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Tous les autres exemplairas originaux sont filmds en commenpant par la premidre page qui comporte une empreinte d'impression ou d'illustration et en terminant p^r la dernidre page qui comporte une telle empreinte. Un des symboles suivants apparaitra sur la dernidre image de cheque microfiche, selon le cas: le symbole — ► signifie "A SUIVRE", le symbole V signifie "FIN ". Les cartes, planches, tableaux, etc., peuvent dtre film6s A des taux de reduction diffdrents. Lorsque le document est trop grand pour dtre reproduit en un seul clich6, il est film6 A partir de Tangle sup6rieur gauchd, de gauche k droite, et de haut en bas, en prenant le nombre d'images ndcessaire. Les diagrammes suivants illustrent la mithode. 2 3 5 6 ii wmmmm< iPiiiii /■ I »'•' V ;,:vS 0^ i'l .j\ V. I .*^ I yA\ y ^^ l! 'Wv ^ ^A/PM./ W-w. , l,^^' * f ^ PrI • SCHOOL HELPS" SERIES. ARITHMETIC EXERCISES FOR FOURTH BOOK CLASSES, BY G. E. HENDERSON, Editor of The Canadian Teaihir" and " The Entrance." AND VV. E. c; ROVES, Principal of Church Street Moiiel He/tool, Toronto. Price, 16 cents; Teachers' Edition, with Answers. 20 cents THE EDUCATlONAI, PUIiLISHING COMPANY, . Toronto, 1897. PROVINCIAL LIBRARY VICTORIA, B.C. 6* C, mm Entered accordiiiR to Act of the Parliament of Canada, in the year one thousand eight hundred and ninety-seven, by (Jko. E. Hknuekson and VV. K. Gkovks, at the Dei>artment of Agriculture. PREFACE. r one and The authors of this series of Arithmetic " School Helps " offer no apology to the school public for the placing of their books as candidates for popular favor. The several numbers of the series are prepared by teachers actively engaged in the busy work of the schoolroom, and as teachers they know the great difficulty that the average teacher encounters in the presentation of new and crisp problems for his Arithmetic classes. The authors would most respectfully request a consideration of the foUowmg points in connection with their series : — I. Mechanical Work. After pupils have passed the Second Reader the usual text books provide but very scanty practice in the mechanical operations. Pupils instead of l)ecoming swifter and more accurate as they advance in years frequently lose the speed and accuracy which they had acquired in the lower forms. To meet this difficulty the present series provides over 5,000 operations in mechanical woik, which the teacher will find tested for him without the labor (and loss of time) of performing the work himself. This feature alone should commend the present series to every teacher of the subject. , II. No Ansvtrers. In the Pupils' Edition no answers are provided ; the Teachers' Edition alone contains the answers. III. Saving in Time. The ^>:.ie of the teacher is too valuable to be taken up in the dictation of problems to a class, when for a mere trifle each pupil may be provided with a set of exercises for himself. msma W d IV. Writing. The possession of these excrci.ses by the .scholars will tend to preserve his handwriting — it prevents the nia>l rush in copying questions from dictation. V. Understanding of Terms. Without giving formal definitions of terms, problems are specially constructed to fix ill the pupil's n^ind a thorough understanding of the technical terms of Ariwimetic. VI. Mew Problems. The great majority of the problems of the series have been written specially for these " School Help-." They are not simply a re-arrangement of old, slert^olyped problems. \II. Problems Grouped. The problems are not arranged in the ordinary ".hit and miss " fashion, but are groupetl according to types, and carefully graduated in degree of difficulty. VIII. Time Tests. The purely mechanical operations of addition, subtraction, etc., are intended to be done at a pupil's best speed, a specified time being allowed as the teacher's experience finds suited to the ability of his class. IX. Book of Exercises. This series is not in any sense designed to displace either I he teacher or the authorized text. There is no attempt to show how to teach ; this is taken for granted. It merely furnishes ready to the teacher's hard bright, crisp, new problems with which to enforce his teaching. Tiiic Authors. g» M Toronto, August, 1897. CO hi sti cu to ca th #n Arithmetic for Fourth Book Classes. I.-INFORHATION. $1 — lo dimes = loo cents - looo mills. Contains 22*A grains |)ure K*>l I gallon pure water at 62" weighs 10 lbs. 1 cubic foot of pure water contains loooozs. = 62>^ lbs. II.— PRELiniNARY EXERCISE. (i) In a trial trip a torpedo boat made 33 knots in an hour. Express this in statute miles. (2) A ship's sounding line registered 6748 fathoms. Express this in miles, rods, etc. PRELIMINARY EXERCISE. tcept 1700, oard . lbs. itol il. nded (3) Bought 1000 tons coal at $3.50 per long ton, and sold at $5.25 per short ton. Find my gain. (4) A race horse was sold for 455 guineas, and pay- ment was made in an equal number of ;^io notes, sover- eigns, crowns, and half-crowns. P'ind the number of each. (5) Express 4 miles, 151 rods, 3 yards, i foot, 6 inches in metres. (6) A surveyor's book showed the dimensions of a rectangular township to be 560 chains by 480 chains. Find the area in acres. (7) A j)ile of stone 36 feet long, 16 feet wide, and 4 feet high is broken at $2 50 per cord. Find the bill. (8) A commission merchant sold 124 cheeses averag- ing 48 lbs., at 9X^1- per lb. Find the value of the sale in Canadian currency. (9) Wheat is ouoted in Liverpoo! at 24 shillings per quarter. P^ind the price per bushel in cents. (10) A provision merchant bought flour Oi^ $4.96 per barrel, and sold it retail at 45 cents per stone. Find the gain on a sale of 1 5 barrels. III.— PRELiniNARY EXERCISE. leas. i lbs. n an oms. (1) Freight was charged at the rate of 21 cents per cwt. on beef and salt. Uf two merchants, one bought 40 bbls. salt, and the other 4c ,is. beef. Find the difference in their freight bills. (2) A bin of soft coal contains 3327 cubic feet. Find its value at $3.50 per ton of 2000 lbs. (3) 168 bushels of oats worth 21 cents per bushel are exchanged for an equal weight of rye worth 43 cents per bushel, the balance to be paid in cash. Find that balance. (4) A druggist buys c|uininc at $3.50 per pound Avoir, and sells it for Jo. 72 per oz. Troy. Find his gain on a purchase of 4 lbs. (5) WHiat is the least distance which can be exactly measured when we use the yard, the rod, the fathom, the chain, as the units of measurement ? 16 AklTHMETlC (6) What is the least sum in Canadian currency whiich can be exactly measured, using guineas, sovereigns, crowns, half-crowns, and shillings as the units ? (7) One day's operations on the Chicago wheat ex- change amounted to 240492 centals. Express this in bushels. (8) What price per cental is equivalent to 54 cents per Inishel ? (9) Find the number of barrels in a circular cistern of 4'8"diameterand83. 1822 inches deep, (i gallon = 277.274 cubic inches). (10) A water-works coal shed in Toronto is 125' x 112' and the coal is 23.10416 feet high. If it be filled with Anthracite coal @ $3.25 per ton, find the bill charged to the City of Toronto. TIME TESTS IN ADDITION— SHEET I. Third Rook Scholars should aim to do each of these additions in 1 X minutes, and Fourth and Fifth Book Scholars in 1 minute. Take, say, not more than i or 2 at any one time. (0 (2) (3) (4) (5) (6) 57986 68795 76859 89765 65789 59678 79865 86795 68597 97658 57896 96785 986; 7 67958 85976 76589 78965 67859 86579 79586 59768 65897 89657 78596 65798 95867 97685 58976 96578 85067 57986 58679 76859 8976=; 65789 59678 79865 86795 68597 97658 57896 96785 98657 67958 85976 76589 78965 67859 86579 79586 59768 65897 89657 78596 65798 95867 97685 58976 96578 85967 57986 58679 76859 89765 65789 59678 79865 86795 68597 97658 57896 96785 TIME TESTS IN ADDITION. tt (7) (8) (9) (10) (n) (12) 98675 86759 67598 75986 59867 57689 86759 67598 75986 59867 98675 76895 67598 75986 59867 98675 86759 68957 75986 59867 98675 86759 67598 89576 59867 98675 86759 67598 75986 95768 98675 86759 67598 75986 59867 57689 86759 67598 75986 59867 98675 76895 67598 75986 59867 98675 86759 68957 75986 59867 9867 j 86759 67598 89576 59867 98675 86759 67598 75986 93768 98675 86759 67598 75986 59867 ■ 7689 86759 67598 75986 59867 98675 76895 («3) (14) (15) (16) (17) (.8) 76895 68957 89576 95768 86579 65798 68957 89576 95768 57689 65798 57986 89576 95768 57689 76895 57986 79865 95768 57689 76895 68957 79865 98657 57689 76895 68957 89576 98657 86579 76895 68957 89576 95768 86579 65798 68957 89576 95768 57689 65798 57986 89576 95768 57689 76895 57986 79865 95768 57689 76895 68957 79865 98657 57689 76895 68957 89576 98657 86579 76895 68957 89576 95768 86579 65798 68957 89576 95768 57689 65798 57986 . IV.- -L.C.M. AND G.C.M. Find the L.C.M. of : (') A.11 the prime numbers between 1 1 and 29 inclusive. (2) 11.^, Hh I 8,^, 19R. (3) 37, 43, HI 129, 185, 215. ■,** 12 ARITHMETIC (4) 5 guineas, "jY^ sovereigns, 5 crowns, 8 half-crowns, 5 shillings. (5) 5 oz. Troy. 8 oz. Avoir. 4 drams. Apothecaries. Find the G.C.M. of: ^6) 21087 and 10989. (7) 41829 and 1 66 1 7. (8) 2193, 2967, and 3999. (9) $16.25, $21.25, and J28.75. (10) 1507 yds.; 2 miles, 1549 yds. 1 1 1 rods, Yi yd. and 3 miles, v.— L.C.n. AND Q.c.n. (i) What length of board would make fencing for fields having sides 22 1 ft., 299 ft., 611 ft., 1261 ft., or 741 ft., without waste ? (2) What is the least sum of money with which I could buy horses at $120, oxen at $84, cows at $36, or sheep at $18 ? (3) What numoer will divide 153 and 566, leaving as remainders 10 and 7 respectively ? (4) A lady desires to purchase cloth which may be cut into lengths of 5, 6, 7, and 8 yards, without any waste. What is the least number of yards which she can purchase ? (5) What must be the least length of a box which will contain blocks 4 in, 6 in., 8 in., or 10 in. long, wit' -"'^ loss of space ? (6) What is the least sum of money with which I can purchase horses at $i54f, oxen at $io2';f, cows at $45, or sheep at $21'^? (7) What is the least number which may be divided by each of the following numbers and leave a remainder of 27 in each case 1—36, 72, 108, 144, and 180 ? (8) A merchant has three portions of flour, containing respectively 1457 lbs., 2491 lbs., and 3337 lbs. He has only one size of bag above i lb., which might be used in putting up the three lots of flour without leaving any ovijr. What weight of flour will the bag contain ? ''■*',*■ L.C.M. AND O CM. 13 (9) A certain number will divide 17167 and 23032, leaving as remainders 104 and 93 respectively. Find the number. (10) A rectangular yard is paved with square granite blocks. The yard is 23 yds., i ft., 7 in. wide and 24 yds., 2 tt., 3 in. long. Find a side of the largest block possible to use. VI.