1 share = $1,270 -4- 5 = $254 = C's, ..As share = $508, and B's = $4o8. (5) -t^f-lLtJLff if. ^ ¥ + ¥ _ GO + 225 285 ^ of iii - i of 4 of 2§ TlTf - 2r:~s- == l9 ('») (1-302 + 3-2589 + 40-93) x '00 297 90^09 = 45-4909 X -00297 -^ 90 09 = 6-4987 X -003 -j- 13 = -00149962. (7) Price = ^.^.Zj^ x IGJ 123 = ^r^ =lo 2000 = ^792 X 65 8000 •224 X 05 = $14.56. (8) A must allow B a start of 1 min., i.e. i of a mile -293 J yd (9) Gang do J of work each day ; in 5 dy. # work done • i work finished by 2 men in 5 dy. ' .'. 1st man did | work in 5 dy. Ans. ^. (10) Interest = $275.80 x ,V^ x ih, ^ $4-813. June, 1884 (Paob 33). ^^^ ^if m'v^ n-°°^ Arithmetic, page 29, for the principle. 70 070 An?'''''°'" "^ ' ^ ®^'^^^' ^*^- (2) (a) 243 contains 27 and 81-11 and 77 nm n«„* - j • 96,509 = 7x17x811. acM 7 s. i7 -la , --' • ^- ^- '^- =7 x 17-ii9. AN8. • ^ ^ pff'-"ii*^^ ?^°- ' 23 hr. 56 min. = 1,436 min Bequir^d fraction = tA, - H. - -00278565 . . i An«. I ; I j 126 AKSWBSS AND SKELETON SOLUTIONS. (4) (a) 1st fraction (6) h (5) Gain per bushel = 8Jc. ; ?1^^2nd4^,7HAKS. Number bushels = (3,616 - 112) ^ 34 « ^^^^ 17 1752 _ .J, „„ _x^^ = $8.76. (8) (Us. 6Jd.) 4- 21(i. = -1. = No. square inches in surface. . 554 1 277 , u- . 1. . , . . — - X 5 = -5- = number cubic inches in plato. *f ^ u .Weight of plate = 17-73456 oz. Ans. 277 277000 125 jg^ 1728x9 ^ 2 ^ 9x12x12x12 (7) A, B, C do 4 times the work in 48 hr. A, B "3 " " 48 hr. .-. C does the work in 48 hr. Again : A, B, C do 3 times the work in 36 hr. A, C "2 •« '« 36 hr. .-. B does the work in 36 hr. ; A in 28| hr. (8) 1 in 10 = 10 in 100 ; 3 in 25 = 4 in 100. Suppose 1,000 men at first ; .-, 900 after first battle and 792 after second battle are left ; 3,960 -^ 792 = 5. Ans. 5,000 men. (9) 16% of 1,200 = 16 X 12 = 192 ; net weight = 1,008 each. 1,008 X 8 X li = 1,008 X 11 = $110.88. (10) (a) 8% for 12 mo. = 32% for 48 mo. = V for 16 mo. Interest = $24-0426. (6) 3| - 3i = J yr. Interest for J yr. = $4.80. .-. Interest for 3| yr. =4.80 x 15 = $72. .-. Principal = 312 - 72 =r $240, of which interest for J yr. = $4.80 ; or interest on 60 for 1 yr. = 4.80 ; .-. rate = 8%. December, 1884 (Page 34). (1) Divisor = quotient ; /. dividend = (divisor)'' ^ 80,407,089. (2) To leave no remainder the numbers must be 11,050 and 36,681, and of these the G. C. M. is 221. urface. xl2 le and ) each. est for 3: 7,089. )0 and ANSWERS AND SKELETON SOLUTIONS. 107 (3) S34-375 + 01 .45 ^ 8.9OG + 10.453 + 9-605 + 42 = ,loo.809 (4) (a) ^ + 14 + 1(5 = 0093 i^T R T .1 observe that by general agreement 9A*7i a" ^^ '^''°"*^ ^^^^nd. It would preven? all ambfguTv ?f br Jw * ^ ^* .= ^^J -f 11^)7*. in such cases. **™"^guity if brackets were invariably used ^^^7i ^ 1^ X ~ X 1^ X 17 X 3 _ 104652 10 11 100 1000 16 "^ 2 ~ iT0~00O0O = -00951381. (5) ^^% 90c. = 2,250c. ^.width = (O2.50x|)-^(5x9).3Jyd..liif, («) Boy does Iplece^of work in 4Sdy. Boy " 3 '^ . iVdy^.^-^^'- Man " 7 " u {ly' Bothdol0piecesinl4dy.,or5^plecesin7dy. (0 460-360 = 100; U?- - 5 mt, . been d^^creased by -A- of itself ~ tCf ^^'^ ^^*^« Per gallon has increased by A of itself to nrl ' °'^u^^^ 'Zwan^^ must be ' -'- "-"al' S:^Ex:rcreT/^ 'tj\T^ -"-« P-e ; I'tf of 92 = 0^5 ~„i o "V."" '■:"^^^^>'« tne 6'am .« i««. ^ ^'''''^'' ^^-^ P^g« 16. (o; 1»84 was leap year; time = 423 dy. = $19-163. S275.60 X ^^ X 365 _6_ loo J?i8\?d^L^%Tcef'^^^^^^^^^^^^ Hand must hour, or 11 spaces every iTmin or'l ILS'^'A"" ^■^^''' ^""^'y Ans. 4 : 19,x- min. ; 4T2i'mTn ^ '" '^ "''"• June, 1885 (Page 35). (1) -005904 = five thousand nine hundred and four millionth. (2) 1st fraction = 2 : o,,^^ = * v ^^22 13 "" 194- Result = 2 X 1! X iy =1261 4 3722 3722" (3) 17-654 = 17-65454545 4-835= 4-83683583 6 -408= 6-40888885 28-89&270r7 Ans. l-:ttj 128 ANSWERS AND SKELETON SOLUTIONS. (4) 2.53 + 2.99 + 9.25 + 27.60 + 21. 87J + 29.25 = .S93.39^. Ans. (5) $7.50 + .7i) = $8.25 for 100 lb., .-. Sjc. Ans. (6) Interest = S167 x 3.75 x .07 = $43-8375. (7) $100 yields $6 in 1 vr. .-. 100 yields $100 in ^p yr. = 16| yr. Ans. (8) Give A 2 shares, B 7 shares ; .-. $1,200 = 9 shares, .-. A gets $266.66§ ; B $933.33 J. Ans. (9) First before the minute hand passes the hour hand. Suppose the hour hand has moved 1 space, then the minute hand has moved 12 such spaces from the figure XII. and it is still 1 such space from the figure III. .•. 13 spaces = 15 min, on the clock 12 " = } 3^ of 15 min. =13 min. 50+^ sec. past III. Ans. Second when the hands are together, which takes place at 16 min. 21-^ sec. past III. Ans. (10) $720 - sum + 7jsum = $1,30^ 6isum = 1,305 - 720; .-. $90 Ans. December, 1885 (Page 36). (1) See Public School Arithmetic, pages 22, 93 and 94. (6) 2, 3, 5, 7, 11 are the prime factors. (2) (a) ii Ans. (&) 1,224 = 2' X 9 X 17 ; 1,656 = 2' x 9 x 23 ; .-. L. C. M. = 2' . 9 . 17 . 23 = 28,152. Ans. (3) § of t fortune = $900 ; .-. fortune = $1,890. (4) 12i X 12 = 154 ; 159f - 154 = 5| remainder. (.5) 1 wk. = 10,080 min.; 3*74976 + 10,080 = -000372. (6) $27 J xll| = $323.12J. (7) Public School Arithmetic, pages 32, 34. (8) Interest = $5j x 8 x 3 = $132. AN8. ASeWJCBS AND SKELETON SOLUTIONS. 129 July, 1886 (Page 36). (1) (88,176 X 9,1.2) ^64 = 12, 604,280J. ^*^ No^'-ttlVS'A^' = 827,658,432. (3)(« + 180)2.,H5 = «526.70. Ls W (a) 14 price + 82 = 170 + 8 >, 'id price - (278 - 83) ^li_«,, . (*) '3,640 ^(09 +37^12) :ta- /;;■ (6) Interest on sum = 2 sum !.e. sum X 25 X rate = 2 sum • ^A. "''"^'°"^''^'»--*.i«%AKs. ^ ' t B •SZre^'Vc';^ V *" - ^C-s sh^ n» u -^s share - 60 Cs share = C's share p,f ' ? s ^"d C's = 5C's share - 60 = i OCO C s share = l^OGO -^ 5 = $21o • B's - «'ir? a , (7) The gan, does the work in 20 dy ~ '' ^' " ''''' ^e. iJ work in 19 dy.. Wing ^ for the sixth man Avs ''' tBToe^Jthn^^,--^ ■ that he runs, or 10^^ ^rin 440 ^IZ ''^' "^ '"''^ '' (1) (2) rrr AnS. December, 1886 (Page 37). 52 Ans. Ans. 52 _1_ 10000' (4) $12.50x3 =$37.50. 4ns (5) 80 + (£ ^ 10) ^ 200. Ans (6)6 30 yr. Ans. cows. M ! I II 11 180 ANSWERS AND SKELETON SOLUTIONS. (7) Interest for 3 yr. = TJc. x 3 = 22Jc. Int. for 219 dy. = 7Jc. x ?1? = 4ic. Amt. $1.27. Ans. 36o (8) 50c. X 900 = 450 ; time = 150 mo. = 12J yr. Ans. (9) ^ X 12 X 810 = $9.90. Ans. ' 10 9 (10) A number is divisible by 9 when the sum of its digits is divisible by 9. (11) Cow gives 25 qt. in 2 dy. --= 24 oz. butter .-, in 1 dy. 12 oz. butter, 84 lb. Ans. (12) 1 oz. = 1 lb., .-. 12 of $64 r^ $60. Ans. lb 16 July, 1887 (Page 38). (1) 695 X 595 « 354,025. Ans. (2) $300. Ans. O 7 (3) ^ of _ investment = $100 ; investment » $1,000. N.B.— This problem Is not clearly expressed. The words "worth $100 less than before " probably mean that ne has ifiOQ less In the investment than, etc. (4) ^. Ans. ^ ^ 39 (5) $685. 71i Ans. (6) 12 lb. Ans. (7) 1st farm cost $2,500 ; 2nd farm cost $3,750 ; loss = $250. Ans. (8) On hand 12,000 rations ; 2,000 consumed ; 10,000 left ; 6§ mo. Ans. (9) Cost price = 1 x $24 = $32 ; $2 gain on $32 = 6^%. Ans. December, 1887 (Page 38). '1) 5 doz. oranges + 7 doz. lemons = too apples + 105 apples = 205 apples. ANSWERS AND SKBLBTON SOUTTIONS. 181 (2) In 10 sec. boat goes 100 yd. .•. in H dy. it goes l^^JLi^ x 24 x 60 x 60 « ^^^ lOlTTYeo " ^' ^°° °^^ (3) Interest for 1 yr. = $7.50; 146 dy. = * vr .-. interest = # of $7.50 = $3. . ^ ^^^ ^?''i:i ""^P^^*^ ^°0 was borrowed. 847 " 700 '< (5) J in. sq. represents 640 sq. ac rfiV /^ " 640x4 = 2,560 sq.ac. (6) 1st charges $2. 25 for 6 hr. work. 2nd " $2.33J <' u Wages of 1st fortnight = $27. ^^^ ^^ n cub" ff ^T-^''^^ V^« «^™« ^« 10 ^'^b. ft. of water 1 'nil *. ?•• °^ '*'® ^^'^b 10,000 oz. ^"^ 1 cub. ft. of ice weighs SOdj}^- oz. • (8) Bought 1,000 yd. at 60c. ?, !S? y^' ^°^ *he cost of 520 yd 100 " U gQ ., ii ti aU ti 1,200 yd. = $720. (9) Length of walls = 308 ft Cub. contents = 308 x 8 x 2 = 4,928 cub. ft.' (10) House and lot = house and | house • I, *. ^ i house = $2,100 • • bo"se = $1,200, and lot = $900. (11) Cistern contains 5 x 5 x 5 = 105 cub ft = 125 X 1,728 cub. in. ^-^ c«»- ". .-. No. gal. == (125 X 1,728) ^ 077.374 - 779^^7 gal. July, 1888 (Page 39). (1) See Public School Arithmetic, pages 137, 157, 125. (2) $39.75 X 486 = $19-3185 385 X 13 '5 = 51-975 ^71-2935 which ^ -375 Siv68 190-116 as the. number of pounds received. Ans. -4 m I I ; 41 . I i ;>• ■ i M If i' ■ 'J; III ANSWSB8 AND SKBLBTON SOLUTIONS. (8) 25 X 3i « 80 mi. Ist train was ahead. Distance gained per hour by 2nd train was 12 mi i'T^^t^ ^^ " ^'* ^'■- ; 6§ + 4i = 10 hr. 62 min., when 37 X 6§ = 246§ mi. from starting point. Ans. (4) f% property = J3,093. 75; .'. J% " ='1,031.25 i. e. 100% property = 1,031.25 x 400 = $412,600. Ans. (5) $1.26 - $1.05 = 21c. ; 21c. - lie. = 10c. But gain = lie. more than loss, .-. the 10c. must be evenly divided ; .-. $1.26 - 16c. = $1.10 = real value of cloth. The gain therefore = 30c. : 30 x 800 = $240. Ans. (6) First row is double, .-. each rafter = 22 ft. 6 in. both rafters = 45 ft. = 540 in. Surface of roof ,. ,- ., ,^, , g^j:j^3^^j^^j^^^ = (o40 X 54 X 12) H- (4 X 6) = 14, 680 shingles. (7) Average daily pay = 92c. Boys get 65c. ; men 110c. .-. 2 boys + 3 men give 92c. average daily wage : for 92 - 65 = 27, and 110 - 92 = 18. But 18 : 27 as 2 : 3 hence 8 boys + 12 men will give the average. Ans. 12. (8) Area = 432 per. sides are as 4 : 3 ; or 1 : _ 4 (9) .-. - of 432 = 324 sq. per. in the square on the least side. hence side H^ of $9,000 = ^ of No. 2's capital V324 = 18. Greatest side = 24. i.e. $10,350 = * capital, 5 capital = $12,937.60. December, 1888 (Page 40). (2) $8.00 - .80 = $7.20; $2.80 Ans. (3) 27 men = 81 boys ; $82.60 -5-118 ; boy gets 70c. , man $2. 10. Ans. (4) $387.66 X 246 X - 100 = $15.68. Ans. (6) $20 - $16 . $5 gain on $16 ; 33J% An*. ANSWERS AND KKELEluN SOLUTIONS. (6) (62,832 - 4,800) x 8 -,128 . 3,627 cords (7) 870 X 4J X R :. 274,05 .•H,,74.05x|.870.7^,„„.,./^ (8) Srods X 11 rods = 148i ft ^ iftii /^ .-. length of sidewlk =\l6oJ i' sVx'j ^ |'" "' "" .-. .rea .n yards - 346 x^ J 9 . 3oVi '.,' yd. A»«. 