— L.C.n. and Q.C.H. (i) I was told to find what number would divide 151, 403 and 562, leaving as remainders 8, 12 and i 1 respect- ively. I ct)uld not find such a number. Can you ? If you cannot, explain why. (2) A, H, and C walk together and take steps of 27 inches, 29 inches and 31 inches. Mow many limes will all three step at the same instant in a walk of 4 miles, 313 rods, 3 yds., 2 ft., 3 in. ? (3) 15120 is the L.C.M. of 12, 18,36,^3, 54,60, and another number prime to them. What is that number.-* (4) The product of three numbers is 66096. One-half of one of the numbers multiplied by one-third of the second is 153. Find the third number? (5) Three numbers between 40 and 170 have 15 for their H.C.F. and 3465 for their L.C.M. Find the numbers. (6) The (].C.M. of two numbers is 93, the L.C.M. is 325=:. Find the numbers. (7) What is the least number that, when divided by 217, 341, 403 or 527, will give 27 as remainder in each case ? (8) IJy what number must 1999 be divided that the i|uotient and the remainder may be the same as the quotient and remainder in the division of 109 by 1 1 ? (9) Find the least numbers whicli taken from 893 and 967 respectively, leave remainders of which 7 is a measure. (10) Uox A contams 22 bush., 3 pks. ; bo.\ B contains 26 bush. ; box C contains 29 bush., r pk. ; bo.\ 1) contains 32 bush., 2 pks. How many pecks would the largest sack hold which would exactly measure the contents of ^ny of the four boxes ? ■ I I ! I- ■ TIME TESTS IN AUDITION. (0 (2) (3) (4) (5) (6) 79865 98657 95768 57689 69587 95876 98657 86579 57689 76895 95876 58769 86579 65798 76895 68957 58769 87695 65798 57986 68957 89576 87695 76958 57986 79865 89576 95768 76958 69587 79865 98657 95768 57689 69587 95876 98657 86579 57689 76895 95876 58769 86579 65798 76895 68957 58769 87695 65798 57986 68957 89576 87695 76958 57986 79865 89576 95768 76958 69587 79865 98657 95768 57689 69587 95876 98657 86579 57689 69587 95876 58769 (7) (8) (9) (10) (II) (.2) 58769 87695 76958 96785 67859 78596 87695 76958 69587 67859 78596 85967 76958 69587 95876 7S596 85967 59678 69587 95876 58769 85967 59678 96785 95876 58769 87695 59678 96785 67859 587^)9 87695 76958 96785 67859 78596 87695 76958 69587 67859 78596 85967 76958 69587 95876 78596 85967 59678 69587 95876 58769 85967 59678 96785 95876 58769 87695 59678 96785 67859 58769 87695 76958 96785 67859 78596 87695 76958 69587 67859 78596 85967 (13) (>4) (■5)' 7i6) (17) (i8)~ 85967 59679 96795 67959 79596 95967 59678 96795 67959 79596 95967 59679 96785 67959 79596 95967 59679 96795 67859 79596 95967 59679 96795 67959 78596 95967 59679 96795 67959 79596 85967 59679 96795 67959 79596 95967 59678 96795 67959 79596 95967 59679 96785 67959 79596 95967 59679 . 96795 67859 79596 95967 59679 96795 67959 78596 95967 59679 96795 67959 79596 85967 59679 96795 67959 79596 95967 59678 96795 67958 79596 95967 59679 u MEASURES. 15 VII.— HEASURES. (i) A b.ittle-ship under trial steamed 22 nautical miles (6086 ft.) in an hour. Kind her rate in statute miles. (2) Find the cost of wire necessary for fencing both sides of a railroad 50 miles long, 6 strands high, at 4 cents per lb. -I rod of single strand wire weighs i lb. (3) Ice expands ^\, in freezing, and a cubic foot of water weighs 1000 oz. Find the weight of the ice on a pond 242 ft. X 384 ft. and 9 in. thick. (4) A bar of iron 1 inch scpiare and a foot long weighs 3>^ lbs. Find the weight of a piece 8 ft. long and iyi" x (5) h rom Wingham to Clinton, a distance of 24 miles, the Huron County Council let a contract for gravelling the roadway, 12 ft. wide, and 9 in. deep, at 15 cents per cubic yard. Find the contractor's bill. (6) A boy takes 1320 30-inch steps in going round a rectangular Held 220 yards wide. Find the area. (7) Find the cost of digging a cellar 27' x 3O' and 7/^' deep at 35 cents per cubic yard. (8) A grazing farm of 259 rods x 407 rods is divided into square fields of the largest possible size. How many fields "^ (9) A man sows 2 lbs. timothy seed on every 121 sq. yds. of his ground. At $5 per bushel find the cost of seeding 10 acres. (10) I lb. thread made 3 yds. cloth 27" wide. Find quantity needed to make 1 5^ds., 45" wide. VIII.— HE/iSURES. (1) A man sows 12 oz. wheat on a sq. rod of his farm. How many bushels would a Manitoba farmer require to seed a section ? (2) From a patch of oats i yard square, there was harvested i quart. What rate per acre is this ? (3) Hought sugar for $65.00 per ton and sold it at the rate of 7 lbs. for 33/4^ cents. Find gain per cent. i6 ARITHMKTIC (4) For every 3 oz. of ^'recii tea in a mixture of 24 lbs. there are 5 oz. of bla«:k. Kind the number of lbs. of eath. (5) Houj^ht 37 tons, 15 cwt. bran for $377.50, and sold it at 75 cents per < \vt. Find ^'ain. (6) A grocer sold four lots of tea weighing respectively, 6 cwt., 39 lbs., 13 oz. ; 6 cwt., 64 lbs., 15 oz. ; 13 cwt., 93 lbs., 7 oz. ; and 7 cwt., 94 lbs., 11 oz. Find the weight of the tea sold. (7) 1869 sovereigns arc coined from 40 lbs. Troy of gold. How many could be coined from 40 lbs. Avoir.? (8) What fraction of 4 lbs., i oz., 8 dwts., 15 grs. is i lb., I oz., 9 dwts., 15 grs .? (9) Fxpress 1 oz. Troy as the decimal of i lb. Avoir. (10) lU)ught at the rate of $2.00 per oz. Troy, at what price per lb. Avoir, must 1 sell to just recover value ex- pended ? IX.- riEASURES. (1) Find the cost of oats for 12 horses, 8 weeks, if 3 times per day they are each fed Yz gallon, which costs 25 cents per bushel. (2) Exchanged 40 pks. clover seed worth $4 perlnish. for manure at 60 cents per cwt. How much manure was purchased ? (3) Which is the cheaper, wheat at 58 cents per bush., or at 96 cents per cental ; and what would be the ditifer- ence in buying wheat enoug^ to seed 12 acres, allowing 2 busliels, 40 lbs. to an at re ? (4) 3 lbs. wheat makes 2 lbs. flour. How many barrels of flour can be made from 147 bushels of wheat ? (5) A bin is 12' x 1 1', 6>^" and 6' deep. Find the value of the wheat it will contain at (to cents pc bushel. (6) A dealer sells to five customers respectively, 4 gals., 3 qts., I pt. ; 3 gals., i qt., I pt. ; 10 gals., 3 qts., 1 pt. ; 14 gals., I qt., I pt. ; 7 gals., i qt., i pt. of maple syrup. Find the amount of the sale. (7) A water tank 10 ft. x 6 ft. contains 3000 gallons. Find the depth of the water, (i cubic ft. -62^2 lbs.) MEASURES. 17 (8) A liquor dealer has an equal number of half-pint, pint, and quart bottles which he exactly fills from a barrel of wine. How many bottles of each kinci has he ? (9) A hhd. of brandy costs $220.50. Find the selling price of a 5-gallon cask to gain 'j of its cost. (10) Find the quantity of water added to a barrel of $4.20 brandy so that when sold for $4.41 per gallon there may be a gain of X of cost. X.— riEASURES. per per per Note. — For the greater part of this exercise we desire to make due acknowledgment to the "Canadian Teacher" of April 15, 1897. Calculate answers to nearest cent. (i) What is 2896 lbs. of wheat worth at 78 cents bushel ? (2) A farmer sold 6859 lbs. barley for 43 cents bushel. How much was received for it ? (3) Exchanged 1726 lbs. wheat worth 81 cents bushel, for 2584 lbs. oats at 37 cents per bushel, the balance to be paid in cash. Find cash paid. (4) A gardener sowed i >^ acres with onions, and weighed the crop off one sq. rod, and found it yielded 93 lbs. What was the whole crop worth @ $1.^5 per bushel, if each sq. rod yielded as much as this one? (5) Find the total value of 1650 lbs. Indian corn @ 44 cents per bushel, 1368 lbs. peas @ 58 cents per bushel, 1924 lbs. buckwheat @ 61 cents per bushel, 743 lbs. timothy seed @ $4.30 p' , bushel. (6) The following crop was taken off a field of potatoes, the wagon and its contents being weighed for each load: 1st load, 2146 lbs. ; 2nd load, 1963 lbs. ; 3rd load, 2345 lbs. ; 4th load, 1874 lbs. ; 5th load, 2740 lbs. The wagon weighed 739 lbs. What was the crop worth at 38 cents per bushel ? (7) ^ of a lb. of rye was sowed on each sq. rod of a lo-acre field. The total yield was 16800 lbs. Find the profit on the field allowing $20 for labour and marketing, when rye sells for 42 cents per bushel i8 ARITHMKTIC (8) How many lbs. of flax seed worth $1.50 per bushel will pay for 6528 lbs, of oals at 25 cents per bushel ? (9) On a fiefd 120 yards by 242 yards there was raised 27 tons, 720 lbs. of carrots which sold for 1 5 cents per bushel. At the same rate find the value of a similar crop on a I co-acre farm. (10) Find what weight would exactly measure 28 bushels of oats, 42 bushels of barley, and 70 bushels of hemp seed. XL— HEASURES. (i) By how much does 7 hrs., 14 min., 26 sec. exceed 325 min.? (2) By what was 3 weeks, 6 days, 23 hrs., 15 min., 20 sec. multiplied to give 39 weeks, 6 days, i6 hrs., 33 min., 20 sec? (3) Vi o^ the time from noon till now is i "^ times the time from now to midnight. What is the present time ? (4) A boy resolves that each day he will go to his studies 20 min. earlier, and will remain 20 min. later. Allowing 44 school weeks to a year, how much time does he gain in his High School course of 5 years, counting 6 study days in each week during the school term ? 4 yards wide costing $1.40? Kind the difference in the cost of carpeting a room 12 feet X 18 feet with carpet as described above, the carpet run- ning lengthwise. (4) 12 barley grains laid side by side make i inch and they are X of an inch in length. If 2400 of them fill a pint measure, find the quantity which would cover one acre. (5) Find the value of the turnips grown on a lo-acre field at 10 cents per bushel, if on a patch 22 yards square there was grown i ton, 16 cwt. (6) Ice expands ^ in freezing, and a cubic foot of water weighs 1000 ozs. Find the weight of the ice on a pond 242 ft. by 384 ft. and 9 inches thick. (7) Find the cost of digging a cellar 54 ft. by 3^ it. and 7^2 ft. deep, at 35 cents per cubic yard. (8) A bar of iron an inch square and a foot long weighs 4)4 lbs. Find the weight of a piece 8 ft. long and having an end 2}i"x2)4". (9) The G.T.R. ran the full length of a man's farm iX miles and took a strip 4 rods wide, for which it paid at the rate of $150 per acre. How much did it pay him.? (10) Find the G. CM. of 14 inches; 6 ft., 5 inches; 21 yds., - ft., II inches ; 2 rods, 3 yds., 7 inches. XIV.— MEASURES. . ' (i) The fore-wheel of a carriage is 7' in circumference and makes 792 more revolutions than the hind wheel in a trip of 3 J^ miles. Find the circumference and the dia- meter of the hind wheel. MEASURES. 21 (2) I set my watch at noon on Saturday, and at 10.30 a.m. on Monday it had gained ^'/i minutes. What will be the real time on Tuesday when my watch is at 3.30 p.m. ? (3) The product of the tst and 2nd of three prime numbers is 377, of the 2nd and 3rd is 481. Find the numbers. (4) By what factor will the number of ounces in i ton, 19 cwt., 2 qrs., 3 lbs., 8 oz., require to be multiplied to give a product equal to the number of inches in 12 miles, 7 fur., 33 rods, 2 ft., 10 inches. (5) Seven trucks of coal weigh 31 tons, 3 cwt., 3 qrs., 6 lbs. ; two of them weigh 7 tons, 17 cwt., 2 qrs., 18^2 lbs. Find the average weight of each of the others. (6) A boy rolls his hoop, the circumference of which is 5 ft. 6 in., a distance of 1^ miles. How many times did it turn ? (7) The town of Wingham let the contract for granoli- thic w.alks 8 tt. wide on both sides of a street, ^4 of a mile long, at 10^ cents per square foot. Find the contract price, allowing for kcrbing at 75 cents per linear yard, and six street intersections, each 45 ft. wide. (8) The "Daily Mail and Empire" publishes a daily edition averaging 12 pages of 18 in. by 24 in. Find the area covered by a yearly edition of 313 issues, if the avemge daily issue be 24200 copies. (9) A roadway 35 ft. wide is made directly through the middle of a square field of 140 yards side. What fraction of the field was taken for the road ? (10) Quebec City, Canada, and Valparaiso, Chili, are situated on the same meridian line, but the latitude of the former is 46°, 45 mins. north, while that of the latter is 32", 45 mins. south. Find the distance they lie from each other measured along the .ame meridian line, if a degree of latitude measure 69 miles, 60 rods, 4 yards. TIME TESTS IN ADDITION. (I) (2) (3) (4) (5) (6) 98758 87589 75-98 58987 89875 87967 87589 75898 58987 89875 98758 79678 75898 58987 89875 98758 87589 96787 58987 89875 98758 87589 75898 67879 89875 98758 87589 75898 58987 78796 98758 87589 75898 58987 89875 87967 87589 75898 58987 89875 98758 79678 75898 58987 89875 98758 87589 96787 58987 89875 98758 87589 75898 67879 8987:, 98758 87589 75898 58987 78796 98758 87589 75898 58987 89875 87967 87589 75898 58987 89875 98758 79678 (7) (8) (9) (.0) (M) (12) 79678 96787 67879 78796 96876 68769 96787 67879 78796 87967 68769 87696 67879 78796 87967 79678 87696 76968 78796 87967 79678 96787 76968 69687 87967 79678 96787 67879 69687 96876 79678 96787 67879 78796 96876 68769 96787 67879 78796 87967 68769 87696 67879 78796 87967 79678 87696 76968 78796 87967 79678 96787 76968 69687 87967 79678 96787 67879 69687 96876 79678 96787 67879 78796 96876 68769 96789 67879 78796 87967 68769 87696 ('3) (•4) ('5) (16) (17) (18) 87696 76968 69687 59857 98575 85759 76968 69687 96S76 98575 85759 57598 69687 96876 68769 85759 57598 75985 96876 6S769 87696 57598 75985 59857 68769 87696 76968 75985 59857 98575 87696 76968 69687 59857 98575 85759 76968 69687 96876 98575 85759 57598 69687 96876 68769 85759 57598 75985 90876 68769 87696 57598 75985 59857 68769 87696 76968 75985 59857 98575 87696 76968 69687 59857 98575 85759 76968 69687 96876 98575 85759 57598 22 MEASURES. 23 XV.— FRACTIONAL PROBLEHS. (i) The sum of three fractions is iff. One-half the least isfVj. and one-third the largest is ff . Find the other fraction. (2) I have % of an acre in one plot, \^ of an acre in a second, W of an acre in a third, and 4/^ acres in a fourth. Find the value @ $96.00 per acre. (3) I exchanged 46 ^'^ bushels of oats at 23^^ cents for wheat at bxyi cents. Find how many bushels of wheat I bouL'ht. (4) (a) 7x3 (b) 7^3 (c) 7 + 3 (d) 7-3 8x3. '-' 8-1-3. ^''8 + 3. ^"'8-3. Find how much each of the foregoing differs from ^, and write any rule which you might deduce from the results. (5) Two men who are 79J miles apart travel till they meet, during which cne has travelled 7f miles more than the other. Find the distance tr?. veiled by each. (6) Reduce % f, ^, y\> to fractions having a lowest common denonimator, and arrange in order of magnitude ^o fractions having lowest common numerator. (8) After spending y% of n.y money, then % of it, and lastly % of what now remains, I have $92.82. What had I at first ? (9) I spent ^'^ of my money and had then $1378.48 more than I spent. Find original sum. (10) Find the value of HiJ - (l + t) + 2i-(i-i). XVI.— FRACTIONAL PRORLEHS. house be $1575. Find the (i) If J of the value of a value of three such huuces. (2) § of the cost of a steamer is $18000. I pay for a § interest in the vessel ? What should 24 ARITHMETIC. (2) What should I pay for f of a field, if ^ of its cost were 5^480 ? (4) If I of the cost of the fence round your school-yard were $35, find the cost of 'j of the fence. (5) What is the value of 3 of a British Columbia gold mine, if /^ of it could be bought for $1872 ? (6) If -g- of an insolvent estate be worth $3768, find the value of I of it. (7) What should be given for y\- of a farm if f of it sold for $7590.? (8) I of ^ of the cost of a house is $2472, find ^ of its value. (9) f of I of a load of gravel covers 14 square yards of walk, find number of loads needed to cover a yard, 48 yds. wide and 64 yds. long. (10) ^ of 6| times the cost of a factory is $33808. What is the factory worth ? XVIL— FRACTIONAL PROBLEMS. (i) I invest ^ of my money in farm stock, '}- of it I paid for the farm, the remainder $900 I put in the 'aank. Find the price of the farm, and how much money I had at first.-' (2) A boy spent J4.30 less than J of his money and had iio.45 left. How much money had he at first ? (3) A man who owns t] of a farm, sells i of his share for $4872. Find what I paitl for J- of tlie farm. (4) ^ of a piece of work can be done in 25 days, what part will be done in ^yl days ? (5) i of a gross of pens cost 75 cents, find the cost of 5 dozen at that rate. (6) How many words on 25 printed pages, if there were 350 on Jj of a page ? (7) A boy spent i of his money, iost | of the rcniainder, and had $2.73 left. How much had he at first ? (8) After spending $12 less than {J of my money I had $3 morQ than | of it left. Find the sum, FRACTIONAL PROBLEMS. as »f its cost hool-yard ibia gold ?, find the 1 if ^ of it d ^ of its e yards of I yard, 48 s $33808. s. '■>■■ ; tf it I paid tik. Find id at first .'' oney and rst? his share lys, what c cost of i, if there Mnainder, ney I had I of I of a cargo of tea, if a mer- sells 'i of |i of his share for (9) Find the value of chant who owns f of it $728.7S. (10) After seUing f of ^ of my land I have 42 acres more than .Pg of It remaining. Find the number of acres at first. XVIII.— FRACTIONAL PROBLEHS. (i) After spending iV of my money and $5 more, I have $1 less than | of my money left. What was the original sum ? (2) What number diminished by ^ of Jg"- of itself, will leave as remainder 148? (3) By selling ^ of my turkeys for $693, I would re- ceive 15 cents each less than by selling them for $787.50. Find the number of turkeys. (4) I sell goods at an advance of \ of the cost, but for cash payment I throw off Jr, of the selling price. Find W'hat fraction of cost represents the clear gain. (5) A docs ff of a piece of work, i> does '^ of it, C does J\ of it, while I) gets $14 for doing the remainder. Find the money paid A, 15, and C. (6) B gave away ^ of his money less J4, then spent $2 more than ^ of it, and had $20 left. Find the origuial sum. (7) After subtracting \\ of ij'l^ of a number and 5 more, there still remains 128. What was jf of the numijer ? (8) .^j of value of a house is equal to .\ value of its con- tents, } the difference of their values is $159. Find the values. (9) § of the cost of 4 lb. loaf is 5^ cents, find the value of the 2 II). loaf (10) 5 of the value of a barrel of apples is worth $1.33, how many barrels will cost $191.52 ? XIX. -REVIEW. (i) 2 the selling price of a piece of silk is equal to ^ of the cost, find the advance on the cost at which it sold. 26 ARITHMETIC. : (2) Bought syrup at 80 cents per gallon, J of it was lost thiough leakage. At what price per quart must I sell to gain ^ of the outlay ? (3) A can do a piece of work in 6 days, B can do it in 8 days. Find the time for both together to do ij of it. (4) Divide $275 among 3 persons, giving the first $2 for $3 given the second, and to the third -J- more than to the other two. (5) Two pipes feed a cistern which could fill it in 3 hours and 5 hours respectively, and a third v '.ich could empty it in li hours. If the cistern ijc full and all three pipes opened at once, in what time could it be emptied? 2I (6) --J of a pole is painted blue, § of the remainder is 9 painted red, and the rest, 27 feet, is painted white. Find the length of the pole. (7) From a bankrupt estate I receive $1.75 for every $4 owing to me, thereby losing $472.50. What was the debt ? (8) If 4 men or 6 women can do a work in 30 days» find the time required for 6 men and 4 women. (9) A certain piece of work can be done by 20 men in 16 days ; if after 5 days 9 men leave, how long will the re- mainder require to finish the work ? (10) Divide 1903 into two parts so that c~"i may be ^ of the other. XX-REVIEW. (i) $774 is the money invested by three young men in a business, the first has !f of that invested by the second, while the third invests $5 for every $13 put in by the other two, find the investments of each. (2) 12 men do J of a work in 3 days, after 4 days they are joined by three others, how many days will the work still last ? REVIEW. 47 (3) Sold a lot which cost me $903 gaining ^ of selling price ; also second lot which cost me $600 gaming } of the selling price. Find what friction of my invest- ment I gained. (4) After spending } of my money and $8 I had still left $1 more than ^ of it. Find my money. (5) A and B can do a piece of work in 6 days, B and C in 7 days, A and C in 6| days. Find the time when all work together. (6) Divide $1736 among three brothers in the propor- tion of .7, .14, .28. (7) I own J of I of a pleasure yacht and sell } of my share for $55. What would be demanded for a half in- terest in the vessel ? (8) Bought an equal number of horses, cows and sheep, paying therefore $1360, the horses cost $113 each, the cows $47, and sheep $10. Find the number of each bought. (g) I sold ^ of my sheep, then exchanged \ of the flock, then ^\ of them died and the remainder, 1 5 sheep, were worried by dogs. How many in the flock ? (10) Sold lead pencils at 10 cents a dozen, which I paid 75 cents per gross for. At what advance on cost did I sell them ? XXI.-COnPLEX FRACTIONS. The following complex fractions have appeared on the entrance papers during the past fifteen years. (I) Simplify (I x/TX^aXt¥j)-H of §. ;^I5 los. 2d. (2) Simplify/. (35 +9]^)^ 1*3 of I (3) Simplify /3 of A + J_; - 3 + i. l6s. 2d. 28 ARITHMETIC. I ! (4) SimplifyCif + lof ^^-|) -2/,V (5) What numberdividedby(,^4-,'3)-(3-i)x(J + i) will give A of 1^ of — 'J of 247 1 6J 11^ (6) Simplify & of 2 !? X 11 ^|of,8.^of^^ (8) Simplify |i±^f +|(||4.3i_,j)-(7^_6S)_9gg. (7) Simplifyiof3if--ilof^g+-Vof 6^-5i (9) Simplify I ^-f 39^' l6^ ia + 2i "^ ^^/ (10) Simplify 425. '5of5-74S' WEEKLY MAIL STATEMENT. Mon. 9243 659 2129 843 257 I 1698 Tues. 8564 827 2214 296 328 12325 Wed. 9204 655 1986 321 201 14276 Thurs. 7695 238 • 873 655 •99 16883 Fri. 7368 •346 989 495 276 17319 Sat. 9986 399 1655 378 301 20205 Total Ordinary lett'rs Registered let's Post cards Book packets. . Parcels Newspapers. . . Total ADDITION. 29 RELIGIOUS POPULATION OF A CITY. Ward Ward I 2 Episcopalian Presbyterian Methodist Baptist Roman Catholic Other Denominations. Total Ward! Ward Ward 3 4 5 38722147 6321 1986 32392196 92612489 2149 1987 867 326 3879 1895 2749 1986 2786 874 II46 1527 13742496 1849 7^3 3'23 974 726 1095 Ward 6 948 1347 I 148 875 Total 874 1947 589 843 AGGREGATE ATTENDANCE AT A PUBLIC SCHOOL. Division i Jan. Feb. 1040 1003 1113 1098 3 J2I4 4 I no 5- 6. 