183 July, 1889 (Page 41). (1) 60 lb. wheat = 40 lb. flour .-. No, barrels flour = 343 x 40 ^ 19G == TO barrels. Ans. (2) 5 mo. 12 dy. = 5| mo. = 1 yr 20 ^ ' Interest = $597.50 x^^^J._jn7.11. Ans. 4 ini B 3?24 tn^ ' ™'- '"^^'^ ' °f *^- 7 mi. A will walk (4) Diameter x ^ x 360 = l mi. = 5,280 ft. Diameter = 5,280 x J. ^ 3G0 = 4 ft. 8 in. Ans. (o) 10°/ ^'J /o - 10 J ••• at the end of each year population becomes 10 °^ ""^^^ ^* ^^« ^^ first ; ,. final population = 10,000 X 11 X 11 X ^^-iqqin A 10 10 10 '^^^' ^N«- (6) 1 linear inch = 8 mi. : l sn in ra ""• , .. 1 sq. m. = 64 sq. mi. •■■ '^' "'* ^- -• 4M X «" X «*0 - -60,480 .0. AK.. (7) $7 pays for $35 for 40 mo. .. 2^ pays for $1 fori mo.; .-. rate = 8,750 ^200 « $43.75. Ans. il! 184 ASSWEBfl AND SKKLETON SOLUTIONS. (8) ^mi. -1,820 ft.; .•. planks - 1,320 x 8 x 2 - 21,120 ; Scantling = 1,320 x 4 =. 5,280 . 26,400 ft. oi lumber 26-4 X 17 - «448.80. Axs. (9) $1,171.41. Ans. i\\ December, 1889 (Page 42). (1) ($82.80 - $72) -^ 12c. = 90 ; $72 -^ 90 - 80c. Ans. (2) Time « 567 dy. .-. Interest = $84.25 x^^^x-J^ = $9. 17 nearly. Ans. (3) One pint reaches 3,000 in. =2o0 ft.; 1,147 pints reach, etc., 54 mi. 543 yd. 1 ft. Ans. (4) The question should have stated wliether the ditch lies mside or outside of the orchard. We take it outside :. 24 g rods by 15J rods = 407 ft. V 251 f ft • p ?®"S*ViQ'?/^^ = ^^^ t^^^ + -°^§ +251i + 7J + 7i = l,332ift. Price = 1,332J x 3| x 4 x IJ = S349.71A. Ans. (5) 12i% = - ; 15% = j_ ; .'. I X n cost = $306 ; $320 Ans, (6) 12 ft. 3 in. - 9 in. = 11 J ft. = height of paper. Area of ceUing = 26J x 16§ = 441 § sq. ft. " walls = 86| X llj = 992"g " Doors and windows 1,434J 98i Amount to be papered = 1,336 sq. ft. 1,336 - (|1 X 3) = 169H ft., or 56 yd. 1 ft. 7Hm. Ans. (7) $16 per ton = 8 mills per lb. price of hay = $24.12 Price of grof'eries — $4.80 + 5.85 + 2.75 + 6.15 + 2.37 = $21.92 Balance in cash = $2.20. Ans. ANSWERS AND KKELE-rO.V SOLUTIONS. ]8fl (8) _ mill cost $4,034.55 ; .-. mill cost ^ of «4,064. r)o. At _. more cost Smith pays «j 01 Ofi ^^Y^^k'^m'' •■ '^"^^'^^'^^^ 431 910" (9) 24 i sq. yd. = (24-2 ^ 4840) sq. ac. - -L 200 ,< 95 200 •48 ac 76 sq. rods = (76 -r- 160) " Farm = 184-48 ac. 3-85 + 9 147 + 76 9 + 23 •608 + 34 = 147 -505 ac. Uncleared part = 184-48 - 147-505 = 36-975 ac. .-. ^ uncleared = 3697 5 -f- 184-48 = 20-0428 +. Ans. (10) 12,648.78. Ans. M JoLV, 1890 (Paob 43). (1) $2,213.47. (2) Father : age = 5 times boy's apre = 3 (boy's age + 6) 2 times boy's age = 18. Ans. 9 yr. old. (3) (200 X 20 X 33) ^ 27 = 4,888S cub. yd. Ans. (4) 12 men = 72 boys ; 16 women = 48 l,oys ; wiiole = 150 boys .-. 1 boy gets $2.20; each woman SJ.60; each man 913.20. Ans. (5) Total tax = 7 mills x 9,600 = $67.20. (6) Time = 071 dy., 1892 being leap year Interest = 3| ^ ^1.3^ ^ 671 ^ ^^.^^^^^ ^^^ ^^ ^^ Amount = $16.50 + 1.98 = $18.48. Ans. C) 15 drains, 80 rods long, at ;)3c. per rod 30 ac, 2 bush, per acre, at GGc. per bushel (16 X 80 X 33) 4- (30 x 2 x 66) = 10 yr. Ans. •:«a 1S6 ANSWERS AND SKELETON SOLUTIONS. III (8) 18 men do the work in 450 hr -? ;; " (450x'6)hr. ^° " ('*50-5)x6 = 60dy.of9hr. Ans. Otherwise :— _ less men require ^ more time, or 540 br. = 60 dy. of 9 h^. each. (9) Distance = 5 mi. ; difference of rates = 1 mi. per hour .. time = 6 hr. ; A goes 20 mi.. Ans. December, 1890 (Paob 45). (1) $2,495.08. (2) At $60 we get | ac. for $50 = final remainder = g of 3rd rem., • 3rd rem. = 5 ac. = ^ 2nd remainder o .-. 2nd remainder = 25 ac. = ^ of original ; 100 ac. Ans. (3) l|c. per pound on 600 lb. = 675c. = profit 5,210c. = cost price 600 - 65 = 535 lb. sold for 5,885c. lie. Ans. (4) When A starts B is 37 J mi. distant ; they approach at 6 ^\T.lT ^".- "'T '"^ ^i^'- ^ '^^'' 15 hr.'^to'^^each K or 8} hr. after meetmg A, i.e. he goes 8f x 2J = 21 J mi. has 15^l"^^br";n JL^'fr ^^l^- i° ^^^^^ Belleville; hence B nas 10 - 12? hr. to walk, or 2f x 2J mi. = 5,^ mi. (5) Time = 365 + 318 = 683 dy. Interest = $162.50 x ||| x ^1^ = $16-7241, say $16.73 Amount = $162.50 + 16.73 = $179.23. Ans. (6) L. C. M. of |, 4, I yd. is 15 yd. .*. cost - 20 X 15 X 1 X $1. 10 = $440. Ans. AMSWBRS AND SKBLlDTOIl SOLUTIONS. ^^^ }?L'^- ** C^^^'^ + tW.TS) . 12,943.00 (180 + 96) i. rods at $1.35 - 745.20 i«7 $3,688.20 = 1,177.20 Deduct $1,160 + $17.20 Net cost = $2,511.00 Cost per acre = $2,511 -j- 108 = $23.25. Ans. (8) $120 X I X rate per $ = $11. Rate per cent. = j x 5 x J_ x 100 = 5i%. Ans. (9) 20% = _, ... cost = I selling price; ^ cost = 1 seUing. Farmer's gain = 5 bush, at 90c. = $4.50 25% = J, .*. merchant's gain = 1 of selling price. 1 - = - of $25 = $5 ; merchant's advantage = 50c. Ans. ! P July, 1891 (Page 46). (1) $2,543.22. (2) Time = 438 dy. Interest = 360 x 1!§ x ii = ^240 ^3 .q,^^^ .^ .^ 365 200 loo *" . $^9 J. 40 Ans. (3) He pays $20 for 144, He gets $20 for 100 ; gain = 44%. /v«\ 3 . 1 1 7 ^^ 8 *°' ■*■ 4 **'• + 4 ^^'^ = ^ ac. Ans. (5) 065 +.105 +-27 =.44; Seieft; ^of •66=•14 = 280 8heep,• .•. -01 = 20 sheep ; whole flock = 2.000 sheep. Ans. (6) -_ of $9,500 = $2,500 = A's share ; $7,000 left. If B ^ts 3 shares, C gets 4 shares - 7 shares .-. 1 share = $1,000 ; B gets $3,000, C $4,000. An*. 186 m """mu AKD SMUtTOH SOIOTIOOT. (7) ,1,3.75 +.69.175 lb. = weight of A 4. 2olb. = " A - B (8) 16 X 10 X 2 X 20c. = $64.00 16x10x100. «_^6^o = 380. AN8. (9) 112.60 + 118.00 + $11.00^. ,8.75 + $4.90. 155.25 Account s= 54.45 Balance due fanner = .gOc. July, 1892 (Page 47). *'' -m-!slt:'' * '■"' + '•«» + '-SBl + 1.87» +4.06+ .5» (2) W a X 3J X 3 for «3 = no ft. t„ ,3 ^.•^128 ,t.c«t 800^^,3^^^^^^ ^, W^X400 = «3.43J per cord. Ans. (3) Dimensions: 12 vd ii xtA j /» ^ Outside area = 46^'x'6'Lfc' yd"^'* Floors « 11 X 10 X 2 =220 (4) Time - 146 dy. ''^ '''' '^'' '* '°" ' *''•'^' Interest = $80 x li^ x ^^ - ti «« 365 '^ 4"00 - *^'^®- Amount = 80 + 1.68 = $81.68. Ans. (5)L.C.M. of 1 1. 3 o - - -. ,^^ •420 + $15 = $435. Ans. (6) 1 year's wages = 10 sheep + $160 i^^''i''^^.,Ll.':'^rr^^«p'+V7fo "^ wsneep, .. 1 sheep = 18 a«« ANSWDHS AND SKBLBTOU SOLtmONS. (7) 69.1661 + 8-2 + 5-445 + -065 + 2008.0J - 102.96 6-05 X 17 = 102'85 Remainder ■■"' 139 'i 11. Akbl /pv 23 Amount »«21. 16 x^«|368. Ans. (9) (a) J|5p 000 assessment pays $1,800 taxes fl,oOO " a 5J8 w $4,500 '« u J54 ,, (6) $150,000 <. u $300 per annum •^ " " *^ " =2mms. Ak8. 500 )/;7«Lio School Lbavino, 1892 (Pagb 48). (1) (a) See Public School Arithmetic, page 93 (6) 13,230 = 2x33x5x7* 22,050 = 2 X 32 X 5» X 7» 23,625 = 3' X 53 X 7. (c) G.C M. =3'x5x7«315. li. C. M. » 2 X 3' X 5' X 7» » 330,750. (2) 1st income - 8,940 x -^- =, |402.30 2nd income - 8,940 x ^^|i x .!_ = $369. 16^ Annual loss =» $33. 13-iV ^^^ ^TTrom M^ on July 3rd JO 400 + $<50 interest » $2,460.00 Int. from May 22nd to July 6th at 7% (45 dy.) = 20.66 (4) - cost of first = I cost of second Net proceeds » $2,439.34 .-. 5 cost of first = 3 cost of second Jjet 15a; = selling price of each /. A cost 12a; and B cost 20a; Cost of both = 32a; ; both sold for 30aj Loss = 2a; = $9.60 • lO-M •;i'7 en 1 » « ' ' II"' — '»'"<• "'J = cose 01 A 20a; -$96.00- .« b. Ans. I !/ 140 AM8WBRS AND 8KBLBT0N SOttmOMS. (5) H% conunission on $27,500 «= $687.60 Freight and storage, = 250.00 $937.50 $27,500 - $937.50 = $26,562.50 to be spent in pork, $6.25 + 2J% = $6.25 + -15625 = $6-40625 cost of 1 cwt. $26, 562. 60 ^ $6 -40625 = 4, 146H cwt. pork purchased. Ans. 24% =» Tjr ; .'. -— of the cost is the total cost of pork 40 40 .'. commission = _ of money spent 41 2nd commission = i. of $26,562.50 = $647.87 41 1st commission = 687.50 Whole commission = $1,335.37 The account sales stands thus :— Cr. by wheat $27,500 Dr. to 4,146fH cwt. pork at $6.25 = $25,914.63 '* storage and freight = 250.00 " commission on sale and purchase = 1,335.37 $27,600.00 (6) 5 mi. of fence will require : — 3,302 posts at 12Jc. = $412.75 35,200 ft. lumber at $14 = 492.80 30 mi. wire at $12.80 = 384.00 Total cost = $1,289,55 Ans. (7) (a) 1 gaL = 160 oz. ; .*. 1 gal. occupies 160 -^ 1,000 =— cub. ft. 100 No. gallons in cisetrn=4 x 4 x ?? x 6 x 1^ = 1.8855 truJ. 7 16 (6) The volume of the sphere = Z x — x 8 3 7 00 4 Q9 /. 4 X 4 X _ X height = J x " x 8 j .-. height = IJ ft. • o 1 (8) $64,277.50. ANSWERS AND SKELETON SOLUTIONS. 141 lift. Algoma and Parry Sound (Page 49). (2) (a) 11 - ^ + 18n = 18t% (6) 7A + 7| + 6«V + 7H - 27H + 1? 44 Sum of remaining fractions = 52 4V + — 44 Difference «= - 24-i*^. (3) (10 yd. at ^c.) + (1 yd. at 8c.) = !?lc. 28 ^08 11 yd. at _c. = c.; gain = 28c. on 1 1 yd. Ans. 44 yd. (4) In 300 dy., A and B do 15 pieces of work, B and C 12. A and C 10 ; .-. C does 7 pieces in 600 dy., and B 17 pieces, and A and B 30. Hence A and B do 1^ in 5 dy., C li in 20 dy., and B will do bO 60 the |1 inl8Ady. (5) (? No. + 14)* + 8 == No.; No. = $48. /5 (6) Cost price = 58Jc. ; at the given prices there will be a gain of 28Jc. and 18Jc. on the first two ; and a loss of 218c. and 25c. on the other two ; these are equal. Ans. 20 lb, of each kind. (7) 1st income = .1_ sum invested ; 2nd = — sum invested in 44 44 Ist, .-. _ sum = 1,400. Ans. $4,400, $17,600. (8) True discount = — ; bank discount = J- 11 10 1st + 2nd = 400 ; i^ 1st + J: 2nd = 38 ; $180 Ans. (9) Down rate = 12, up rate = 4, i.e. 3 : 1 is the ratio of the rates j . . 1 : 3 is the ratio of the times ; 2 hr. going down, 6 hr. going up. Ans. 24 mi. : M if; m I! 142 ANSWEUS AND SKELETON SOLUTIONS. (10) 1 gal. « 10 lb. = 160 oz. = -"^ cub ft 100 ..TlJJgal. = -g-X-^^.=__ cub.ft. Cylinder - ^ x 8^ x 30 x _l_ = ^^ cub. ft. Paper A (Page 50). (1) - horse « $50, etc. Ans. $250. (2) If the lots had been equal in number the average price would have been $o ; as it was the copt was $20 more than this average, therefore the selling price wab $30 + 20 = 50 over this average, i.e.%\ on the average gave $50 ; number sheep = 100. (3) Add the two lots and 11 wheat + 1 1 oats = $16 94 .'.11 bush, oats = $3.74, or 1 bush. = 34c. Subtract the prices, difference = 86c. , which = 1 bush, wheat - 1 bush, oats ; .*. first lot contains 6 of wheat and 5 of oats. (4) Ans. g ^y. 00 (5) _ A's money gives $800 interest in 6 yr. at b"/ ; A's = $3,555^, B's = $5,925|f. (6) Shares have 2, 4, and 5^ yr. to run : Interest on $1 for these periods = J£ At ^_ • 100' 100' 100' Discounts = ^2 24 33 . 112' 124 133' Present worths = J|« ||0 1|, and these are the pro- portions of the cash values of the respective shares • The shares are $1,092.76, $987.01, and 1920.23. ANSWERS AND SKELETON SOLUTIONS. 143 (7) The 6% loan + the 6% loan - $98 ; also 1< -. ( (< <( ) " $81. X through by - and 3 ) = $108. ) - $10. Ans. $50, $48. (8) 3"!^% = =rr> •'• SI fiost is intended to produce _ sales. 00 55 .-. for every - yd. bought he got JZ x - = ill cost of 1 yd. o 5o 5 275 and for every | yd. but. he got ?(2 - 20.")= Ill cost 1 yd. -fc. 5 5\iD / 275 5 .-. for every 1 yd. boughv he got — cost of 1 yd. --c. 275 "^ 5 Actual gain on 1 yd. = J^ cost of 1 yd. - Ic. = 11 of proposed gain 21o 5 15 2 ., 4 11 9 .-. — cost per yard - _c. = __ of -± cost per yard. 00 5 lo 5o 4.2 4 • • 15 °* 55 °°^* = -°- J <^°st = 82Jo. per yard. (9) A, B and C do respectively i, i^, ^ per day; •. let lo oU do 4,950 shares = whole work ; average for 25 dy. = 198 shares per day. A does 77 shares above, B 33 below, and C 48 below the ' average each day. Now A must make up for the deficiency of B and C ; hence as in alligation we must find some multiple of 77 = the sum of some multiples of 33 and 48. We may take A 63, B 35, C 77 days respectively, as one solution out of many possible ones; so that if the work lasted 175 dy., A would do (63 X 77) shares over the average, and B and C together would do (35 X 33) + (77 x 48) under the average. Hence when the work lasts only 25 dy., A must work I of 63, B 1 of 35. C 1 of 7 '7 7 77 dy, HfinP* nna cof ,-it anBTrraf,^ Jr. Q R •*■* Jl^ flTU - J. . «?' ^ - -"5 — »-• i»..t3VTero JO If, o, ±1 uy. xu« wuruing of the question might have been made more precise. V.'i. ■ M ■''iM mm 1 ILJ j m 144 ANSWERS AND SKELETON SOLUTIONS. aj(l + 1.05 + 1.05» + etc. + 1.05" + j 05»^ - i ^nn i n- . o or a. + 12-57666 = 1,500 x 1628835:'^^ ^469+' etc l^"^^'o~;^^^®'"i°'"[''''J^ *^® w°^^' carry out 1.05» 1 05' Paper B (Page 61). (2) $1,400. (3) x/(40» + 30») = 50 mi. Euc. I., 47. (4) Area of base = 20» x -7854 • Content == 314-16 x 9 = 2827-44 cub. ft. (5) Bank discount on $1 = -09 x -^ = $01575; ■•"' $i^00". '^JfiSor **^ T^ °^ *1 = «-98925 ; .. *l,JOO -J- -98925 = $1,213.04 + . {«) Second cost = | first cost ; ., seUing price wiU be 5 « pt a gain per cent, on second cost as it is on firs! cost ; 6 " 6 "" 6 ~ ^^^' •"• 6 ^*^" P®^ *'®"*- = 150%. Verification ;— 100 x 1^!? = 190 v ^^5 100 ^" "^ 100- (7) H $100 .C's, then $150 = B's, and $005 _ *♦« Hence A has 125% more than C ; ^"^ - ^ «• C has ^ of A's, or | less than A, i.e. 55^/, less. (8) First income = 4,875 x J. x 3 = 150 2nd income «= 4,875 x _L x ^^ x 4 - isn t 195 no ^°"' ^crease = $30. (9) Ex^n8^ = 65% net earnings = 45% of $500, 000 = $226. 000 ANSWERS AND SKBLBTOM SOLtTTIONS. 145 (10) The final value at the end of 8 yr. of $10 invested at the end of 6 mo. and every following 6 mo. at 10% compound interest = 10 [(1-1)^ X (1.05) + (M)^ + (1-1)» X (1.05) + (l-l)' + etc. . . . . + 1-1 + 1.05 + 1] {N.B.— Sum of first two terms = 1-1^ x 2.05, of second two = 1-1« X 2.05, etc.), hence sum = 20.50 [1-1^ + 1'1« + 1-1 ■» + I'l* + 1-1' + 1-1» + 1 -1 8 — 1 1-1 + 11 = 20.50 ii t -• 11-1 jN.B.— £c^+x« + a;'^ +£C* +ac' + x^ + aj+ l = (x'' -l)-r(a;-l)} = 205(1-1' - 1). This is the amount of the debt Jan. 1, 1900. Its P. worth = 205 (l-l" - l)-r(M)'' =205(1 - J-J = 205 - ^ = 205 - 20500000000 ^ g^. _ 9-^3 ^ ^,09.37, cash value. ' 214d5oool {N.B.— 11" = (11* X ivy = (12P)* = 14,641' = 214,358,881. } i ' a Paper C (Page 52). (2) 440d. + Hid. + 350d. = £3 7s. O^d. (3) The cost is the same. Paper at 9c. , 27 in. wide, costs the same per square yard as paper at 24c. , 24 in. wide. (4) L. C. M. = product -r G. C. M. .-. 634,938,944,494 x 9,187 + 85,044,059 = 68,590,142. (6) At first chicory = ? = 270 lb. = -^ of 2nd mixture. .-. 2nd mixture = H x 270 = 655f lb. , coffee added = 25^ lb. (6) Interest - 1^ of 1 » -^, .-. discount = ^ = 7i^%. ^ ' 15 10 25 27 ^^^° (7) (? capital -4- 90) x 3J + (f capital + 95) x 4 = |1,340 3 capital (- M capital (1 + 1?) = 1,840 x 25 = ?i? capital VI8 19^ ' 342 .-. capital - 1340x 25j<^ ^ $32,828.08. o49 IM AmwBM un, smwoM solotmss. rai .«<> - 87 . «™Ur .„d have their sides pr^oSar "~ «'*'"^'« and Paper d (Page 53). (2) Expression = 8q.rt. of 8640x753 .., ^, ,-_^ 72 X square root of 3 -209718 + = 72 ^ .no^. . . ^^^ = 3095 X 10-618 Il%\''^ll^^^ f ''' - 26,545 (4) g /«*« in price will require 1 more in .n k , H « ^ wore m number of apples .*. 120 apples = I number for «;, * '''^^^^^'^""^ber^ 480 apples. quUon"'" ■" '^^'"^^ + 2 boys + 1 gM get $100- and (2 boys + 1 eiri) . ro u ' ^ P®"* ^e. 6 b"oys\^^'g!;7^etVl0i;''^^ if ^o^« -^ 1 ^irl «et ,100 are. AJiaWBKS AND 8KSLST0M SOLUTIOMS. (6) 1 metre - 39| + 36 - !5 yd. ; l i anc - £l • 32 86' 147 42 centimes £i?_ 2500 No. yards bought =. £1,000 ^ fl - 20,000 ^ 3 ; 3d. . No. metres sold = ^1^^ x |. ^^^.h^if ^, «^ ^^^j^^j, ^^ g whole at 7 francs per metre. Hence the gain on whole 80 ^3 35 2500// -e^^%1%i)('-4)-(--T%^) 20000 32 7 94 / i v -— - X _ X _L X ^1 _ 1000 f 1 + M 3 3o 25 100 ^ i2>' 8 X 32 X 94 13000 7814 = £520 18«. Sd. 15 12 15 (7) Int. - dis. = $38.84 = int. on dis. = interest on $310.72 Rate = 3,884 -f 31,072 = 1 = V2^y Sum = «349.58 x 8 = $2,796.64 ; rate per annum = 6^%. (8) Price of wheat = $6,000; .•. 6,000- 500 = 5,500 cost of silk *^ "25' ^"'^°°"^- =^220; 1st com. =$280 on $6,000; rate = 4§%. (9),rHxl8 = 3xl,728;H=(.3xl,728)-C!2xi8Ui44xI ^7/11 •'• »• = 12 VA in. = sl-?-x ft. = diameter = 2 Vi^r = 1-59 ft. li/^l^V^i^'i? ^^^ ^^® ^^® segments of hyp., then 5v-hyp. Let a and 6 be the sides of triangle ; then a» + 6» = 25v', Euc 1. 4 ^ iiut by the same theorem a* = 16 w* + 10^, 6' = w^ + 10» Hence a= + 6» = 17y^ + 200 ; ,. X ^3) gain per cent. = ^^'9^ x '^^ - ^^000 „ _ , 51 X 53 80" ~ "2703 " ^ nearly. (7) If 75 shares represent the whole property, 33, 24 and 18 shares represent the farms. Each should geV25 shares ' 1 pays B 1 share, and C 7 shares ; i.e. i. and — of $2,000 75 75 ' or $26.66§, $186.66§. (8) Perpendicular = area x 2 -MO = V\r>/399 = ll-gSS ft. (9) Side* X 2 - 4« ; side' =. 8 gq. eh. = area » 128 8q. rods. AMSWKRS AMD 6RBLBT0M SOLUTIONS. 153 (10) Solidity of ball = ^ cub. ft. = 1 x —- soUdity of cube 4o0 3 113 whose side = radius of ball ; .-. soUdity of cube = 11 x ? x H! x 1,728 cub. in. 4o0 4 Boo 4 X 17 X 3 X 113 X 12' 12' x 17 x 113 900 X 10 X 71 5' X 71 X 6 J21 426 5 (radius of ball) ' Diameter of ball = __ cube rt. of ~— = — ^4-509389 = 7 -932 in. o A9.R R '■' ]* Paper K (Page 57). 50 53 51 (1) Q. - (28 ^ ^) - (9H - 5|) = HJ. (2) Reduce fractions to common numerator, 144. The greatest fraction will then have the least denominator and vice versd The fractions are already in the order of magnitude, the first being greatest. (3) Area of 1st = _ area of 2nd 9 104,976 sq. in. ; side of 1st = 9 yd. ; area of 3rd = 16 area of first : side of 3rd = 4 X 9 = 36 yd. (4) Mother's age = |^^ of 35 = 29 A yr., eldest child's age = 3A yr., and youngest child's age = 2 A yr. Difference between mother's age and eldest child's age at starting = 26-^ yr. ; at end of voyage difference is represented by 728 - 94 = 634 units • or difference is _ mother's age. The difference between their ages is constant, therefore _ mother's age = 26-^ yr. ; mother's age at end of voyage = 30 yr. 4 mo. Her age at starting 29 yr. 8 mo. ; time of voyage = 8 mo. (5) Interest for 1 yr. at 4% is $5-815, which x 2 - $11.63, and the smallest multiplier that will make this an integer is 100. Ans. 200 yr. (6) Simple interest « $866 -486 Pomjpound interest = $890-957; difference - $24.47, 164 Answers and skisliston solutions. A s rate : B's rate = le x (9) Bate of toterest - 1 = ^^. interest for 9 mo. = i ; diB0,»nt.^,P.W.=«xI60-«46|. , (10) Whole solidity =|. 22 /,3y^^^j_^ Hollow space = f X "^ v ^^^%„-. • Solidity of shell - 1 x "^ v 1^68 , . . 44, Paper M (Page 69). 1,080 ft. hy 720 ft. is the St '^tangll" ''" *■"* ^ " =>««■ " (2) Weight =. I weight of gold + 1 weight of alloy. Value = _ gold 4- ^ o-ni^ 251 ,, ^ 01 6 ^°'^ + 300 ^°^'^ = Too ^""^^ = 21*. =, ^ o,. ; weight of gold = £1 x ??^ = ^^^® 78 251 3253°''' ^^^ "^ "* ^ * *^^° ' «""^ " 100 X 97i = $9,760 T„f*^ ^i^i-^ ^ " SO shares "■■;t;fo^J-!So.:|ii«iS.%1:?:?,^.--.- Total interest = $123; profit on a«lp« =. ^so" i^Bs oa the transaction 123 - 90 =='$33/ I I ANSWERS AND SKELETON SOLUTIONS. 165 (5) A year = 360 dy. nearly ; .-. int. on 11 for 1 dy. =6c. ^360 = - mill. Hence interest on any sum , = - mill X days, x sum = 1 mill x (1^ x sum), which is the rule. ((>) Int. = _J_ face, .-. disc. = _!_ face, .-. proceeds= ^^^face 300 ••• 307 face = 1,267 ; face = 1,267 x ^^ = n,296.f.^. (7) Ai-simple interest, (1 + 3r) 100 = 120 (l + 1^\ ^ lOO/ .". l+Br= 1-368 ; 3r = -368 ; r = 12-,46-7. At compound interest, 100 (1 + r)' = 120 (l + _J_ V V 100^ ' .-. (l + r)3 =i^(l-07)« = 1-37388 1 4- r = cube root of 1 -37388 = 1 -1116 + , r = 1 1 ,*, % nearly, (8) Compound interest must be taken; amount of mortgage = 2o0 (1 -07^ + 1 -07 + 1 = P. W. X (1 -07)« P. W. = 250 (1 -07- + 1 -07 + 1) ^ 1 -073 = 803 -725 4- 1 -225043 = $656.08. (9) Cost prices, 60 and 42 ; and 51 pence. Then 1?^ X 60 = 12?--. 4., ,.,... ^^y„ .-. selling price = 42 + £ x 42 = 49tV(f. Loss on 51 = It^ ; ... loss per cent. = 3,V\r%. (10) If the planes of the rectangles are aU perpendicular x = number feet in shortest edge, .-. 6a;' = 786 cub ft 4x « 15 -236269, the lengths of the ed^es, 1*'" If/ ^#« 166 ANSWERS AND SKELETON SOLUTIONS. PApi^r N (Page GO). (1) ?i3 ^ 13 ^ 22 .9 (2)98,400,180^159,982 = 615-070320, (3) 150 X 6 X I X 1,728 -. (c, , 4J X 3,000) X ..2i, == ^m Ans, .