7- 8. Total 1224 1316 1097 1243 1 194 1 201 1085 1213 1 109 1046 Mar. April. May. June 947 959| 1087! 1038 1049; 1 118112431 1193 1 136 1 187 996 1179 1087 1058 1 196 1208 1096 1099 1153 1 198 1253 1179 1278 1257 ii57!ii95 1 196 1248 1187I1235 1249 1207 Total 30 AUrrHMKTlC XXII.— AREAS. (i) Find the area of each of the following : (a) 3' x 4', (b) 15 rods X 20 rods, (c) 35 miles x 35 miles, {d) 45 miles square. (2) Find the area of each of the following : (a) 3 yards X4 feet, (b) 16 rods x 5 feet, (c) 25 yards x 20 rods, (d) 2 miles x 200 rods. (3) Find the area of each of the following : (a) 5 yds. X4 ft., 6 in. (b) 10 rods, 5 yds. x 10 yds., 2 ft. (c) 3 miles, 200 rods x 180 rods, 5 yds. (d) 3 miles, 200 yds. x 2 miles, 100 rods. (4) Find the length when (a) Area=i440 sq. yds.; width = 36 yds. (b) Area = 270 sq. yds.; width = i5 feet. (c) Area = 27225 sq. ft; width = 6 rods, 11 ft. (d) Area = 8400 sq. yds.; width = 2 10 ft. (5) Find the second dimension, given (a) Area =10 acres; width = 220 yds. (b) Area=>^ acre; length = 165 ft. (c) Area = 8 acres ; width = 32 rods, (d) Area = 48400 sq. yds.; length = >^ mile. The following is a somewhat common type of problem in areas : The area of a field whose sides are as 3 to 4 is 3 acres, 4680 sq. yds. F'ind the sides. :, . '• . '' »■■' ■ ' ' (4) AREAS. 31 a) 3' X 4', {d) 45 ) 3 yards 20 rods. a) 5 yds. (c) 3 X) yds. X sq. yds. ; = 1 5 feet. I) Area = fV.rea = lo length = ) Area = type of es are as Area = 19200 sq. yds. Area =12 squares, per figure. .'.Area of small sq. ^i-'^Hp^ sq. yds. = 1600 sq. yds. Divide 1600 into two equal factors by process of fact- oring. Each equal factor is 40, a side of a small square, .'. end of figure = 40 yds. x 3= 120 yds., while side of figure = 40 yds. X 4= 160 yds. (6) The area of a field is 35 acres, and the length is to the width as 8 to 7. Find the sides. (7) A field of 8 acres has 4 times its length equal to 5 times its width. Find its sides. (8) Find the area of a field 30 rods x 40 rods. ^9) Find the area of a square field of 320 rods to a side. (10) What is the area of a block of land i mile square? XXIII AREAS. (i) What is the difference in acres between (a) i mile square and i square mile, (b) 2 miles square and 2 square miles, (c) 4 miles square and 4 square miles, (d) 6 miles square and 6 square miles, (e) 9 miles square and 9 square miles ? (2) A boy walks at the rate of 3 miles per hour for 2 hours round a rectangular block of land twice as long as wide. Find number of acres therein. (3) Find the area of a similar block he would walk round in twice the time. (4) How many town lots, each 4 rods x 5 rods, could be laid out in a block of land containing 24 acres, allow- ing X of the block to be needed for streets? (5) A rectangular farm cost $7806 at $65 per acre. Its width being 600 yards, find its length. (6) A sheet of glass 12 ft. long and 9 ft. wide is cut into panes 18 in. X12 in. How many panes are thus obtained, and what is the total distance in feet around them ? (7) The cost of a fence round a rectangular field 220 yards wide at 45 cents per rod, is $79.20. Find area of field in acres. 32 AklTHMETIC. (8) $102.50 is the cost at $H per rod of a fence round a rectangular field 176 yards wide. Kind the number of acres. (9) Find the area to be plastered in a room 15 ft. x 18 ft., and 10 ft. high, allowing for 4 windows 6 ft. X4 ft., 6 in., and 2 doors 4 ft. x 6 ft., 6 in. (10) What will be the cost of stone flags to pave a court yard 210 ft. x 324 ft., the flags being 2 ft. 6 in. by 4 ft. 6 in., and worth 62 j^ cents each .' XXIV.— PAPERING AND PLASTERINQ. In this exercise the papering questions are solved by the following rule : — " Deduct half the areas of the onf-.- ings in square feet from the area of the walls, also in square feet, and divide the remainder by 30. Take near- est whole number to denote number of rolls." The reason why all the area of openings is not deducted is because there is always waste in matching, etc., and why 30 and not 36 is used as divisor is that very few rolls of paper will run 24 feet or 8 yards, the length given in the Public School Arithmetic. 18 inches is the width for Canadian and American wall papers. The English width is 24 inches. The rule in quotation marks above is that given by one of the largest wall paper concerns in Canada. With 30-inch papers divide by 50 instead of 30. Why? Plasterers and painters deduct one-half the areas of the openings from the total area of the walls, and calculate the area to the nearest yard. We shall follow the same rule. (i) Find the cost, at 15 cents per single roll, of the paper needed for a room 15'x 12', and 9' high, allowing for 2 doors 7' x 3>^' and 3 windows 6>^' x 3J[^'. (2) Our school board decided to paper our school room with paper costing 30 cents per double roll. If the room be 24 ft. X 32 ft. and 12 ft. high, find the bill for the paper, allowing for 2 doors 4 ft. x y}4 ft., and 6 windows 4}^ ft. X9 ft. -_.;.• ;,. ^■.:-- -....:-; :;^-;--. ; nee round lumber of 15 ft. X 18 t. X 4 ft., 6 to pave a 6 in. by 4 solved by the op'-.- Is, also in Fake near- rhe reason is because hy 30 and 3 of paper the Public • Canadian ■idth is 24 that given n Canada. . Why ? e areas of d calculate the same oil, of the , allowing :hool room f the room the paper, iWS 4}4 ft. PAPERlNd AND PLASTKRING. 33 (3) The managers' board of a local church decided to decorate the church auditorium. The room was 60 ft. x 40 ft. and 18 ft. high. There were 8 windows 8 ft x 14 ft., 2 doors 8 ft. X 6 ft., and 2 smaller doors 3>^ ft. x 7 ft. The walls are covered with 30-inch ingrain paper worth 75 cents per roll, while the ceiling is covered with 30-inch paper costing 50 cents per roll. Find the bill for paper. (4) A library 12 ft. x 18 ft. and 10 ft. high is decorated with paper costing 25 cents per single roll, both walls and ceiling. There is a border 14 in. deep, worth 15 cents per yard, at the top, and a base-board of 12 in. at the bottom. Find the bill, allowing the paper to go within 12 in. of ceiling, the border covering the rest, 2 doors 7)4 ft. X 4 ft., and 3 windows 7 ft. x 4 ft. (5) Find the cost of decorating a room 30 ft. x 42 ft. 16 ft. high. The paper on the walls was 30-inch ingrain costing 75 cents per roll, the ceiling paper was 30-inches wide and cost 60 cents per roll. The border was 18 in. deep and cost 25 cents per yard. The labor cost 25 cents per roll for the paper, and the border 2 cents' per yard -allow a saving of paper equal to full depth of the border, 4 doors 8 ft. x 6 ft., and 8 wmdows 6 ft. x 8 ft. (6) Find the cost of plastering a room 20 ft. x 1 5 ft., and left, high, at 15 cents per square yard, allowing a base-board i ft. deep round the bottom, 2 doors 7^ ft. x 4 ft., and 4 windows 6 ft. x 4)4 ft. (7) Find the cost of plastering the walls of a room same as above, having only I door, 6 windows and no base board, at $.20 per square yard. (8) Find the cost of plastering a room 18 ft. X12 ft., 10 ft. high, base-board 12 in., 2 windows 6 ft. X4^ ft., i door 7 ft. X 4 ft., at 18 cents per square yard, and of painting the ceiling when dry at 1 5 cents per square yard. (9) Find the cost of painting both the interior and the exterior of a i octangular box without a lid. The box is made of 2 in. material, and its external dimensions are 2 ft. 6 in. by 3 ft. 4 in., and i ft. 8 in. high, and the cost of the painting is $.00125 P^'' square inch. 34 ARITHMKTIC. (lo) The roof of a Inirn is 62 ft. x 25 ft. to each side. Find the cost of British C^olumljia shingles, each 4 in wide and laid 5 in. to the weather, the row at the cave being laid double, that would be necessary for such a barn, if the price were $2.40 per 1000 shingles ? XXV.— PLOWING, REAPING, ETC. (i) A man turns a furrow of g in. How many miles will he walk in plowing a field 40 rods long and 20 rods wide? (2) A land roller is 6 ft. wide. How far does a man drive who rolls a field 80 rods long and containing 12 acres ? (3) The knife of a reaper is 4 ft. 6 in. wide, and the horses walk three miles an hour. If the working day be from 7 a.m. to 6 p.m., with a 2 hour rest at noon, when will be finished the reaping of an 18 acre field ? (4) A lawn mower is 18 in. wide, and a man pushes it at the rate of i >4 miles per hour. How much should he earn in a day of 10 hours, if paid $1.76 per acre ? (5) The plowman of No. i above walked 132 miles in plowing another field 40 rods wide. Find its length. (6) Find the cost of fencing your field in No. 5 above at 35 cents per rod. (7) Find the cost of wheat necessary to seed the above field (No. 5), at 90 cents per bushel, allowing 6 oz. grain to 1 1 square yards. Note. — Combine all the rec|uirements of 5, 6, and 7 above into one question. (8) An electric sprinkler in Toronto sprinkled the street car track allowance of 12 ft. If the car runs an average of 6 hours per day, and at the average rate of 5>^ miles per hour, find the area sprinkled during the months of June, July and August, allowing 13 Sundays in the quarter. _ . . (9) Ii round a rale of 6 number < days, the (10). an averai he has le of the rol COM PL H Clerk. A.H.. CD.. E.F.. C.H.. J.K.. L.M.. Daily tot Clerk. A.B.. CD.. E.F.. C..H.. J.K.. L.M.. Daily toi each side, each 4 in t ihe eave for such a ? ETC. T»any miles ;id 20 rods Iocs a man ntaining 12 de, and the ving day be noon, when 1? an pushes il li should he :rc? 132 miles in , length. No. 5 above ed the above r 6 01. grain 5, 6, and 7 prinkled the car runs an ;c rate of 5 >^ a^ the months [idays in the pr.owiNc, kKAi'iN(;, f.tc. .^5 (9) In printing wall-paper the blank paper is wound round a large roller. The paper is l)cing unwound at the rate of 6 miles an hour. If it be 18 in. wide, find the number of sc|uare yards of paper printed in a week of 6 days, the presses running 8 hours per day. (10) A contractor in levelling a road drives his horses an average of 2 miles per hour for 8 hours. In that time he has levelled with his roller 15J5 acres. Find the width of the roller. COMPLETE THE FOLLOWINC; SALES SHEET, HORIZONTALLY AND VERTICALLY: Clerk. A.B. CD. E.F. G.H J.K. L.M Daily totals . Mon. s c. 28 79 23 «7 16 99 29 13 18 47 19 02 Tues. $ 34. 30 27, 33 32 27 c. 71 03 Wed. $ C. 35-33 29.38 72130.81 29 06 Thur. 26.73 29.04I29 $ 30. 33' 30. 39. 34. c. 10 Fri. I S.->t. 27.97 84:26.77 1624.95 1728.47 45 04 28 29 88 5' 1$ 47 48 43 50 54 61 c. 81 77 07 05 39 93 Clerks' Totals. Clerk. .\. li CD K.F C.H J.K L.M Daily totals . Mon. Tues. $ C.!$ C. 95.6589.24 71.58 58.47 69.29 45.81 63.42 65.4 57-99 I Wed. I Thur. $ C. $ C 59.7978.04 Fri. Sat. 67.24 50.60 80. 0719 1 .87 93.5682.54 77.68 79. 18 62.49 71.08 93 74 57.96 86.60 $ c.|$ c 59.37198.16 67.02 51 .45 82.91 76 Clerks- Totals. 63 36 72. 12 87.3' 89 90.21 67 82 96 75 36 ARITHMETIC. Clerk. A.B CD E.F G.H J.K L. M Daily totals Mon. $ c. Tues. $ C. 65.95 24.89 58.71 41.65 47 -S^ 99-57 29.69 70.80 81.45 56-93 42.63 68.77 1 Wfid. I Thur. $ 79. 