$GHi,.%. ^° •*"i«rest = $81. 56. (5) Ist iEcon.r, ._• 250 x 8 = $2,000 2nd incoiiie = 250 x IrP x 8i - ilS9 mn . • •125 ^ - *J,040; incrusse = |40. (6) The losses are 4, 3, 2 ; gains 1, 2 : yo n? Sf ""'^.n' '".^^^ ^'l^'^J J so we may take (7) F^nd the value of 2,000 o^. and take one-6323rd. ^ of 2,000 at $17 = 31,450 ~ of 2,000 at $H =_1^ ^ 6323 _ s.;s a 40- 10 31615 * '^- -^N^- (8) $12 X ^^^i-fi or 8-, 9 Too ~ *^ == 2^'^° francs 12,000 francs = ^^ x ^^^ v l^^ , ^ ^^^ 9"'^400''2685^^-^^^ = «2.4ia.41. (9) Value ; value = weicht • w«iw]if ~ a . p. Area : area = 100 : 121 ' ^ =4:5 = volume : volume. .•. thickness : thickness = _i_ • ^ _ .p. ,q. 100 ' 121 ~ ^ ^"^^^ •"• (10) They travel tor j her 231 vA i^ gr fl ^ ANSWERS AND SKELETO.V SOLUTIONS. m THIRD CLASS. 1H71 (Page K1). (1) 701,014,000,100,014,001); 701 ,uaariIlions, etc . (2)^Write A.M. afrev 11 oVlock ; 8 y. ,1 ,„o. ,. dy. 19hr. (3)G._C.M.of;;xl7x71ana.')xl7x.-nis.>l anvm^ulSfot A-^lf:?' '"^^^"^ ^^ ^ -'Valso measure (4) L. C. M. of 140 eighths and 85 eigtths = ITJ ^ 097.^. '.m or by adding somethim- to k ,?, "V" , '*'^;'"« the ««»,erato-, dimmishmg\he nS„'„°, 'he ea*il parts J? i' 'i"":'."*'' ^• numemtor, or by subtracting aeSSmii ^t^A /"*',""' 31 ^ 44.'] 2G 21 ^ -80 ^ 10 = -^^***' (fi)2H + 2Aac. =4S.ac. (9J ^ 25J) roods (^ of 1,1-) per. 4 ac. 140 j)er. 15 ]»or. Subtract 4 155 26 J) yd. 9 12 129 pr. 27 J yd. J' 1 168 AKSWBRS AMD SKELETTON SOLOTWNS. (7) - (- farm + 80 ac.) + (^ farm + 80 ac.) = farm 7/4 . ••• 1(5 farm + 80 ac. j = farm .-. 140 ac. = farm. Ans. 630 ac. y (8) Sum = 3 '882 ; difference = 3-03i Product = 3-458 x -42^ = (;J1 -11 x 3-83) -^ 81 == 1 -4710637. (9) £2-25 X 2-7345 = £6-152625 n-5625 ac. x 2-7345 = £15-21065025 ae 6 -54 oz. X 2-7345 = 17-8654 oz. (10) ($331.62* - $78.37J) -. 209 .. $1.21,Vo per hundred feet. (11) $5 ^ $4.86§ = ||; 62,720.40 x ^ = $2,794-923 + . (12) 95% sales = $4,100 ; sales = $4,315.79 nearly. (6) Commission = 5 on 105 ; JL of $4, 100 = $195. 24 nearly. 1872 (Paok 82). (1) Increase = 5 = 1H%. (2) Number 4- ishs^jr Number = » 11 (4) 25 + 33 + 42 + 40 = 140 ; 10,500 + 140 = 75 • A s share is 25 x 75 = $1,875 ; B's, $2,475 • ' C's, $3,150; D's, $3,000. ' (5) Gain per M. = $3J ; 106J M. at 3J = $332.03J. (fi) 18c. per yard = 2c. per foot Walls, $17.02J + ceiling, $7.30 = $24.32i. (7) Number hours =. ^AjL^ x 3 x 60 x 12 x 9 .... 40 X 15ir2V50T25~ " ^^^ ^''' AN8W£3R8 AND SKELETON SOLUTION^;, 169 (8) The price is decreased hy^-o! itself, ,. quantity must be increased by 1 of itself = 150 gal. (9) 15.84 x?^= $16,684. In 2nd case int. = JL ; disc. = 1 : P W - -^ of ftfii «675 25' 26' • "^^ " 26 °^ *^* = *I08 Gain per barrel = $_^, which x 500 = $231.48/,. m 187.S (Page 8.3). (1) Jl. ' 196 (2) ^^ = $9.23^,. (3) -4787878787878 •3213213213213 •322222222'2222 •7856485648564 •555555555555.T •4326432643264 2 •8^61788070696 (6) 1 •4710037. See No. 8, 1871. (4) WaU = 100|x2x22=4,433 Roof = 48^ X 60J = o 9941 Gables = "'5i3|. Ans. 7,880/, ft. Two to carry from the next line which IS the same as the second line. (5) 93 dy. = ^ yr. at _L 36o 100 651 . c\^ oK-oj^ int. ; .-. disc. = ^^± liifference = 65J (-}. _i_\ ^ 9500 - 21190050 ,„ „„ ^36500 37151/ "" "^^"^ = 2712023" " ^^'^^^' 1f~- 160 ANSWEJCd AND SKELEn-ON SOLUTIOKS. (6) 98 X 12 X L> = $2:3.02; 30^ x 18i x ^ x ^ x 180 = $150.4«i (7) Killed - -1 ; wounded ^ -9 y -On ■ J -^rence 055 of army Army - 1 ,100 ^ -055 = 20, JuO men. ^ ^^^ Y(iQ o^ '">' stock - 297 ; stock = 275 shares. (9) Cubic foot of water weighs, say 1,000 oz. • Jo o " ' j7 is O ; Jl is H. An'S. 882VV oz. ; 117+1 oz. (10) 1 share yields $60 cash, whi h purchases (OfJ ^ GO) share paymg $7, .-. (1,680 x 96) ^ (60 x 7) i ;5S4 shares." ' ^ (11) Cost = 100 X .^ X 640 X .i!24.7r) = $28..')50. 6 21 Ans. «^i,000. lit !! 11 1874 (Page 84). (1) m X 1) + (7i X X 495) ^ 3J. (2) 1 cub. yd. = 27,000 oz., of wh .h ^^^, or 24,003 oz. isO, and 2,997 oz. H. (3) Each woman gets -L of 480 = $24 .•. a man + a chilv gets $48 15 men + 30 children get $936 15 men + 15 children get $720, etc Man, $33.60; child, $14.4' (4) Debts = I X 6,300 = $16,8( ■. o (5) I*ta.= width. ..2J4_>L5x|x^ = $^^,= 16i ft (6) A man does 1 ; boy ^ ; 5 men and 3 boys do 1 ^1 + 1\ °1 1 - 3V51 85^ of a job three times as big. ?.«, Jl{^u.^\- ^ m: ««, , 5rv3 ' 5>'~45" ^^"^^^-^--S ^J-- ANSWERS AND 8KELKT0N 80LUTI0N.S. ig^ (7) 3811 - 38-6876 yd. Cost = $3-825 ^ 3.75 x 38-6875 = «39-4(il25. ^^^ ^ ~ '2 "*■ 5 "^ e) = yo^°^'"°e = |8,000; fortune = $60,000 (10) UO + 130 + 90 + 7 -J A. (in Aa- Tx vf JU+ '-> + 00 = 490 marks out Of 850 = 581%. 1875 (Page 85). /«^ . '^ 3 69 107 '>':>l4q* (2) hM 636al ,,0OShalf,,ints; He must sell 1,008 half-pints for 175 x ?^ - 20 ' interest on $1 = -033 : p. W of SI - -Qr,? Face of note = 240 ^'-967 = $248.20~near];. (4) At first the shares are ^ ^ ^ . n^^, 2 14 3' 3' 3' "^^*9' 4' 15' lastly A has 1|!, B and C together have L"^ • "*" ran ' •■• ^ '^"«*^ have 1^1 of $37,300 = $16,700. 540 (5) $20 for 500 = 4c. per bushel : amount of 1.24 in 6 mo. at 8% = $i.289G Loss at end of 6 mo. = 500 x'°-0lJ4 1 $5.20; or $5 cash (6) Ans. 17«. g/fff. (7) I remainder cost $1,.'344; remainder cost $1,680 ; ^0 barrels cost $120 ; $1,800 - $6 = 300 bari-els. 1 * . 162 ANSWEUS AND SKELETON SOLUTIONS. (8) 133 J greenback buys 100 gold ; 10 greenback - «7. 50 gold. (9) 151-,fi^ X 35 = No. x.l5^; .-. No. = 334 yd. 2 ft. l\k in. (10) Tare = _ ; duty is collected on 1^- 100 100 .-. duty = 4 X 1,280 x ^ x 11 cents 100 4 (11) 293.05 x|x^^4»|l,426.17S. $121-088. 1876 (Page 85). (1) 1st expression - 1? x 1 + fz^ = 25/ I 17v 200 28 36 432 24 Vji ■*• 18^ " 189 . 2nd expression = ?!, which i.s /«*,nhan the 1st expression. Difference = ??^ _ 25 ^ 25/8 _ l ^ 85 189 98 7 ^27 W ~ 378' The question has evidently been spoiled either in thft making or m the printing. If < < added to " be changed Jo s^ traded from the answer is — 878" f?M^ ^ " '^^°' ^ = '^25, we have (cc' x v') - te' - aru + 7j^\ and this is = ic + y = -075 + -025 ^ \i_ ^ >* • ^^ «^y + y ) (3) d^A- X y = l^!i!! X ^i = J58477 _ 458477 37 49995 37 4545 x 37 ~ 168165 = 2-72635209 + . (6) J- (l2 + ?i + 1^0 - M - 1 /'12257 - 2\ 817 . 100^16 ^5^-3- 120^ - Too(-240-) = im ^'' ("i) £q^ marked price = li^ cost price ; .-. marked price = ?? cost price ; ?! x $3.80 = $4.60. ly 19 (B) 7 : 5 gives a majority of 2 in 12 votes poUed, or lof votes; m X 6 = 1,440 ; 1,800 - 1,440 = 360 not polljd. fpression. AM8WBK8 AND 8KBLBT0N SOLirTTONS. Igg (6) Length of pathway to be made = 140 + 100 + 60 + 45 = 345 ft. Price of pathway - ^^^JL!L x ^ - «119.79i. (7) A's capital : B's capital = 6:3; .•. B's gain is '1 A's gain. Expenses $140 + $400 = $540 ; net gain - $2.%0 A's share = $1,250 ; .-. B's share = $750 ; .-. B received $260 as manager. (8) If simple interest is meant, interest = $213.75 .-. 1,520 X 2i X r = 213.75 ; • ;• == J_ „ Ri7 16 */°' (6) Interest on $100 must = $100 ; .•. 100 4- 6|| = 15 yr. (9) I^t 20^ = price of a sheep ; . . 8,000a: = cost. 150 at 24a; + 120 at 2Sx + 130 at 18a; = 8,700a; • 8%: = fed '""^=*'"'--"'«'^ -•«'■• ' ^' 1877 (Page 86). 9 (^) j^ of 41 oz. pure silver = 69 thalers 1 oz. pure silver = ^IJL}^ thalers. 9 X 41 37 41 Also _ oz. pure siver = i' shillings 1 oz. 69 X 10 t( 205 37 (( 205 .. -^-^^^ thalers ^ -^ ; i thaler = 2s. 11^^ (2) 1st fraction = 12 ; 2nd fraction = 4 ; difference = 8 dy. B's work per day = _ - _ = r B's time - 2§ dy. 164 ANSWERS AND SKELETON SOLUTIONS. (3) Waste = _ ; .'. ^ of original quantity = 170 lb. ; original quantity = 175 lb. ; 33 5.0 24 , ^. 112' 112' ll2 ^^® ^^^^^'' ^^^^' *"^ ^^* respectively. (4)£l = $^xl.09| 9 .-. £'18i = ^ X 1.091 X 18i = $89.02 nearly. ' (5) To insure $96§ costs |f3J " $1 " $1 29 " $48,628i costs .1S1,676.83J. (6) N = D X |,. .-. D X 1^ = 352; D = 160; fraction = 1^ T7) No. square yards paper = 178^ x* ^ = 104 sq. yd.^ 36 Length of walls = 2 (width + I width) = ^ width 6 3 IS .-. -1 width X 4 = 104 ; .-. width = 6 yd., length = 7 yd. Coste x7 x^ x! = $98. ^^^ ^' fi^qi^-^ToP.7^r/ -^iJ- ^' ^- ^^ "^ = unknown No. .-. 634,938,944,494 = 85,044,059a: ^ 9,187 .-. X = (634,938,944,494 x 9,187) - 85,044,059 = 68,590,142. (9) Interest = _^ principal ; discount = 1. principal " (50 ~ 5?) P"°^'P^1 = ^9-80 ; principal = $570, .-. breadth = i)9-89 + yards ; length = 299-69 + yard*. ANSWERS AND SKELETON SOLUTIONS. 166 on _ 192 ^d. ath X = 7 yd. 1878 (Page 87). (1) Product -^ G. C. M. = L. C. M .-. 391 No. = 12,121 X 23; No. = 713. (2) -1 X -Lx -1 = ^'2247 130 170 170 3757000' (3) -9840018 - -00159982 = 615 070320 + . (4) Ans. = ??^£^iii8l_ac._93yd. 4 ft. x 3 x 439 767-9 ac. 2797drTft7" . ^ 580659 2401 x 3 x 439 ^33452239 ' ^^""^^^^ ^^^ ? ^ 1741977203 _ ^-._ ^ 76201 *228,603. a I h "" j 5 •• ^' + & represents the amount. Now h is the interest on a, and the discount on a + h .'. interest = | of the capital ; discount = _ _«_^ of the debt. (6) ^ capital = 110 ; ±_ = 88 ° a + 6 Divide one equation by the other, and ?*±iL' = HP . ah 88 ' l+^-ij-l. « 1 ^ 6~4' ■fi'l" Capital = $440. (6) One brick with mortar = 162 x .12 cub. in. Wall = 7,050,240 cub. in. ^^ No. bricks ^ 7,050,240 x 1^> x -i_ = 40,960 bricks. (7) Letl0.129 = r>'- ■ ini oqqz % ^U t^TJ = 10,259,664,100 + etc. .-= lo'260,27l,849, 'Iin^o.";fcr,?>J.=^^^^^^- + 60a.+9 166 ANSWERS AKD SKELETON SOLUTIONS. Ji ^^^ i^^^ilSife- Now 25x47,619 = 1,190,465, so that the square root must be a trifle less than - 5 (9) Times are as 40 : 60 = 2 : 3 ; .-. rates are as 3 : 2 1st rate = 3 mi. in 40 min. ; .-. 2nd rate = 2 mi. in 40 min. .'. rate of stream — ■ 1 mi. in 40 min, ; .-. up rate against stream = 1 mi. in 40 rain. = 3 mi. in I'^O min. Ans. 2 hr. (10) 100a; at 80, gives - x stock at 5 = Z^x, income from Ist. 4 4 loOic at 120, . 65a; « 5 cj? " at 8 = 10^', 2nd. = $520 ; 5a: = 160, 100a; = $3,200, 150a; = $4,800. 1879 (Page 88). (1) 1st addend = ^ ; 2nd = 1 ; 3rd = -L ; sum = !21 2 2 100 100 ^ X ^ X ^ of 1,400 ^oot of (1 -76077 X 34-625) = oy-d7 + inches, Ans. '' (5) The ratios are 7 : 6 ; 5 : 6 ; 16 : 9 ; a? : 3. 