24. 67194. 26 50.6080.71 c.|$ c. 79,40.78 Fri. $ 37- c. 59 Sat. $ 89, 87.91 54.82 74-93 96.57 81.79I60.86 70.2642.51 91 .82J89.76 36.6321.90 12.72 96.67 31-87 75-82 Clerks' Totals. XXVI -AREAS. (i) A rectangular plot of ground 50 feet long by 40 feet wide is divided into four equal sections by paths running paii^'lel to the sides, and crossing in the middle of the plot, if the path be 10 feet broad, find the number of sods each I '4 feet by 6 inches necessary to sod the four smaller plots. (2) Find the cost of painting the walls and ceiling of a room 45 ft. X 54 ft., and 12 ft. high, at 15 cents per square yard, allowing for 2 do^rs 7 j^ ft. high and 3 ft. wide, and 8 windows y '.4 ft. high and 4'^ ft. wyde. (3) Find the difference in acres between a square having 4620 feet to a side and the largest circle which could be inscribed within it. (4) I have a board 8 in. wide and 16 ft. long. How much must be cut off one end to leave a surface (on one side) of one square yard ? (5) What would it cost at 24 cents per square yard to paint the exterior of a rectangular bo.\ with lid, 2 ft. 3 in high, 2 ft 6 in. wide, and 3 ft. long ? (6) I have two fields each of 10 acres. One has a width of 40 rods and the other of 32 rods. Find the differ- »">nce in cost of fencing the two fields at $.28 per rod o( 1 nee. Sat. Clerks' Totals. C. 9.61 2.51 9.76 I .90 6.67 5.82 AREAS. 37 ig by 40 feet ths running e of the plot, of sods eacli four smaller d ceiling of a is per square ft. wide, and en a square circle whicli long. How face (on one |uare yard to lid, 2 ft. 3 in One has f ind the differ 8 per rod of (7) Church street, Toronto, is i l/z miles long, and the track allowance for the street railway is 12 ft. wide. The track allowance is paved with granite sets, with a face of 8 m. X4 in. Find the cost of the sets necessary at $25 per thousand. (8) I have a field 2t6 yards long and 140 yards wide To accommodate my neighbor I allow him 10 yards off my width, if he allows me to extend my lot 1 7 yards to the rear. Is my area increased or diminished, and by how much? (9) How much carpet is wasted in carpeting a room 18 ft. by 2 r ft., with carpet 27 in. wide, running lengthwise (^ ft. x 18 ft. Find its thickness in the decimal of an inch. * (3) Find how many cords of 16 in. wood could be ob- tained from the followinij : — 6 pieces 18 in. x 15 in. to an end and 24 ft. long ; and 3 round pieces 28 in. diameter and 24 ft. long. (4) A round sti(k of timber 24 ft. long and 42 in. dia- meter floats with |j of its volume above the surface of the water. P'ind »he weight in tons of the log, (i cubic ft. of water weiglih 62, '/2 lbs.). (5) A rectangular cistern is 5 ft. 6 in. by 6 ft. 4 in. Find how many inches the surface will sink if 836 gallons be drawn off", (i gallon = 27714 cubic inches). (6) I ton hard coal contains 28 bushel of 80 lbs. to the bushel. Find the value of .> bin r^f coal 1 5 ft. x 14 ft. x 10 ft. at $5,54 'i per ton. (i bushel = 22 18 cubic inches). 40 ARITHMETIC. • '*■■■ 'i ^ ■^ ■■ ■ ■ '■>•■' • (7) Find the weight of a circular lead plate, 14 in. in diameter, and j^|^| inches thick, given lead 11. 4 times as heavy as an equal volume of water. (8) A cylinder of wood 4 in. to an end and 2 ft. long, was reduced till it was just two inches in diameter. Find what portion of the cylinder was cut away. (9) There are 46^ lbs of wheat to a cubic foot. Find the value of a bin of wheat 5 ft. 4 in. high, 6 ft. wide and 6 ft. 8 in. long, at 72 cents per bushel. (10) Water weighs 1000 ozs. to the cubic foot, and expands ^ in freezing. Find how many tons of ice can be stored in an ice-house 48 ft. long, 33 ft. wide and 20 ft. high. XXX. -CARPETING. A. — To FIND NUMBER OF YARDS. (i) How many yards of carpet i yard wide will be needed to cover a room 1 2 ft. wide by 1 8 ft. long ? (2) Find number of yards required to carpet a room 18 ft. X 24 ft. with carpet 27 in. wide. (3) Find the number of yards of carpet 27 in. wide necessary to carpet the following rooms : (a) 18 ft. x 21 ft. (b) 20 ft. 3 in. X 24 ft. (c) 24 ft. 9 in. x 30 ft. (d) 15 ft. 9 in. X 33 ft. (4) Find number of yards necessary to carpet the following rooms with material 30 in. wide : (a) 15 ft. x 18 ft. (b) 17 ft. 6 in. X 2: ft. (c) 12 ft. 6 in. x 15 ft. (d) 20 ft. X 24 ft. (5) Find the m^mber of yards of matting 45 in. wide necessary for the following rooms : (a) 22 ft. 6 in. x 24 ft. (b) 42 ft. X 27)4 ft. (c) 20 ft. X 27 ft. (d) 14 ft. X I2f ft. B.— To FIND TOTAL COST. (6) Find the cost of carpeting the rooms of questions 3 and 4, at 75 cents per yard. CARPETING. 4> e, 14 in. in 4 times as 2 ft. eter. long, Find foot. Find t. wide and c foot, and i of ice can ie and 20 ft. ■ide will be pet a room 27 in. wide [8 ft. X 21 ft. (d)i5ft.9 carpet the l) 15 ft. X 18 ft. (d) 20 45 in. wide 3 in. X 24 ft. ft. X 12ft ft. )f questions (7) I received a bill for the carpet for my house, (a) parlor 18 ft. x 27 ft., with Axminater 27 in. wide, at $2.50 per yard, (b) dining room 15 ft. x 21 ft, with Brussels 27 in. wide at $1.50. (c) 6 bedrooms each 12 ft. x 15 ft., with Brussels 27 in. wide, at $1.10 per yard, (d) library 12 ft. X 30 ft. with Wilton 27 in. wide, at $1.80. (e) halls $36. Find my bill. (8) The officers of a church have their church parlor to carpet, and have a choice of a Wilton 27 in. wide at $1.80 per yd., and a 30 in. Axminster at $2.10. If the dimensions are 30 ft. x 36 ft., and the carpet runs lengthwise, find difference in cost. (9) Find the cost of carpeting a room 18 ft. by 23 ft., with carpet 30 in. wide, and costing $1.35 per yd., the strips running lengthwise of the room, and allowing 12 in. on each strip for matching. (10) Find the value of the carpet 30 in. wide, and cost- ing $.90 per yd., to cover a floor 19 ft. x 23 ft., the strips running lengthwise, and the pattern 32 in. long. XXXI - CARPETING. C. — To FIND WIDTH OF C.\RPET. (i) The cost of carpeting a room 15 ft. X2i ft., with carpet worth 75 cents per yd. is $31.50. Find width of carpet. (2) $75.60 is the cost of carpet for a room 18 ft. x 27 ft. when the carpet sells for $1.05 per yd. Find width of the carpet. (3) Find the width of the carpet used in carpeting a room 33 ft. X 45 ft. when the cost is $148.50, 90 cents being the price of the goods. (4) My study is a room 13 ft. 6 in. x i8 ft. I bought tapestry carpet 27 in. wide and paid 80 cents per yd. for it. My total cost was $28.80. Find the width of the carpet. (5) The cost of carpeting my library was $64. Had the carpet been 30 in. wide it would have cost $76.80, Find the width. 42 ARITHMETIC. D. — To FIND DIMENSIONS OF ROOM. (6) The bill for carpeting a hall i8 ft. wide is $120. If the carpet be worth $1.25 per yd., and be 27 in. wide, find length of room. (7) The cost of carpeting a floor io>^ yds. long, with carpet 27 in. wide, and costing $1.35 a yard, was ^85. 05. Find the width of the room. (8) I paid 80 cents a yard for carpet 27 in wide, pay- ing a total amount of $28.80. I f the room be 18 ft. long, find its width. . (9) What width of room wc ild give a bill of $141.75, for carpeting a room 45 ft. long, with carpet 30 in. wide and costing $1.05 i (10) I paid a bill of $46.08 for carpeting a room 16 ft. wide with carpet 32 in. wide at 96 cents per yard. Find length of room. XXXII. -CARPETING. E.— To FIND PRICE PER YARD. (i) If it costs $48 to carpet a floor 24 ft. long by 18 ft. wide, with carpet 27 in. wide, find price per yard of the carpet. (2) I have a room to be carpeted 30 ft. x 27 ft. The cost of the carpet is $1 00, and it is 27 in. wide. Find number of yards of carpet, also price per yard. (3) Find the price per yd. of carpet 27 in. wide suffi- cient to cover a room 24 ft. x 27 ft., if the total bill is $115.83. (4) $40.80 is charged for a 30 in. carpet for a room 15 ft. X 17 ft. Find the price of the carpet. (5) A room is 17 ft. x 20 ft., and is covered with a 27 in. carpet. The strips are laid lengthwise, and 6 in. is allowed for matching. The total cost being $43-73^5 Find the price per yard. CARPKTIXG. 43 F.— Miscellaneous Prorlems. (6) What would be the cost at $i. lo per yard, of car- peting a room i8 ft. by 24 ft. with carpet 30 in. wide and running lengthwise of the room, 9 in. being allowed on each strip for matching? (7) A house-wife wishes to carpet her parlor 18 ft, by 20 ft., with 27 in. carpet worth $1.40 per yd. The carpet runs lengthwise, and 12 in. on each strip is lost through matching. Find cost. (8) Find the cost of the 45 in. matting worth 80 cents per yard, to cover the lecture room of a church. The room is 30 ft. by 45 ft., and the matting is laid crosswise. (9) Find the cost of enough stair carpet worth $1.20 per yard to cover a stair of 18 steps, each of 12 in. tread and 8 inches rise, allowing 15 inches extra at top and bottom. (10) A linoleum is purchased for a kitchen 15 ft. x 12 ft. The linoleum is 45 in. wide and sells at $1.20 per square yard. The material is laid crosswise and 18 inches comes off each end for matching. Find the cost. PRACTICE IN SUBTRACTION. From each of the following j»^/ra^ feet in length at the rate of 1 5 miles per hour. Find time required to cross the bridge. (2) Telegraph poles arc placed 55 yards apart. A train passes 16 in a minute. Find rate of train in miles per hour. (3) A train leaves Toronto for Montreal at 6.30 p.ni., at the rate of 25 miles per hour ; at 9 p.m. a second ttain follows the first at the rate of 35 miles per hour. How far from Toronto will the second train overtake the first.'' (4) A train leaves Montreal for Toronto a distance of 333 miles at 6.30 p.m. on Monday at the rate of .25 miles per hour. At 9.30 of the same evening a second train leaves Toronto for Montreal at the rate of 35 miles per hour. When and where will they meet ? (5) There are two trains moving in opposite directions on parallel tracks. The first, 320 feet in length, and mov- ing at the rate of 24 miles per hour ; the second, 340 feet long, and running at 20 miles per hour. Find time re quired to pass. ^6) A man rows down stream a distance of 12 miles in I yi hours, :\nd back again in 3 hours. Find rate of row- ing in still water. (7) A train 150 yards long running 25 miles per hour crosses a bridge in 22]/^ seconds. Find the length of the bridge. (8) A bridge 243 yards long is crossed in 22 j^ seconds by a train moving at the rate of 33 miles per hour. Find length of the train. 46 ARITHMKTIC. (9) A bridge three times as long as the train crossing it at 36 miles per hour is crossed in 22^ seconds. Find length of the train and the bridge. (10) How far may I travel by train at 20 miles per hour, and return by bicycle :'t 8 miles per hour, that the round trip may occupy 5 nirs 36 minutes ? XXXV.