6x6x9x3 X = 7 X 5 x 16 = IW dy. Ans. ;t liii / 170 ANSWERS AMD SKELETON SOLUTIONS. / (6) No. men - g_x ^Q x 2000' x 1000 , __^ 12 X 30 X 1600' — " '°^^* "'®" ^^»- (7) In 15 min. (true time) the minute hand will pass over , j^ of 15 minute spaces = 13J spaces. In 15 min. (true time) the hour hand will pass over — of - minute spaces = l-Sg- spaces. Distance apart = 13J,- l^^ = 12,3^- spaces. Ans. (8) $.3,700 yields $270 interest ; $100 yields 7^. Ans. (9) The company gets compound interest for its money .-. Sum (1.08)^ = 70 (1.08) + 70 + 1,000 = 1,145 60 1882 (Page 92). ^^L ^t^ ^e the point in the fore-wheel, and B in the hind- Tn ? 18 37 ? "^/"^ ^V^^*°P ^'^^^ *^« ^^^"age has moved fTo •' •.•',' ^.^'i' ^^^*' *°^ ^<^ 3^ ft. A and B will he together at 6 IS^^t" oT^""". °" '^ ^'^°^"*^- As A is never at tfe top a mei?'is;;fdeVcomc'^^^ *^« '^^ (2) Fractions =- 1 : Ans. ^ 10000' (4) P. W.=320-fl.08=^ = 200,001)^(9x9x9) = $274 -8484 + . (6) (1.16)<* = 2.01 + . Ans. 5 yr. nearly. .-. a: = 5,250 X 1,500 - 1,085 = 7,258 francs 6^^, centimes. (7) Apparently the note does not bear interest. Banker pays $486§, gets back $500, 9 " ": 73 "^ ^ "'^^/o nearly. ANSWERS AND SKELETON SOLUTIONS. 171 (8) B's cost + B's gain = |19 B's coat - _ B's gain =« $13 J B's gain = 6 j B's gain = t- 8 B's cost = 19 - ^ = A's selling price 8 49 B's gain = 8 on 49 = A's gain = 1 per dollar. 57 A, ^ ^49 .. — As cost = $_ ; A's cost price = $14.04-r^T. (9) Value of mixture = 21 times silver in mixture. Turned into gold, the volume of sUver in mixture is worth —^^ times 35 ^^Lfln.'^'''^ !^ ^^? "'^''' ^""^ ^^® eold already present is worth 20 times the silver now in the mass. Hence when whole mass becomes gold its value is 0-^ + 20) times = 1984 1984 35 times the silver in the mass. Hence it would be ^^-^ -i- 21 = 2Hi times more valuable. (10) 4-1888 = I of 3-1416= !«.. Let r = req'd radius of circle. Then - TT rMs given = 1,728 cub. in. to find ir r\ the area of circle. .-. r^ = 1,728 - |r ^ 36 X 36 - TT ; /. r = 6^6 - f^ tt .-. Trr^ = 36,?^36 7r = 36^36 x 3-1416 = 216,^ •5236 = 216 X -80599 = 174-09384 + square inches: 1883 (Page 93). (1) 1 of £39 = £5 11«, 5|rf. ; jL of £2 12». = 3*. 8K ; • 14 s of 45d. = QM. : sum = Pit In* 8t^ 7 '~ "■'■■*" (6) 13i -^ 19J - 107 -h (12 X 13) » -6858974^. / 172 ANSWERS Xmd skeleton solutions. (2) The price of 8,596 lb. at £10 ISs. 7jd. ^ 10,000 = Ans. £8,596 0*. 0o*-«'&^« that the examiner meant by the question, -How much less per cent, did he make on his invest- ment?" If so we should say 7 on 95 is I on 5, or 7^%- on 100, rate = 7^,^% on 1st chance; 7 on 110 is 1 on 10, or6Aon 100, rate = e-,\-% on 2nd chance. Difference of rate per cent, on investments = 7-,^ - Q^ = If- - 112 = uofl _ M _ 140x8 210 ,,., '' ''" ^'9'-^^° 19 X 22 "" 209 - ^^'^/o' -^f "6 ->> " 1»« 174 ANSWKK8 AND SKELETON SOLUTIONS. 102 (7) $4.96 = ^ par, etc. Ans. $4.86^. 37 1 ^^^ i?^ weight in ources x 1,700 + £ weight x 110- 1,000c. Number ounces = 4,000 -r- (),32.'j. (9) Length : length = 1:14; weight : weight = 77 : 89. .-. weight of copper rod : weiglit of iron rod = 11 : 178 • -r;-or -— = ol6'2 oz. Ans. 11 10 (10) $52.80 - 46.20 = 6.60 ; 52.80 -f 6.60 = 8 yd. Ans. (b) The thickness has become — of what it was, 16 hence t' ■) ♦rcadth must be made — of what it was : 27 decroase - _ breadth = il of 42 in. = 17^ in. Ans. 27 27 1885 (Page 94). (2) 211Jyd. cost $810. 43|. .-. selling price per yard = $810. 43| x - -^ 211^ =$4.59Hi o (3) 555. + 2s. 3d. +ljUd. .^. £2 17s. i^^^d. •oi^i-'^^mu^® P"*^ = "^"^^ P^'^ ^"^^6^' a<^ which 110 bush, give *y2.9o. This IS $2 less than the real price. Now the difference must be made up by taking more at the higher price ; $2 - -25 = 8 bush. more. 55 + 8, 55 - 8 ; the quantities are 63 and 47. (5) $120 = 60 yd. cloth; $96 = 48 yd. cloth. Suppose an increase in the cloth instead of an advance in price. Say he buys X yards at $2, sells (x + 60) yd. at $2, or (x - 48) at $2. The loss in the supposed case = 108 yd. = 1 (a; + 60) ; a; = 480 yd. (6) $100 on policy costs $_ premium ; net proceeds = $99^. 7 7 .'. premium = _ of proceeds = _ - of 47,580 = |420. ANSWERS AND SKELETON SOLUTIONS. 176 (7) Interests -*2- , 1^ ^ 1600' 1600' 1600' 14A'8 = 15B's = 18C' :.A : B : C = 45 : 42 : 35. Divide s. loo etc A'8 share = $1,822.50 ; B's «1,701 ; ^lin 50.' (8)90 + 3 = 93dy.=3A-mo. Int. - 11 .-. face of note = $884 -2652 800' ^'""^ s = 769 HOO fa ,ce (9) Gains are as 29 : 3f) ; A's capital !?, B's ^ of total. 39 ^^ ^^ /. - capital = 78,000 for 1 mo., ,. A's capital = 58,000 for 1 mo. He withdrew 14,000 for 1 mo. = $2,000 for thP 7 mo ^'"^ mHH;=J"f );/ !«;=;--" -2)' + w. euc i. 47. wan = Jo ft. ; ladder ^725 = 26-925824 ft. 1886 (Page 95). (1) A's = C's - 17, B's = C's - 10, Cs = C's • A gives 12 to B and 5 to C, and C has $46 more than A. /OS 1 , 2 _ 11 . , 1 ^ 4 3 ~ l2' ■'• 12 °^ *^"^®' *^"^® " ^^ ^^• 3 hr. at 14 + 8 hr. at 25 + 1 hr. at 7 = 249 mi. (3) At 4^ o'clock, minute hand is 20 spaces behind, gain 22 spaces = __ of time required since minute hand gains 11 spaces outof every 12 it moves. Time = l|x22=24 min. past 5 o'clock. (4) Wages are as 5 : 1 ; rates as 2 : 1 ; times as l' • 1 2 " ' or as 5 : 2 ; i.e. boy's time = ? man's time = ? of 1.^ = 6. Hence man alone takes 15 + 6 = 21 hr J2 H'r ^^ ^^^' T^ ^J^ 5 ^"^"*'*y «ol^ 4- ^ ^2) = 15.888 cul,. in. fc)ince the boards are 1 in. thick, there are 15,888 so. in. of lumber .-. cost = 15,888 4- (144 x 50) = $2.20^. (12) Cubic inch taken out = 8 x 30 x 462 1 in. deep of cistern contains IT x 42* cub. in. Cistern is lowered (240 x 462) -I- (^ x 42^) = 20 in. m 1890 (PA(tE 100). (1) 10,080; 110,250. (2) £3 13s. id. + 4s. 9(/. + £2 18i-. bd. = £6 his. 5d. (3) 133J lb. = 133J X 1-^* X 16 = 1,755? oz. Avoir. 1= ^ 10 40 .-. 6,144 -4- 1,755? = 3J sover-igns. (4) ,1 + 7 + o = r^i of a day's work lost ; I + o < V 12() y Net loss = -^|1 ; leaving l^ dy. lost ; 1 7 -- less for 17 men. Ans. J. less. ^^ 30 (5) One brick = ^ cub. ft. ; brick + mortar = 1! x 1 16 32 named 32 cub. ft. Ans. (45 X 17 X 4 X 32 X 16) ^ 3 x 17 = 30,720 bricks. [fii I 18S AM8WERS AND 8KBLBT0M 80LVTtON8. 22 22 (r + »',)2L> yd. (6) 12 ao. -68,080 yd. - ^ (r + r.) (r - r.) .-. r + r, = 840, and r - r, = 22, .-. 2r, = 818. (7) 1,100 sq. ft. of wall ; .-. ?f x 1,100 x 2 = 2348 (8) When pressures are as 2 : 3, volume of air is as 3 : 2 i.e. volume becomes _ less; 1 volume = 2 in. Ans. fi in. o 3 (,9) First income = 200 x 5 = 1,000 Second income = 200 ^ ^^0 '< ^^ x g^ = $1,101.85,^, Difference = $101. 85 ^V (10) Cash value of $5.70 due in 4 mo. at 4%, with 6|% adde.l = 570 X !^ X 1^ = $6. 7b 1 o Hence 12c. is the interest on $6 for required time, i.e. (i mo. (11) Direct exchange, $4,150. Circuitous exchange, 10,000 x i- x 12 x — - x ?^* 45 9 400 400 = $4,262.09H. $112.09H = difference. (12) Dr. 950 X = for 1 dy. after July 10th. oOO X 50 = 15,000 '« '» it 250 X 101 = 25,250 " «« ti 150 X 83 = 12,450 «< '« it $1,650 and $52,700; = $1,650 due in 32 dy. after July 10th, or Aug. Uth. ^''' t^ "" Q? = io .nS ^°" 1 ^y- ^^t^' J"ly 10th. 350 X 36 = 12,600 '< " «« 200 X 57 = 11,400 «' »< if «1,000 $24,000 ; = $1,000 paid 24 dy. after July, 10th or Aug. 3rd. Difference 650 due in 12|.^xJ . 12 dy. after Aug. 11th, i:e> Aug. 2Srd, AMSWBRS AND SRBLSli'ON SOLUTIOKS. 1891 (Paoe 101). (2) Policy - I of 17,600 = 50 hundreds ; rate - 2% 188 •. premium = 60 X _ = 5 $90. (3) Taxable income = $700 ; tax = $1.05. ^^^ lo^^ J «n° "^S^i* A* ^''^ P''^^^' «^0 ; $72 = bill ; 90 - 68.40 = 21.60 gain on $68.40 : * ^ ' gain on $100 = 31^. Axs. (5) Proceeds = (12,000 ^ 75) x 80 = $12,800 Ist partial income = Q of 12,800 -f 9G) x 8* = 155| 2nd partial income = ? of 12,800 x 5 = 426 J . . 2nd income = 582 if 1st mcome = (12,000 4- 75) x 3 = 480 Difference = $102^. ^^^ ^ = \ ''}:^^ = 1 -0* ; 1 04^ = 1 -0816 ; 1 04 '^ = 1 -124864 • 1 •04* = 1-16985856. i i^40b4 , Sum = 5'416322.56, which x 350 = $1895-712896 Ans. 400 . 300 000 441+_3l_. 200 1.05» (7) P. W. of debt = i^^ + 1.05 1.05* ■ 1.0.5^ ^^^ ^ i? X I? '< I? = 7,648,000 - 90,261 = $825.83 nearly. (8) Area = 84, • 1684-1?; 4- 14; - 15 = perps. 12+^, 12, 9,Vft. (9) Area of lid and bottom = 144 ; sides = 103 ends = 107 A sq. ft. ; total external area "='374 A so ft Capacity = (82 x 94 x 106) 4- 1,728 = 472/^, c^b.^ (10) External diameter of wall = 84 in. ; internal = 70 in Area of top of wall = ^ x 1 (84 + 70) (84 - 70) = 22 x 77 sq! in. Solidity of wall = (22 X 77 X 28 X 12) ^ 1. 728 =.1 X 77 X 77 cub. ft. But 1 cub. in. weighs | oz. ; 1 cub. ft. weighs 72 lb. Weifi-ht of Troll _ ^ (-77 ^J -T-r , -.c»N ._ - _, ..„. _ __ ^, / X . . X (2j 4- if,:f40 = lOffr long tons. 4 Ift4 ill AK8WER8 AND SKELETON' S 19. OQ 2^- and C = 23 . 29 . 7. 3\ 5^ And again •'»•-"• -^ , A = U.13.2\3^; B = 7. 17 . 19 . 2>*. 3\ 5». etc etc. Fraction = 2". 3^ 5 . 7 . Ip'. 13^ 17^ 19^ 23 . 29i 3i .S7, (3) Length of regiment =-- 247 yd.; to which add 3 mi. 44yd.. and 3 mi. 343 yd. is distance travelled to clear bridge ;. length of step = (5,513 x 3) -^ (.56^ x 96) = S^VbV ft. (4) Cost = $750; risk = $825 + J_ risk. Axs. $831-234 + 400 (5) Let a; = amount ; ,. ^^^^ - ^^^^ = 31 J. .« = $17,415. (6) Interest = $165; int. on $2,417..50 for 1 yr. = $163-18125 .-. time required = 1 yr. + iHl^IJ,^^ = 1 y,.. 4 ^|^, Ans. Jan. Bth or 6th, 1891. 163-18125 250 1-02 250 1-02 (7) P. W. = ^ + ^in. + .— + 250 102' 250 1-02^ 250^ 1-02* - (l-02> + 1-02=' + 1-02 + 1) = etc. = $951-932 +. (8) $5,000 = 26,041Sfrancs; 25, 21 1§ francs = 11, 345 J florins; 10,8454 florms = 18,075 A shillings = £903 1.5. SKELETON hOLfflONS. 18A (9) (a) Area .. ^((JO x 4 x 21 x 25) - 4 x o x 7 x 3 . 420 (6) Area-(C' - C]) ^ i TT -(2ao» -210-)-=- 4 xy-1459 = (140=" - 10.-)=) -^ :M4ir)f) = 11-1408 -f- . (10) (a) Slant height = 2; coiulhI mirfaco =-- 4r x "'^ -2i - I TT base B TT ; total surface of cone = 'Att ; surface of sphere •I o "' A 1 '> - TT , .