-LUHBER AND TinBER. (i) Express the cost of i foot of lumber when the price is (a) $12.86 per M. (b) $17.96 per M. (c) $23.31 per M., and (d) $31.79 per M. Note. — In solving questions of this type, we need only remember that if 1000 feet costs $1 1.74 that is equivalent to saying it cost 1 174 cents per 1000 feet, /.r., 1.174 cents per foot of lumber. The pnce of any number of feet is then easily found. (2) Find the cost of (a) 5500 feet lumber at $ioper M.; (b) 8750 feet lumber at $12.50 per M. ; (c) 12570 feet lumber at $15.50 per M. ; (d) 28765 feet lumber at $1 1.74 per M. (3) Find the value of the following pieces, (a) a plank 18 ft. long, 16 in. wide, 2 in. thick, at $12 per M. ; (b) 4 scantlings, 4 in. x 4 in., and 16 ft. long, at $16 per M. ; (c) 8 beams 8 in. x 12 in., and 12 ft. long, at $12.50 per M. ; (d) 15 planks 18 ft. long and 3 in. thick, and 14 m. wide, at $18 per M. (4) Find the cost of the material necessary for a close board fence round a half acre lot 10 rods long, if the posts be 8 ft. 3 in. from centre to centre, and cost locentseach, 2 stringers 2 in. X4 in. costing $12.50 per M., and the lumber be set on end and 6 ft. high, at $13.50 per M. (5) Find the cost for the material for a 6 ft. sidewalk around the lot of No. 4 above, placing the walk 2 ft. from the fence. The plank used was 2 in. stuff and cost $15 per M. ; there were three cedar stringers used 4 in. x 4 in, worth $12.50 per M.— allow nothing for waste. (6) Find the cost of inch lumber needed to cover the roof of a barn, each side of the roof being 60 ft. x 24 ft., the lumber costing $14.00 per M. crossing s. Find niles per that the when the c) $23.31 need only jquivalent 174 cents of feet is 10 per M.; 12570 feet rat $11.74 \) a plank M. ; (b) 4 ler M.; (c) > per M. ; |. m. wide, for a close f the posts ents each, , and the )er M. sidewalk : 2 ft. from cost $15 i in. X 4 in. cover the t. X 24 ft., LUMBER AND TIMBER. 47 (7) The sides of a barn are 40 ft. x 60 ft. and 1 5 ft. high Find cost of inch lumber to enclose the sides at $17.48 per M. (8) A contractor is making an estimate for the lumber required to enclose a barn 40 fi, x 60 ft. and 1 5 ft. from the ground to the edge of the roof, the edges of the roof pro- ject I ft. beyond the ends of the building and are 24 ft. to an end ; the point of the gable is 10 ft. above the level of the sides. What is the amount of his estimate at $14.50 per M. .-• (9) A picket fence round a field of 2 acres, 20 rods long, is built ; the pickets are 4 ft. long and 4 in. wide, and are laid 4 in. apart. A base board i in. thick and 1 5 in. wide, runs along the bottom ; 2 stringers 2 in. x 4 in. are used to secure the pickets. Find the cost of the sawn material at $12.50 per M. (10) The following material was received from a saw mill for a bridge : 24 beams 8 in. x 12 in. and 12 ft. long ; 16 pieces 6 in. x 8 in. and 16 ft. long ; 150 pieces 4 in. x 4 in. and 15 ft. long ; 240 planks 3 in. thick, 16 in. wide, and 1 8 ft. long; and 2450 ft. inch lumber. All the material is put in at $15.00 per M. Find the bill. XXXVr— MIXTURE QUESTION,' (i) There is a mixture of 90 lbs. of tea, part at 80 cents and a portion at 75 cents. The total cost is $70.50. Find the number of pounds of each. (2) Of two chests of tea one is heavier than th6 other by 7 lbs. The value of both at 61 cents per lb. is $50.63. Find the weight of each. (3) A merchant sells 1 1 1 lbs. of tea for $56.49, part of it at 55 cents and part at 43 cents per lb. Find how many lbs. of each. (4) 38 yards of silk and velvet sell for $37.95. If the quantities were interchanged the price would be $39.95. The velvet costs 90 cents per yard. Find the number of yards of bilk. 48 ARITHMKTIC. (5) I have 38 more 10 cent pieces than I have of 25 cent pieces. The total value is $30.05. Find number of coins. (6) I have loo lbs. of tea which when sold for J85 gave a profit of 25%. If some were at 60 cents per lb., and the remainder worth 80 cents per lb., find the number of lbs. of each kind. (7) I sold a mixture of 72 gallons of wine at $3.30 per gallon and made a profit of 20%. Tl t are 12 gallons more of the dearer kind than of thf aper, while the difTerence of price is 60 cents per ga Find the prices. (8) 140 lbs. of coffee and chickory when sold for $56.50 gave a profit of 25%. The difference in price was 26 cents per lb., while the difference in weight was 100 lbs. Find the values of each. (9) A farmer sold 1260 lbs. of wheat and 2040 lbs. of oats for $27.60, getting 35 cents per bushel more for the wheat than for the oats. P^ind price of each per bushel. (10) 42 bushels of wheat and 30 bushels of oats were sold for $34.20, the wheat bringing |'4 of a cent per pound more than the oats. Find the price of each per bushel. XXXVII. - RATIO. (1)4 miles, 283 rods, i yard is what fraction of 8 miles, 45 rods, I yard, 2 feet ? (2) Reduce 2i guineas to a decimal of ^61 5s. (3) Express in inches ^ of a mile. (4) Two errand boys were on a message : the first carried 25 lbs. Troy and the second 36 lbs. Avoir. The weight carried by the first was what fraction of that car- ried by the second. . . i: (5) A farmer delivers 63 bushels of barley at one load, and 56 bushels of wheat by the next. The second load is how many times the weight of the first ? , (6) Reduce the weight of 49 bushels of oats to a deci- mal of the weight of 51 bushels of rye. time to I X mil iit 3 m- overtak( speed b Find th How m their ch RATIO. 49 (7) 5Ruineas+io sovcroij^ns must be multiplied by what factor to make it equal to 5 (60 crowns + 40 half- crowns +27 shillings)? (8) Express A of an acre in roods, square rods, etc. (9) Reduce X of ,'y of ijj of 2 miles to the fraction of n ^f A "f 5456"yards. (10) Reduce J of 4^ los. + ,^ of 21 crowns + loS sove- reigns to the fraction of 222|S guineas. XXXVIII.— RATIO. (1) A can run 2 yards while B runs 5 ft. By how much should A win in a 100 yards race ? (2) A can run 4 yards while B runs 3 ; but in a quarter mile race A gives B a start of 109 yards. Who wins, and by how much ? (3) In a quarter mile race A can run 6 yards for B's 5 and to make an interesting finish A gives B a start of 70 yards. At the end of 300 yards A slipped and thus lost 2 steps of 3 yards each in length. Who wins, and by how much ? (4) In a 440 yard race A can give B 20 yards start and C 30 yards, and all three would finish together. B and C run a 444 yard race starting even. By how much should B win ? (5) A and B start together and walk in the same direc- tion, A at the rale of 4 miles an hour and B at the rate of 3 miles an hour. At the end of 7 hours A turns and goes back. How many miles will B have gone when he meets A ? (6) Two men start from the same point at the same time to walk in the same direction around a block of land I }4 miles square. A travels at the rate of 4 miles and B at 3 m'les per hour. How far does A walk before he overtakes B ? (7) A runs a mile race with B and loses ; had his speed been y^ greater he would have won by 22 yards. Kind the rate of A's speed to B's. (8) A can run a mile race in 5 minutes, B in 6 minutes. How many yards start should A allow B in order to make their chances equal .'' 50 ARITHMEliC. (9) Of two horses in a race the ist can take 15 strides of 18 feet each, while the 2ncl horse takes 14 strides of 20 feet each. The ist horse is placed 63 yards in front of the 2nd at the start. Which wins in a mile race, and by how much ? (10) A hound pursuing a hare takes 3 leaps for the hare's 4, but 2 of the hound's leaps are equal to 3 of the hare's. The hare has a start of 50 of her own leaps. How many leaps must the hound take to catch the hare ? PRACTICE IN SUBTRACTION. Find, by repeated subtraction, how many times wi can take : (i) 76944758 from 539402519. (2) 64877436 from 844052426. (3) 89646978 from 1 1660597 1 1. (4) 89646978 from 897118777. (5) 89764576 from 718603362. (6) 78964574 from 869356003. (7) 64798585 from 842860264. (8) 96745885 from 774842036. (9) 96485978 from 1158- 676482. (10) 86947869 from 1 1 3129105 1. (11)76849845 from 999603540. (12) 49765499 from 598133844. (13) 89654679 from 7 1 8 1 92 1 70. (14) 95467894 from 1 1 .165 50206. (15) 89768457 from 719041632. (16) 94637480 from 852235266. (17) 97865768 from 88 1 378661. (18) 998- 75646 from 1099100001. (19) 74958746 from 525548816. (20) 93758648 from 1032139813. (21) 86754659 from 781360725. (22) 75684659 from 757415384. (23)5555- 5555 from 555777772. (24) 87654321 from 105 1962963 (25) 4-,647589 from 320028999. (26) 46758495 from 561699804. (27) 98576897 from 690624857. (28) 5679 7684 from 739128571. (29) 48965785 from 637555204. (30) 79869485 from 559585171. (31) 68976895 from 828768616. (32) 74689759 from 597704826. (33) 69785- 476 from 489256981. (34) 93698756 from 937847238. (35) 87694736 from 965291052. (36) 94786978 from 123- 2799^^3 (37) 64978465 from 520615414. (38) 9837- 6559 from 984564244. (39) 78436923 from 549604674 (40) 45792416 from 412255200. (41) 46598896 from 420078029. (42) 89464998 from 1163614760. (43; 56789654 from 738644429. (44) 45678965 from 50294 8271. (45) 96754897 from 871373019. (1) I] as much (2) D have $60 (3) IJ ikn B. (4) D liave $70 (5) A $17 more each. (6) D receive $ the 3rd. (7) D is to B's ; (8) T 1 f a man w ages of (9) A value of Find the (10) 1 he wee IS 2 won iiare of (1) E }4 as o (2) T Idest so t'cond r St. Fir rres. (3) li s C, fin 1 SHARING 51 e 15 strides trides of 20 1 in front of| ace, and by laps for the to 3 of the own leaps. ;h the hare ? N. times vft can 877436 from (4) 89646978 )03362. (6) n 842860264. J from 1158- 11)76849845 [33844. (13) 1 11.16550206. .637489 from :. (i8) 998- n 525548816. )754659 from . (23) 5555- 105 1962963. 1758495 from 7. (28) 5679- n 637555204. 5976895 from (33) 69785- n 937847238. 578 from 123- (38) 9837- m 549604674. 3598896 from .14760. (43. 5 from 50294- XXXIX -SHARING. (i) Divide $1250 between A and B giving A 4 times as much as B. A, B, and C, that A (2) Divide $1000 among have $60 more than B, and twice as much as C. (3) Divide $30 between A and B, giving A $3. 50 more thin B. (4) Divide $3600 among A, B, and C, so that A may have $70 more than B, and twice as much as C. (5) A, B, and C receive $4032 for a contract, h receives $17 more than C, and $35 less than A. Find share of each. (6) Divide $89.16 among 3 men so that the ist may receive $2.18 more than the 2nd, liut 80 cents less than the 3rd. (7) Divide $1200 between A and B so that A's share is to B's as 2 is to 7. (8) The daily wages of 27 men and 37 boys is $82. (x). If a man receives 3 times as much as a boy, find the daily wages of a man and of a boy. (9) A house and lot ar'; together worth $2100 : }4 the value of the house is equal to y^ the value of the lot. Find the value of each. (10) In a factory are 12 men, 16 women, and 30 boys. The weekly wages is $330. If a man were paid as much IS 2 women, and a woman as much a 3 boys, what is the hare of each ? XL.