-. 4 TT r" = .. jT ; 2 2 '■ = «/« 5 volume of sphere = 1 ar r- » •!>(;•>. o 3 (6) Circumferences are as 45 : ofi ; large wheel gains 1 1 in going .V5 Small wheel gains ^ of a revolution for every revolution of large wheel Small wheel gains 1 revolution for every — revolution of large wheel Small wheel gains 12 revolutions for every 1-* x 12 i-evolutions of large wheel Small wheel gains 12 -olutions every W. J. Oa(.k a Ca's PvuuixnusH. ProWemsJnJrUhm^^^^ Classes. atlapiitl piiMIt 2li- J';r'""^'«'';''^""'f«" nn.nl, Ht. acl..K,l. Tom,,.,,. Mai.,ly ^_^ ^^^ uo.. the .a.,uor the ,.„.,.„.orke., ....... wc. ke,'',:;;;;;;.!:^ cnce of tho.,„.t ,. thus .cure., ,^ the Mv;:,;:^;:^.::^;^^:;^ exorcise ea„ ho ossIk.... with seircci.y . Incnl^aVdcIay "' ^.^.;^.-.,r.rc:;.rrt=rt:^-^^^^^ rae.i.^ri^;s;;::;rc:ntj^^:;r^^^ l..jfofho,„oorcla.sst.x..,vls,.s. Tl.c .^ s notiTin , ' *" "'"/■"''>- so««cc^sn.„ dostn^s a,. ^ir.u.:':^:'!:^'^^^vz:xv^:^ I". i.s .> nuH. lost t.„,o If p.piisr.:^t;./t^, r;,::^^^^^^^^^ :rsi:;r;s;::ir:^s:;:;!; J-- ^- -«■•- --^ -- ticc Talt'Thr ''''"■ 'T ^'^'^''""•' °" ^°"'- ■■"•"•••« ••»>«« baaed on the Prac- tice Table, the answers to which appear only in tho teacher's edition 10. There are 57(5 self-testing excrclMe-s in 1on-r r1!v«».inn, Problems in Arithmetic Foil II. and III. BOOK CLASSES. EIHTKI) ItY Principal Church Street School, Toronto. Edition with Solutions and Answers (Teachers only), 50c. Edition without Answers (Scholar's Edition), . . 25c. TEA€HEKK STBO!V«;£Y KGt'OMMEND TOKM. The be«t I Have seen.- Sam. J. Lattek, Principal Public School, Shall Introduce lninicUlaleI,.-M. A. Stewakd, Principal Public School, LancaaUr. Kecoinmend it. The problems are excellent, and 1 noi)e the Ixjok may meet with the favor it merits. I would re- commend it to busy teachers.— Amy H. Guthkie, Teacher, Port Credit. Unprecedented In the history of Arithmetics. The plan and matter of " Pro- blems In Arithmetic for Junior (Jusses " by W. E. Groves, are uii- precedentetl in the history of Arith- metics. The careful grading and ine absence of answers in Scholars' Edition make it esi)ecially useful to teachers in ungraded schools. Mr. Giwes is highly practical and Iwical—E. R. WixHEKiL, Prin. Heatport P.S. The best I have seen. Ihe Problems in Arithmetic for II and III. Book Classes are the bostti have seen.— Sah. J. Latta. Save time and labor. The Arithmetic will save the teachers tnne ami labor and will prove valuable educationally as it contains a great variety of pro- blems.-W. H. BAKiat, Bayfield. Shall Introduce It Ininie* dintely. I nm 80 pleased with the Arith- metical Problems for II. and III u"??®.^' **y,W, E. Groves, thnt I shall introduce it Into our school immediately. I hope the IV. Class work may be equally pood.-W. A. Stewart, Prin. P.S., Lancaater. Highly Pleased with them. I have made a careful examina- tion of your Problems for II. and III. Book Classes and am highly pleased witli them. The arrange' meut of the problems is the beat I have seen in any book of its Idnd. — Sam. M. HaUCH, Prindnal P.S., Daahwood. ^ G ar E sc-1 M. Sel Problems in Arithmetic FOR IV. BOOK CLASSES. EDITED BY W. IS, GRovns, Principal Churck Street School, Torontc Edition With Answers (fc .aehe.8 only) . Edition without Answers (Scholar's Edition) 50c. 25c. TEACHERS STHOVO^y KEC »MMem» THE^W. LACE, P/7n. Zfe7m'o»-<;i p.^. tonl'.s. ' "''"'"^"f '««■ -Omj/- Savcs valuable time. i^^nppai Mattawa Diatrirt Training Institute. -"««f'*c« cou< }l ItPlightod Willi |(. Kenily excellint. J^. are really excfillPnt no M nf?°"^'' I>e without them -A Miu'Ii pi(>nK(>«i Hith Its -and thei-c are many of us -R i The best out. '«S^ci1&!i^eiif"V!S!i'^ say It is thefeestout-rD Ni?o^* i-ganvtlle P. S. ^'i^icoh, W. J. Gage' & Co. 's Publications. Prize Problems in Arithmetic. Selected and arranged by W. H. Ballakd, M.A., Inspector of Schools, Hamilton, and W. J. Uobertson, B.A., LL.B., Mathemati- cal Master, St. Catherines' Collegiate Institute. There are about 1,1(h» Problems in this book of which about 500 are from Prize Problems conti-ibuted to the Canada School Journal. The object of the book is to place in the hands of teachers and pupils a careful selection of Problems suit.able to the fourth class in our public schools, thus enabling them to prepare thoroughly for entrance examinations to high scliools and collegiate institutes. The selection is particularly strong in interest and percentage. 10th edition. Price 20 cents. Decidedly a help. Will be decidedly a help to teach- ers who are preparing pupils for the entrance examinations to high schools The Problems cover a wide field, and are, most of them, eminently practical.— J . A. Wis- MER, M.A., Head Master, Park- dale. ■utcrestlng and practical. I find the questions in the various departments of Arithmetic pre- sented in great variety, and at once interesting and practical.— J. A. Macpherson, Head Master, Bee- ton P.S. Excellent for home w»rk. Your " Prize Prablems In Arith- metic " contains a great number of excellent Problems for home work or examinations.— J. S. Rowat, P.M.S., Caledonia. Intend Introduclns It. I intend introducing it in iny fourth-book class at the beginning of tl ^ term. It will make an excel- lent review book.— M. P. McMas- TER, Principal P.S. , Thorold. More than pleaded. I am more than pleased with it— Thos. Hammond, Head Master, P.S., Aylmer. Comprehensive and very prac- tical. • The problems are definitely word- ed, comprehensive in range, and very practical.— J. C. MuNRO, Prtncijyal PS., Pr,hnerstov. Will use It. I will endeavor to have my class of next session provide themselves with the work.— A. N. Thornton, Head Master, P.S., Wallaceburg. Best of the kind. I consider it the best of the kind that I have seen.- J. C. Stewart, Principal Pembroke P.S. An liidlspenslbic help. I have thoroughly examined " Prize Problems in Arithmetic," by KolMjrtson and Ballard, and be- lieve teachers will find it an indis- penslble help. — Jas. Duncan, Prin. Essex Model and Windsor Central Schools. Time and labor saving. The questions are practical and will induce a wider range of thought. Anv teacher using this work will find it both time and lalwr -saving in reviewing for ex- aminations. — M. H. Thomi'son, Principal Aurora P.S. !>ihall Introduce the book. The problems involving Interest and percentage are very numerous, and include an almost endless vari- ety of apnlication. I shall introduce the lK>ok to our entrance class.— W. E. Groves, Principal P.S., Wingham. Vsefnl to teachers and pupils. I feel certain that the work will not only be interesting, butalso very useful to both teacners and pupils.— i. O. fjTKEIjE, 1 .iri..u.f Sdt'f'ic. W. J. Gage & Co.'.s t^ouMCATioNS. Hamblin Smi th's Apithmetic. anH r*r''o't,°" A'^thmetlcby J. Hamdlin SMiTn,M.A.,of Gonville SntiT ^ '^!: """^ '"'' '^^'"'•°'- ''' «^ P^'^r's College. (SmbrWee Adapted to Canadian schools hy Thos. Kirkl v\n M a v.T , \ Normnl School. To,-onto, and Wm. Sc^Tfi ^ M^Lm^t^T m" r' Nonnn. School. Ottawa. Eighteenth ^Sol pTi^e rcSlt^. ""'"' Authori, Authori, Authori. Authnri Authori: Authnri: Authori: Authori: :eiJfor 'zed f 01 ledjtor zed for •.edfor •.edfor ;edfor ■edfor use in the f!chnol./t nf Ontario use in the School.<> of Quebec usetn the Schools of Prince Edwnrd Islnnil exclusive use in the Schools ofXovn.<{oUn exclusive use in the Schools of ml?foha exclustve use in the Schools oflirtis Cohimhia exclusive use in the Schools «/AVtX,„dS7 ' B A Ta^ '';fs'i'"'*'^' ^°'™'^' S'-'^^^'- Ton,nCnd W^^^^^ fho1i;arT.ttrs"'^™^^ ^""'r.^.r.'eJrAfl.^-^'' '^^"*^° ^i>-'- to issue ^ ^yryand&ScotrsAmhmetic, French Edition. Edited by U. Schools, Montreal. E. AncHAMBAunr. Superintendent of Fiencli For use In French schools. Price L'i cents. l^eyjojlamblinjm^^ pap^^^rct^dre^lZ^?^ lortne use ufpiivatcstudeuUittud teachers. Price «2.00. ' W. J. Gage & Co/s Publications. R evised Edition Gage's New Map Geography P rimer. Prlce .jo cents. For Pupils preparing- for Promotfon Exnmlnatlong. For Pupils preparing for Entrance Examinations. For Pupils preparing for Junior and Senior Leaving Examina- tions. For Pupils reviewing for Certlflcates or Final Examinations. TO overcome tlie great diflflcultj- of preparing students foi- these exami- nations, some masters throuprhont the province have taken the ordinary text-i)ool{s In use, and from the multitude of sentences, selected what they deemed necessary to be learned by the pupil. Others »j,'aln have used the blacktoard or the dictation l)ook for the facts to be memorized. These plans are objectionable, as the one does not present the words fioin the textbook so as to be remembered reatllly, and the ofhei-3 necessitate the loss of much valuable tniie. Further, the pupil does not recognize tlie word in its written form, and thus the spelling is not taught. Of still more importance and what in itself should commend the work to teachers and the public generally. Is that the exercise book required for the dictation exercises in Geography alone costs as much as this pritner. The work is an-anged in tabular analysis, to prevent the waste of time in poring over a prosy text-book. Brief notes are Inserted at intervals to convey information of special interest. Although merely preliminary, this book will be found to contain all that is necessary to fit a student for any of our examinations in the subject, Geography. As to tvhnt and Iww much to t^ach, those in charge must exercise their own judgments. The attention of l)oth teacher and student is directed to the Railway Map and to its analysis as siKJcial features of the l)ook. The new matter thus ad led relates to such interesting portions of the earth as Australia and parts of Oceania, Africa, the West Indies, and Central America. These places, containing as they do sister colonies, claiming a common origin with ouraelves from British stock, ca'inot fail to be of deep Interest to all loyal Canadians. The statistics of the various i itries, particnlary those speaking the English Language, have been brought down to the latest date ; this is possible at this jmicnire owing to the prevailing custom of taking the census every decade. V^. J. Gage A Co.'s Publicatioj riONs. Re^lueil Edition Gage's New Map Geography Primer. The Railway map and letter press iiistnictlon aceoinpanyinfr it whlcli Sr •^'' '""Ppn"""^ "'"' ^'^ '■''""'* ""^•■""- I' ""» "^^ "otJced that tho nlrT*r ^""'^I'i,"'^ •« ^«» •""Pl^Hert with railway fncilities as n,.y ■Zll L '"''•. ?' "'"'"'■■"' ''•^'"^^•''' '""""fetures. trade and com- tnerce, have received special atttention : and, while not claiminff that it contains everything essential to a complete knowledge of GSiphvk il contended that as much useful information has loon p..XHnto he limited space as is either wise or prudent. The Mnin Featiiroit may be summarized as follows :- Brier and €lear.-The whole matter is put in so l.rfof and clear a man- ner that the time of teachers and pupils will iK! savod and most satis- tactory results can at the same time Iw secured. «e learned, or usini.- WacklKjards or dictation l)ooks. the student has presented in this little Primer in clear concise form all that Is necessary to be remembered. Mnp8.-Flfteen l>eautiful maps are in.seited, namely : Map of the World Western Canada, Dominion of Canada, North America, South Amer- ica, United States, Europe, England. Scotland. Ireland. As'a Africa West Indies and Central America. Mexico and Australia ' Man „C Geographical terms. Among the special features of the new edition will bo notod : Sew Hallway Map.-The Grand Trunk Railway System is indicated bv a Red Printing and Canadian Pnciric Railway indicated bv a Green ofclnad^ showing at a glance these two great Railway Systems Xew Ma,w of West Indies, Central America and Mexico have been added, also a map of the Domfnion of Canada showln- atlve rela tlons of the different Provinces of Canada. " ' i- rcu- W. J. Gawk A Co.'s PirunoATioN^;. Revised Edition fiagre's New Map Geography Primer. New Doable !»««« Miiii of Oiitarlo.-Prlnted from relief plates In three colors with all of the most recent Information available. New Donl>l<> I'aji;*. Miip of Rrllinh <.'oliiniIiln brought down to date. Donble Paao Maip of Quebec. New Stat iAticH of various countries have been inserted, giving informa- tion to latest dnt<( in accordance with the recent census, in which Pi-oducts, Mannf.u'tures, Trade and Commerce have received special attention. A (.'haptei* on Topicnl «e«graiitay for Language I^essons. Mpecinieu Proiiioilou E.vaniiiiatiou raitrriD. I»rlce,— Notwithstanding the book has been printed on beautifully calen- dered paper, entirely re-written with a large number of additional maps, the price remains the same, viz., 40 cents, and is about one-half of that of oj-dinary texts books. ftouiity EflltioHN have l)een issued, the Counties being grouped together rnd beautifully engraved maps of each County, with every post-office, population of villages, towns, etc., and other useful information sup- plied. CONTENTS OF COUNTY MAPS. Each map marks the location of every post-office, shows the popula . tion of Aach villose or town, shows the location of telegraph stations, tl-e main travelled roads and the distances between stations on the various lines of railway. County Edition A. With County maps of Essex. Kent, Lambton, Middlesex, Elgin, Perth, Huron. County Edition B. With County maps of Oxford, Norfolk, Brant, Wentworth, Haldl- mand, Lincoln, Welland, Waterloo. W. J. GAaB,& Co.*s Publications. RoTlged Edition Oagre's New Map Weoyraphy Primer. County Edition C. m„.^' r^""o^ "'"'*" *'*' "^''""' ^*'^'' '^""'' D"""*"-'". Wellington. Sinicoe, Grey, Bnioo. also double pago map of the City of Toronta County Edition D. » .^^'' ^?"'^ '""•'* ''^ °"*'"^*'' Durham and Northumberland ^^f„'■^7,'^^ "'^"'^•"•^"- Victoria, HaatiuKS. Prince EdwnrTS: nox and Aduington. County Edition E. .nH^"*" ^T't "T *"■ ^''^"te"'^^. Leeds and Grenvllle, Russell mL^^ ' '^"''*' ^^''^*°"' °"""^'«' s««"^°t 4 Ga ge's Map Geograpliy-Quebec Edition. Contolna a large double page map of the Province of Quebec also Tf^'^^^'^^^^^'^ownship,,togethevwitU additional TextScri^ tlve of the Province of Quebec. Price 40 cents. Gage's Map Geograpliy--Manitoha Edition. Contains double page map of Manitoba, together with the dp« criptlvetertofthatProvince revised uptodak PriceJoclnte. Gage's Map Geography-Britisli Columbia Edition. w1h!5!!S'm"T ^'*"^'.^ P"*^® "^P °f British Columbia, together wlH. descriptive text revised to date. Price 40 cento. "^""'er m W. J. Gaob & Co.'s Publications. Recently Authorized by the Board of Education for use in the Schools of British Columbia. I i Keeommend It. I have used your Map Oeofn-aDliv and recommend It to mypuplls. many of whom use it in prepartnp their lessons, and with good results -Robert W. Bright, Drayton, Recommend Itfi use. Your New Map Geography :?_\"^.^.l*''»« amount of informa- GAGE'S NEW MAP GEOGRAPHY PRIMER. ••The Hnviiia; or lime, the nwakenliiK of interest nnd theflnni nitniiinient of HiirresH will be realized, I believe. In every ?T,'*"'crr */ *" •""« "-J- A. Hill, PhB., Headmaater Dundan rublic School. Consider It e> "ellent. It is quite an Improvement on the old edition and fontains nn im- mense amount of information for such a small liook. Tlio maps I consider excellent.- A. Dorskt, Essex, Out. (•rently Iniprovt'd. I have carefully examined youf New Map Geography Primer nnd find it enlarged nnd gre.atly im- proved. The type, pajier. binding and mnps are all excellent. Teach- ers will find that it l.f it to them as tlic best of its kind for their work. It is now in the hands ot nearly every member of the • lass for use at home, and the jmpils are delisrhted with it— S. C. wooDWORTH, Principal Model School, Wetland. lliShly delishtcd. I anri highly delighted with your Map Geof?raphy Primer.— A. A. Mclean, Slar, Ont. illoHt ngcfhl help. I consider your New Map Geo- srraphy Primer one of the most use- nil lielps to both teacher and student. The statistics are up to date. This feature alone, to say nothing of the mass of other infor- mation. Railroad and County Maps, and scores of graded E.xaminatlon Questions, should phe it a place on every public school teacher's table. I liave used your old Map OeoRrajihy Primer for years and would not be witliout such a book. The new edition is quite an im- provement on the old— W. A GUAHAM, Prin. Oil Springs P.S. Already I'scd. Many of my pupils already use tlie Map Geoi?raphy.— L. P. Hah- Kop, Prtn. Niagara Falls P.S. I»3ensert with mniiy fentnres. I .\m highly pleased with many features of voiir new Map Geo- graphy Primer. Tnos. IIam- uosv, n.M., Aylmer P.S. >Vlll rccctiiiiiiend llieiii. I will recommend it to those of iny aa.'^istiiiits wiio teach geos? raph v. - A. M( Kkk, Head Master, (Ji bridge! P.S. I'sefiil inntlor. The Geography contains a great deal of useful matter not easily found c.lsewhere.~W. H. Bakek. Bayfield. Good M:\\\n niid conri.<4«>ly ar« rnii;;!>il liifornialloii. The G(>ography contains good maps nnd a^rcat deal of concisely arran«-cii information. — H. R. Lo.NdH. Principal Model School. Clinton. A perfect work. * The new Geography Primer should be in the hands of every teacher and pupil who wish the greatest amount of information in the shortest time. For review for examination it is a perfect work-. Ihe Railway Map alone is worth more than the price of the Ixwk. I should like to see it extensively used.-B. C. H. Beckkk, Priti Brighton P.S. Is plea.sed to sec them u.sed. I am plen.<(ed when I see your Map Geography Primer in the hands of my pupils. Some of them are using them with the regular textlKjoks.-G. E. Hendkrso.n. Prtn. Kingavilla School. Very miieh hiiproved. I consider the Revised Edition of your AInp Geography Primer vfiy much improved and sh.Tll rpc">»>- mend it to my students.— J. W Land, Pnncipal P.S., St. Marya. W. ,T. GaOB & Co. '8 PUBLICATIOKS. Gage's New Topical English and Canadian History Notes. This little Primer Is prepared to cover the Public School History Course In English and Canadian History, and la printed so as to furn- ish a number of blank leaves to allow students to make additional notes. Prlc« S6 cents. leading Fealnrrs. 1. The Notes are arranged Topically under such hea4ling8 ns l)esc Indicate the True Growth of the nation. 8. The Progress of the People, the Struggle for Freedom, the Establish- ment of Representative Government, and the Development of Edu- cation, Literature and Religion, are given more prominence than wars. 3. The Colonial Extension of the British Empire Is briefly outlined. 4. The whole History Is Classified, so that the Relationships of the Great Upward Movement can be understood. 6. The arrangement of the Notes makes It Easy, Definite and Thorough Reviewing, perfectly simple without a teacher, e. The Notes supply an Admirable Preparation for the study of larger histories, and the best means for Clearly Remembering what has been learned from them. 7. Ample space has been left for Additional Notes, to be written by the stu- dent. 8. The Notes can be used In connection with any Hlstoiy , and are Intended to Stimulate the Further Study of the Important subject with which they treat By the use of this Note Book 1. Time Ifl Saved to teachers and pupils. *. Success at Examinations made more cei-taln. 8. Interest is Awakened in the study of History. ^ 4. A simple, definite Method of Studying History is revealed. W. J. OAifE (fc Co. '8 Publications. Eidian History to furii- Iditional GAGE'S English & Canadian History [lote Book. indicate itahlish- of Edii- ice than I. le Great lorough ' larger hat has the stu- itended which From PMOF. WILLIAM CLAKK, M.A., LL.D., Trinity College, Toronto. "II in an admlrnble compilation, rqaally viiefal to lecturer and stadciit, aud I am very glad to perase It. i shall often refer to 11," A loiig-relt want. Your Engiish and Canadian His- tory Notes till a lone-felt want. There ceems to be no text book at present suitable for junior pupils, and the notes will save the teacher much time in arrnuKin^ class work. They are Just the thiupr for oral teaching and review, and may be used with any English or Canadian History.