— SHARINQ. (1) Divide $1209 among three men, giving to the 1st I'A as often as the 2nd gets $>^, and the 3rd J^. (2) Three boys are given farms by their father. The Idest son gels l^ acres for every i>^ acres that the fcond receives, and for every 1 '/j acres given the young- st. Find the share of each, if the whole amount be 1265 ures. (3) If A gets ^ of the whole, and B gets ^ as much IS C, find the share of jach in a legacy of $9500. PROVINCIAL LIBRARY VICTORIA, B.C. f,2 ARITHMETIC. (4) Divide $345 among A, B, and C, so that B will receive $5 for A's $4, while C receives $6 for A's $i;- (5) Divide $510 between A and B, so that % of A's share equals ^ of B's. (6) If ^ of As money is equal to ^ of B's, and their total money is $665, find ihe share of each. (7) 702 votes were cast in an election at which X, Y, and Z were candidates. % of the votes cast for X is equal to ^4 of those cast for Y, while % of Y's made )i of Z's Find votes cast for each. (8) Three churches together have 18 16 seats: {\^ of the seats of the 1st is ecjual to }i the number of those in the second ; but % of the scats in the 2nd is as many as Yi of those in the 3rd. Find number of seats in each. (9) Divide $682.20 among three persons so that the 1st may have twice the 2nd, and the 3rd as much as the other two together. (10) A has $18 less than B, and $23 less than C. After A has given B $7, and C $1 1, how much has C more than B ? Also how much less has A than B and C, respectively ? XLI.— SHARING. (i) A farmer sold an equal number of horses, cows, and calves, receiving $3540 for the whole. X'aluing a horse at $69, a cow at $37, and a calf at $12, find the number of each. (2) A farmer bought a number of horses and cows for $2000 There were three times as many cows as horses, and a horse costs twice as much as a cow. If each horse cost $80, how many cows did he buy ? (3) In a factory 12 men, 16 women, and 30 boys are employed. The weekly wage bill is $330.00 A man is paid as much as two women, and a woman as much as three boys. What is a week's wages for 5 men, 7 women, 14 boys ? (4) A and B were candidates in an election in a con- stituency of 2700 voters. The votes polled by A were to those polhd by B as 23 to 25, and fi was elected by a majority of 100. How many electors did not vote ? SHARING. 53 hat B will y^ of A's and their hich X, Y r X is equal ^ of Z's eats : {\ of of those in IS many as in each, so that the nuch as tht lan C. After C more than espectively orses, cows, Valuing a 5 1 2, find the ind cows for rs as horses, If each horse 30 boys are A man is as much as en, 7 women, on in a ron- iy A were to elected by a It vote ? (5) A farmer employs a number of men and 8 boys. He pays the boys 65 cents and the men $1.10 per day. The amount that he paid to all was as much as if each liad received $.92 per day. How many men were em- ployed .'* (6) Gunpowder is corr 'iosed of nitre, charcoal, and sulphur, in the proportions of 15, 3, and 2. A certain (|uantity of gunpowder ib kii. .vn to contain 20 cwts. of charcoal. Find its weight, and also the weight of the nitre and sulphur which it contains. (7) Lead weighs 11.4 times as much as water, and platinum weighs 21 times as much as water. What weight of platinum will be equal in bulk to 56 lbs. of lead. '' (8) Four men can do as much work ;is 6 women or 8 l)oys. Ten boys in 8 days earn $48.00. Find the sum earned by 23 men and 14 women in 12 days. (9) $264.00 is the weekly wa; of an equal number of men, women, and coys. The men >ue paid $i.33K per (lay, the women 90 cents, and the boj 70 cfrms. Fmd the number of each. (10) iK poulterer expended $128.00 in tiie purchase of an equal number of ducks, geese, and turkeys. A duck ( ost % as much as a goose, and a tut key is worth as much as a duck and a goose together. Find the number of each, when ducks sell at 60 cents per pair. XLII -ALLIGATION AND MIXTURES. (i) 5 geese and 7 turkeys cost $8.25, while 8 geese and 5 turkeys cost $8.55. Find the price of each. (2) 9 lbs. of green tea and 1 1 lbs. black is worth $14. 10, while 8 lbs. of green and 5 lbs. of black is worth $8.95. I'ind the value per lb. of each. (3) 25 yards silk and 30 yards velvet cost $48. 50, while 30 yards silk and 25 yards velvet cost $50.50. Fine! value of 1 I yards silk and 1 1 yards of velvet. (.') 5 gallons brandy and 9 gallons wine is billed at $44.00 ; and 8 gallons brandy and 5 gallons wine on a sfMond invoice totals $37,50. What is the amount of a iliird invoice for 6 gallons brandy and 4 gallons wine .'' i.» fe.,- 54 ARITHMKTIC. (5) 100 lbs. tea and coffee costs $50. The tea cost 60 cents and the coffee 35 cents per lb. Find the number of lbs. of each. (6) A mixture of 67 lbs. of black and green tea is worth $50.40. The black is worth 80 cents per lb., and the green 70 cents per lb. Find number of lbs. of each. (7) How many gallons each of wine at $3.25 and $2.25 per gallon would give a mixture of 72 gallons worth J2.66% per gallon ? (8) In a mixture of 60 gallons ^3 is wine. How much wine must be added so that the wine may be 80% of the mixture.-* (9) There is a mixture of 90 gallons of brandy and water, of which the brandy is 907. How much water must be added to reduce the brandy to 50% ? (10) From a mixture of 60 gallons of l)randy and water, in the ratio 2:1, 10 gallons is drawn off and replaced with 10 gallons of water. Find the ratio between the brandy and water now in the mixture. XLIIL— EXCHANGE OF VALUES. (1)4 lbs. tea are worth 9 lbs. coffee, an ' 6 lbs. coffee are worth 15 IJjs. sugar. How many pounds of sugar are equal in value to 56 lbs. of tea ? (2) If 2 lbs. of tea be of value equal to 50 oranges, and 42 oranges be worth 56 lenuwis, find the value of i lb of tea when 5 lemons cost 9 cents. (3) I franc ^-gH d.,and 1 shilling = 24^^ cents. Express in francs $28.47. (4) In performing a piece of work, i man ^2 women, and I woman — 3 children. Find how many women arc the equivalei in working power of 6 men, 13 women, and 27 children. (5) 9 apples cost as much as 7 plums, and 5 plums as much as "; pears. How much tea worth 75 cents per pound could be bouglit witii the jjroceeds of the sale of 105 doz. apples, given thai 147 pears fill a buFhel a;:d are worth $2.25 per bushel .'' tea cost 60 ; number of een tea is r lb., and )s. of each. 5 and $c.25 H-.li J2.66% -fow much 80% of the )randy and nuch water ' and water, placed with the brand)- lES. 3 lbs. coffee of sugar are oranges, and lue of I lb Its. Express = 2 women, women arc women, and 5 plums as 5 cents per the sale of nhel a;:d arc EXCHANGE OF VALUES. 55 (6) 60 cents buys 1 5 oranges, 20 lemons, or 48 banan- as. How many oranges would be a fair exchange for 8 doz. lemons, and 16 doz. bananas ? (7) Raisins sell for 15 cents per lb. 7 lbs. raisins are worth 15 lbs. currants, 8 lbs. currants cost as much as 4 lbs. of prunes, and 9 'bs. of prunes would pay for 2 lbs. of tea. How many lbs. of tea would be exchanged for 35 lbs. raisins .'' (8) 3 chickens are worth as much as 2 ducks, 3 ducks as much as 2 geese, 3 geese as much as 2 turkeys. When geese sell for $6.48 per do/., find the cost of 10 of each kind. (9) 3 lbs. sugar— 5 lbs. rice ; 15 lbs. rice = 2 lbs. coffee; 5 lbs. coffee = 3 lbs. tea. I get an equal quantity of each of the others in exchange for 61 lbs. of tea. How many pounds of each did I get ? (10) 9 bushels of oats cost as much as 5 bushels of peas, 4 bushels of peas as much as 3 bushels of barley ; and 5 bushels of barley as much as 4 bushels of wheat. Find the value of a feed mixture of 12 bushels of oats, 9 bushels of peas, and 5 bushels of barley, when wheat cost 75 cents per bushel. XLIV.— WORKING PROBLEHS. (i) A can do a piece of work in 5 days, and B can do it in 6 days ; find time when both work together. (2) Tom could dig a drain in 14 days, and Sam in 16 days. Find the time when both work together. (3) To build a piece of fence A requires 6}4 days, and B 5^ days. Find time when both work together. (4) If A can do ^ of a piece of work in 2^^ days, and B can do ^ of the same work in 33/ days, how long will it take A and B working together to do a work twice as large ? (5) Three boys can saw a pile of wood in 3X days, 4 J days, and 5f dtiys, respectively. They conclude to work together. Find their time. 56 ARITHMETIC. (6) To set the type for a piece of book work 4 com- positors could do the work in 22 >^ days, 18 days, 19* days, and 25]^ days respectively. The sum of J48.41 is paid for the work : find the share of each, when all work to- gether. (7) If A can do as much work in 4 days as B can in 3 days, divide $14.84 justly between them, they having re- ceived that sum for a job on which they worked together. (8) Two brothers work together, but the younger re- 3uires li;i days in which to do as much as the elder can o in 9^ days. Divide fairly $31.23 which they receive for a piece of work. (9) A and B together can do a piece of work in 12 days. A can do it alone in 22 days. Find B's time when working alone. (10) Two journeymen can do tho plastering of a town hall in 6 days when working together. B alone would require 14 days, find A's time. XLV.— WORKING PROBLEMS. (1) A and B together can do a piece of work in 6\ days ; A can do it in 9 days. How long would it take B to do it? (2) The wages of A and B together for 22 >^ days amount to the same sum as the wages of A alone for 38^ days. For how many days will this sum pay the wages of B alone .'' (3) A and B can do a piece of work in 6 days, B and C in 8 days. A and C in 7 days. Find time required by each when working alone. (4) Of three men, the ist and 2nd can together do the brick work of a stable in Cj".; davs, the 1st and 3rd in 63 days, while the 2nd and 3rd would require 7t7o days. Find time when each works alone. (5) A can do a Piece of work in 5 days, B in 6, and C in 8. If A and B work at it two days eac:h, how long will it take B and C to finish it .'' )rk 4 com- s, 19* days. 41 is paid 11 work to- B can in 3 having re- ;d together. lounger re- le elder can ley receive work in 12 s time when WORKING PROBLEMS. 57 >■ of a town lone would work in 6^ Id it take B 12\i days one for 38^ the wages lays, B and required by ether do the d 3rd in 6^ , days. Find in 6, and C , how long (6) A, B and C do a work in 1 2 hours ; A and" B can do it in 16 hours, and A and C in 18 hours. In what time can each do it separately ,'' (7) A could alone do a work in 18 days. After work- ing alone 12 days, B comes to assist, and the work is com- pleted in 3^ days. Find the time for B alone. (8) A can lay 4000 brick while B lays 3000. They work together and finish a job in 12 days. Find time re- quired for each. If $84 were paid for the work what is each man's share ? (9) A can do a piece of work in f of a day, B in J a day, C in § of a day. Find time required to do 4 such works, all working together. (10) If A required '\ of a day to complete a piece of work, which B could do in % of a day. and C in \ of a day, how much could the three do in a day if all worked to- gether ? XLVl. ADDITIONAL PROBLEMS. (i) If 3 men or 5 boys can do a piece of work in 20 days, find the time for 3 men and 5 boys. (2) 4 men can do as much as 6 lioys, and 4 men could dig a ditch in 15 days. Find the time if 5 men and 15 boys were employed. (3) 8 men and 12 boys can complete a work in 6 days, while J 2 men and 24 boys would require 37 days to do the Sr.me work. Find the time required for 16 men ;ind J 8 boys. Solution :— 8 men and 12 boys require 6 days, (i) .'