— W. A. Graham, Prin. Oil Springs P.S. A very great aid. Your Notes on English and Cana- dian History will meet the needs of many teachers who are pressed for time. Entrance pupils will tind it a very great aid.— L. F. Hau- UOP, Pnn. Niagara Falls P.S. Admirably adapted. It is admirably adapted for En- trance classes, and will make the work definite and thorough.— S. Y. Taylor, Prin. Public School, Pans. «fuiit the thing. i am pleased when I see your •'English and Canadian History Note-book" in the hands of iny pupils. Some of them are using them with their regular text-books iind iind them just the thing.— G. K. Hknpkkson, I'rivcipal Public School, Kingeville. « CSrent help to students of hls> tory. I have examined your Cana4lian and English History Note Book, and. although I am somewhat pre- Iudiccd against Note Books of any [ind, I must say that yours is the best and most carefully selected Notes that I have seen come from the press, and uncier the care of a Judicious teacher they must Ihj a great help to students of history.— Tho9. Hammond, ILM. Aylmer P.S. Cirasplng points supplied. The History Notes, I am sure, cannot fail to meet the approval or teachers, especially in the public school, where the leading events of Canadian and English History are required. This little book is ad- mirably adapted to the needs of the teacb(!r, since History can be taught to young pupils only by providing them with grasping ix>ints whereby they may retain the hold they get during a lesson, and your book supplies tliose points.— A. H. KiL- MAN, Sidgeway P.S. Fill an Important niche in review. I exnect to find the Notes on His- tory till an important niche in the review lessons on that subject.— I >. M. WalkisIc, M.A., Head Master, Preacott. W. J. GaQE * Co.'m PuBLItATlO.NX. Oage'H Kiijfllsh uud i'onaalaii HiMtory Note Book. "I hMvr »«>ld»ni ||H,| «„o piMrk,.,! |i, UM»rv ntler usiiix till* iMMlh." ROHKH J \V. HhKUIJ, Drayton. Piiiicipal Puhlic School, Jnul wliiit I hiiv4> been look* inx ror. The History is soriii'tlilii)? oxcel- l has tins siiltjcct ifi Itiuid. will HiKi the notes Injth <(.•. venlent and helpful in i)rei)arln>r his lesson and in os3iK:uhnr home vvork.-A. M«Kkk, Head Manter, Lxbrulge I'.S. drfiit iiMitlHluucc to lli«> leachi-r The History will he of great as- sistance to the teacher in nrepar- InK his notes. The tojiics are well '•hosen and the l)ooi{ is a goodout- 'ineot the suMect.-H. R. LONCIH. PrDi. Model School, Clinton. l*l«>aMr«l liifiit, I am particulai-ly pleased with the arrangement of the topics in the English and Canadian Hlstoi v Note Book. It will f,'reatly aiu tear KM s in saving' time, and all <«ndidittu3 preparing for examina- tion — trom promotion to senior leaving. It is an eminently prac- tical wprk.~B. C. H. Beckkh, Pitn. Brighton P. S. Will save time. t* v/l" save the teacher as well 'c > t upils ( great amount of yt\. )Je tfir J. \V ith present te.xt Tt.; 1 " .4,iiry. inipils 'equire an <:■"<■ jpt;^iiia and au 'Plirldged dv ■!:,:: TV to arrive u:' .he niean- i^lf of . le language.— J. G. Car- RUTHEH^. Prtji. Oauuga p H w)th (lie nrrniigv Probal»l4> it Mill iK> ndopti-\«'«>l It'll t Hii|i|ileiiiriit to IliKli Mfhool HlHtory. An immense saving of time is afforded by the use of Gage's New EiiKMsh and Canadian Hlsforv Note Htiok. An excellent supple- ment to High School Historv. Plan unsurpassed.-E. R. With- KHit., Prin. Westport P.S. mil «lo away ivltli writliiir IIUlCM. The use of your History Note Book will do away with the writinir of ehUwrate history notes that we have always had. The blank space leaves room for earl' unrl.r's \\\- (liviiiuality to show ia pluclng his oivn special, and to'iim nmn i;.|.t. in)te.« along side "i vouv reu T.il P.S., LaiiCanftir. I!av«> iH'vcr met any work to <' Hcad'.water «^ W. J. Gaob a Co.'8 Publications. Gage's Practica l Speller. Authorised by the Council of Public Tn$t ruction, Quebec ^^^)^r':^i::"!:^^hX^l!:^^{^^^ Aulhonzed/or use i» the Schoola of New Brunswick la uted largely tn the Province qf If ova Scotia A series of gnvded les^-ons suitable for higl. aiul public .cIk)o1«. with xvoids In Kciifrnl use. witli abbreviations, vM:, words.,, similar pronunciation and different spelling, a collection of the most Mfflcult words In the English language, and a nunU)or of literary seiectlons which may Ih; used for dictation lessons and committed to mnn, ry by the pupil. toRether with Latin and Greek roots, affixes ami p. Axes most freq jcntly found In the Public School Reader, looth thou and. fncc 30 cents. mHE old-fashioned S,,elllug Iwok has iK^en discarded by teachers «,.,. J. erally Many valid objections were properly urged against its u .0 and It passed away. . l!!"^.? '^.T- Uiifortunately for the old sfmlllng »«ok, it was ass.. elated with all the folly and weakness of "oral spelling," and thirJrl accounts for its rejection. '^" -^ What have the relormers given as a substitute for a speller? Thev took our brernl and h .vo given in return but a stone. The bread, even though a little stnl. was much more wholesome than the stone. In Can- ada , purls of the lessons to be found In the Readers are taker, as dictation lessons, and the pupils are turned loose on society to shock It by their Imd spell iig, and disgrace the schools which they attended and In which thev should l.;vo been taught. The Readers do not contain all the words boxs »ll.f ?r " ^ '"f '" "^"'' '^•"^ "■ "'«y 'l'^' "'« lessons are not arrange,! in proper lonn for spelling lessons. Only a con.paratlvely small portion of the Readers can be written from dictation in school. Bad a.s were the old spellers they were inllnitely better than nothing. This fact Is now recognized in Great Britain and the United States, In both of which TOuntries many valuable spelling books have recently been issued. That «Z/rT.,"c'''''?''^J" ^"^'^"'^ '' ^^'^'"•'y ''''''^" ''y the fact that at a recent Civil Service Examination " no less than 1,861 out of l.!»7a failures were caused bi bad siiel ling." «»'iurB8 A practical dictation Speller Is clearly a necessity, and this work has been prepared to supply an obvious want In the programme of Canadian schools. The claim to the name '• practical " is based on the fact that It Is not a mere collection of thousands of "long-talled wonJs In oaity and ation, but conUIns a grn,Jed series of lessons to teach th« minil- th« proper spellinif of the words ail have to use. ' " W. J. Gaob & Co.'s Publications. Gage's Practical Speller. A superior IMtle work. The " Practical Speller " i? a su- perior little work, and ahould find Its way into every public school. The plan is ingenious and tor aught I know may be original.— J. »• Carbon, inspector P.S., Stram- roy. Jast what Is wanted. The •' Practical Speller "appears to be just what is wanted. -Bkv. W. Pilot, Suvt. Church of England Schools, St. Johns, Hf.wfownd- land. Particularly pleased wllh it. I am particulary pleased with the arrangement of exercises and the chSclof wonis in every-day use, ST well as the high character of many of the literary selections. As a hand book both for oral spelling and dictation, the book merits a place in every school. -O.JJ. Platt, B. a.. Inspector P.S., Ptc- ton. Very suitable. " It is very suitable for the object in view."— Canada Presbyterian. Is a necessity. "The 'Speller' is a necessity and we have seen "obook which we can recommend more heartily than theone before us. "-Pre8bl/«ertan Witness, Halifax. Correct blending system. As a rule masters follow only the dictation plan, hence there can be little doubt that the notoriously bad "pellingon the part of the most stu- Tute of the^present day;l8 due to a neglect of the oral method. A coi ■ ?|?t blending of the two s.Y8tem8 is Arrived at^ in Jh.s work -Sam. HuoHKS, Toronto Coll. Inst. •Well pleased with It. I am well pleased with it. I en- dorse every woi-d in the preface. I '*?!.?^ in,/f^ POO u intixxluced In oVPrV flCliooi'.-N. M. CAMPBKLL, K Co! Elgin Model School. No rules. Among the many advantages this text book possesses above all others with wlilch I am familiar, is the noteworthy fact that it contains ««« a single rule/or spelling.— xf . V. MACKENZiK, M.D., I.P.S.,Parr8- horo, N.S. simplicity. The "Practical Speller " In an admirable work ; its arrangement and simplicity commend itselt to a teaohci-s as a text-l)Ook, aiul to all others who are desirous of acE, H.M., Central School, Sherbrooke, Que. Admirable work. I consider It an admirable little work. The chapter on Simi ar Sounds is a partlculariy valuable one. -HOWARD Muuuay, Prm. Academy, New Glasgow, M.ii. Reeommends it. I am much pleased with it. I like the plan of grading the lessons, and also the classing ot woi-ds oertaia- ing to certain trades, professions, etc I have found It very useful in dictation exercises. Have recom- mended it to several teachers.— b.. J. LAY, Prin. Academy, Anna- polis, N.S. Combination of excellencies. The grouping of words In com- mon use, the reviews, the dictation exercises and literary selections are all admirable, and form a combina- tion of excellencies not surpassed in any book of the book of the kind that I have ever inet with.-A. C- A. DOANE, I.P.S., Barnngton, N.S. Excellent work. I can truly say I think it a very excellent work. The preface is very valuable both for teachers ad pSpils, and if it could be pnerany intWuced into our schools, I have no doubt that tlie results. would^ »atistacror>-. ,f'5"''if'o'' ' ' Wol/ville College, N.S. V Y