. to do work in i day requires 48 men and 72 boys ; also 12 men and 24 boys require 3^ days. (2) .*. to do work in i day requires 41 1 men and 82* boys. Hence work of (48 men + 72 boys) -work of (41! men + 82* boys). .". work of 6f men = work of io» boys ; or I .nan ■ JO* 6t! boysi^ I \ boys. c8 ARITHMETIC. Exchange our 8 men for boys in ist assertion, and we get : — 24 boys can do work in 6 days, or I boy can do work in 144 days, or I boy can do j\j of work in i day. Since i man= ij boys, then i boy does § of a mans work. .*. 16 men and 48 boys will do . rr- I work 1 . . Time = = 2 days. J work We hope to be pardoned for the liberty we were compelled to take witn the fractional parts of both men and boys. (4) If 8 men and 1 5 boys can do a piece of work in 3.^ days, and 1 2 men and 6 boys would require 3J days for the same work, find the time necessary for 9 men and 18 boys. (5) 5 men and 8 boys can do a work in 23 days, while 4 men and 10 boys would need 2f days. Find the daily wages of a man and of a boy if $30 be paid for the work. (6) A can do a piece of work in 8 days, and B in 10 days. After 2 days B leaves. How many days more are needed for A to finish ? (7) A and B together can do a piece of work in 15J days ; B by himself could do it in 62 days. How would you divide $64 paid for the work ? (8) Five men can do a piece of work in 20 days. After working 15 days they are joined by another man, and the work is completed in 19 days. How many days would the sixth man require to complete § of the work ? (9) If l" men can do | of a piece of work in 30 days, working 10 hours per day, in what time should 15 men do the whole work, working 9 hours per day ? (10) A does I of a work in 6 hours ; B does 2 of what remains in 2 hours, and C finishes what is left in 30 minutes. Find the time were all working together. WORKING PROBLEMS. 59 tion, and XLVII— WORKING PROBLEMS. f a mans we were both men tvork in 3.^ I days for len and 18 lays, while the daily • the work. d B in 10 s more are ^ork in 1 5! iow would 1 20 days. )ther man, many days he work .'' in 30 days, 1 5 men do s 2 of what left in 30 jther. (i) A farmer hires a farm hand for a year, agreeing to give him $160 and 10 sheep. But the man leaving at the end of 7 mqnths, got as a fair settlement the sheep and $60. Find the value of each sheep. (2) I engaged a lad for 8 months for a suit of clothes and $140. He left at the end of 5 months, when I paid him $80 in addition to the suit. Find the value of the suit. (3) 1 5 men can do a piece of work in 22 days, how many men would do 4 times the work in J of the time ? (4) I engage a sawyer for my mill and am to pay him $2 and his board for every day he works. On the days he is idle I am to receive $1.00 for his board. At the end of 50 days he received $64. How many days was he idle? (5) A piece of work can be done in 11 i hours by 2 men or 5 women or 1 2 boys ; what time would be occupied by 4 men, 5 women and 6 boys ? (6) A boy was to work for a man two weeks for a cap and $5.70. He quit at the end of 9 days, getting the cap and $3.90. What was the cap worth ; also, what was the boy being paid per day ? (7) A man is to receive $1 for every day he works, and forfeits 50 cents for every day he is idle. At the end of 60 days he receives $54. How many days did he work? (8) The wages of A and B for 15^ days would pay the wages of A alone for 29]^ days. Find how long it would pay the wages of B alone. (9) The money paid B for 14^ days' service would en- gage A and B for 8 days. For how long would A work for the same sum ? (10) 3 men can dig a trench in 8 days. They work at it for 5 days when one of them falls ill, and the other two ilnish the work in 5 days more. How much of the work ilid the first man do before he fell ill ? 6o ARITHMETIC. MULTIPLICATION TIME TESTS. 6 For Constant Multiplier. Multiply each of the following factor 12 times in succession : — numbers using 6 as a (I) 986798. (5) 789456. (9) 728397. (13) 489657- (17) 298769. (21) 346827. (25) 471525- (29) 675477. {33) 671427. (37) 615329. (41) 389877- (45) 987657- (2) 789649- (6) 679878. (10) 684927. (14) 826737. 7 ! 8649. 796483. 618829. 415967. 928717. 292485. 521799. (18) (22) (26) (30) (34) (38) (42) (3) (7) {") ('5) (19) (23) (27) (30 (35) (39) (43) 987654. 793865. 579879. 592687. 384297. 827927. 789789- 238429. 647929. 731289. 868257. (4) (8) (12) (16) (20) (24) (28) (32) (36) (40) (44) 456789 986745 928793 682973 792685 2 1 5639 717925 167247 572967 416927 217965 6 For Constant Multiplier. Multiply each of the following numbers using 6 as a factor 10 times in succession : (I) 77668. (2) 88667. (3) 66778. (4) 55489- (5) 58769. (6) 69748. (7) 70549- (8) 77898. (9) 89875- (10)97856. (11)68746. (I2j 73948. (13)88888. (14) 76486. (15)87987. (16)74357- ('7)43878. (18)73848. (19) 98784. (20) 76847. (21) 76847. (22) 76879. (23 j 67989. (24) 96588. (25) 76864. (26; 98974. (27) 76843. (28) 45678. (29) 86547. (30) 88878. (31) 67875. (32; 76867. (33)88767. (34)67324- (35)99999- (36)99789- (37) 88987. (38) 77889. (39) 66458. (40) 57679. (41) 75896. (42)56879. (43)45499. (44)77777- (45)37468. XLVIII.- BILLS AND ACCOUNTS. The following bills are submitted for practice in cal- culation but especially as an exercise in form. Where possible do all the ruling in ret^ ink : — (i) On April 12, 1897, Jas. Henderson, Morris, bought from !). M. (iordon^ Wingham, a billof goods as follows: ; 5 as 456789 986745 928793 682973 792685 215639 717925 167247 572967 416927 217965 ng 6 as a 5489. (5) (9) 89875. 5888. (14) :i8)73«48- J879- (23J (27) 76843. 7875- (32; (36) 99789. 7679. (4') (45) 37468. VS. ice in cal- n. Where Tis, bought as follows ; BIU.K ANn ACCOUNTS. 61 28>^ yds. tlaiinel at 68 cents ; 35 yds. calico at 15 cents ; 3>^ doz. pairs stockings at i6'«j lents per pair ; 7 pairs gloves at 90 cents ; I2>^ yds. linen at $1.12 ; 4 pairs muslin curtains at $4.20. (2) On April 19, 1897, AltVed M. Laird, Norval, bought from ('». R. Anderson & l'>ro., of IJrampton, I2>^ yds. cassiinere at $2.75 ; iHyj yds. silk at $1.17 ; 23^4' yds. flannel at 37 12 cents ; 112 yds. print at 9,^ cents ; 55 yds. shirting at 17,'/^ cents ; 27/2 yds. tweed at $1.12. (3) On April 30, 1897, Paul Powell, Turnberry, sold to r. A. Mills, VV'ingham, to apply on a current account of $54.45 : i6i.'olbs. hay at $15 per ton ; ^l^ cords wood at $4,80 ; 4 bbls. apples at $2.75 ; 350 lbs. flour at S2.5oper cwt.; 30 lbs. loozs. butter at 16 cents per lb. How do the accounts stand now ? (4) May 21, 1897, VV. V. Chapman, Wingham, bought from C. N. (iriffin, as follows : 3?/ lbs. tea at 80 cents ; 300 lbs. sugar at 4^4 cents ; 45 yds. print at 11 K cents ; towelling at 2 'A 2% gals, syrup at 65 cents ; I2>i ydif. cents ; ^ doz. knives and forks at $2.50 ; 27 lbs. cheese ;U 15 cents ; i lb. 10 oz. lemon peel at 32 cents per lb. (5) On June 28, 1897, the pupil buys from Husband Bros., Commission Merchants, Toronto: 10 lbs. 2 oz. Ijutter at 16 cents ; 48 lbs. extra butter at 24,^ cents ; 846 lbs. pork at $6 per cwt.; 6 bars soap at 3 for 25 cents; 139 eggs at 1 2 cents per doz. June 30: 867 lbs. oats at 30 cents ; 7 qts. syrup at 90 cents per gallon. (6) Wingham, July 5, 1897, McLean & Son, sold the jnipil a bill of material, as follows : 1344 ft. lumber :it J16.25 per M. ; 48480 cub. ft. timber at $59.37^ per M. ; 7400 cedar posts at $7.75 l)er C. ; 8400 fence pickets at ji.50 per C. ; 9056 brick at $30 per M. ; 5680 feet of inch lumber at $6.25 per M. (7) Fred Ross, Rose Ave., Toronto, on July 7, 1897, l)ought from Catto& Co., Dry Goods Merchants, King St., Toronto : 23 yds. cotton at 11 cents ; 13 yds. gingham at 23 cents ; 25 yds. flannel at 37 cents ; 18,^ yds. tweed at $1.50; \2]4 yds. serge at $1.75 ; 6% yds. broadcloth at $4.50. Receipt the bill, the book-keeper, James Burns, signing the receipt for the firm. 63 ARITHMKTIC, (8) Reuben Morley, 'I'omnto, bought from P. Conlin, Grocer, on July lo, 1897 : 3 lbs. butter at 28 cents ; 5 lbs. tea at 56 cents ; 6 bars soap at 17 cents ; ;2 j^als. coal oil at 27 cents ; 3 oranges at 40 cents per doz. He is allowed a discount of 10 cents for every dollar's woiih purchased. Find his change out of a $10 bill. (9) Thos. Scott, Esquesing, sold lo Wm. McLeod, General Merchant, Georgetown, on July 21, 1897, 3015 lbs. hay at $16 per ton. He received 6 lbs. i ,1 at So cents ; 22/^ lbs. coflfee at 26 cents ; 33 lbs. ■■:nr^- at 12 lbs. for a dollar ; 32i lbs. raisins at iS^X cents , 14 lbs. 13 oz. bacon at 16 cents per lb., and the balance in cash. Make out the bill on Mr. McLeod's business paper show- ing the foregoing facts. (10) The Rice, Lewis Co., Ltd., King St., Toronto, received from J. K. Hampton, Birmingham, England, a bill for the following goods : 375 tons iron plates at ^8, 15s., 6d. ; 107^^ tons bar iron at £1 1, 14s. ; 10 tons bolt iron at ;^io, los. ; 48 tons steel at ^18, 7s., 6d. ; 15 tons rivets at £1 1, is. ; 17 tons T iron at ^15, los. Make out the invoice in £., s., and d., and find what sum in Canad- ian currency will pay the bill, i shilling = 24]^ cents. XLIX.- INTEREST. Principal, Timk, Rate, to find Interest. Find the interest when : (i) $2500 prin., time 3 yrs., rate 7 per cent. (2) $750 " (3) $1250 " (4) J925 " (5) $850.50" (6) $750.25 " (7) $800 50 " (8) $500 " (9) $450.60 " (10) $420.40" 2 u 2 yrs. 6 mos., rate 4 per cent. 3 " 4 " "6 2 " 5 " "6 3 " 7 " "8 5 " II " "9 INTKRKS'I'. L._INTEREST. 63 Find, to the nearest cent, the interest in the following cases : (1) $2570 prin., from Feb 12, 1895, to April 26, 1895, rate 5 per cent. (2) $385.75 prin., from June 14, 1896, to Nov. 7, 1896, rate 7 per cent. (3) $268.76 prin., from Aug. 27, 1895, to April 2, 1896, rate 3i^ per cent. (4) $673,73 prii ., from March 2, 1896, to Dec. 19 1896, rate 6| per cent. (5) $1 164.35 prin., froMi April '2, 1896, to Nov. 23, 1896, rate 7^ percent. i6) $766.50 prin. from May 2, 1896, to Aug. 29, 1896, rate -;'f per cent. (7) $302.95 prin., from Oct. 4, 1895, t" J''^"- 20, 1896, rate 4^, per cent. (8) $190.38 prin., from July 4, 1895, to Feb. 8, 1896, rate 6^ per cent. (9) $346.92 prin., from Jan. 11, 1896, to Oct. 29, 1896, rate ^i per cent. (10) $379.60 prin., from Aug. 21, 1896, to Mar. 13, 1897, rate 5I per cent. LI. -INTEREST. Interest, Time, Raik, to find Principal. What principal will yield : (i) $420 int. in 6 yrs., a' 5 per cent. ? (2) $75 " " 3 " at 10 " (3) $48.30 int. in 3;^ yrs , at 3^ per cent. ? (4) $195.30 int. in 3 yrs. 4 mos., at 4X per cent. ? (5) $183.28 int. in 2 yrs. 5 mos., at 37 per cent. .' (6) $231.44 int. in 4 yrs. 7 mos., at 9;^ per cent. ? (7) $32.4j int. from May 15, 1896, to" Oct. 8, 1896, at 5^ per cent. .'' • (8) $61.92 int. from March 5, 1896, to Oct. 10, 1896, at 5^ per cent. .-' (9) $5.81 int. from June 4, 1896, to Oct. 28, 1896, at 4§ per cent. ? (10) $6.96 int. from Nov. 12, 1896, to Aug. 31, 1897, at 4f per cent. ? 64 ARITHMKTIC. LIL— INTEREST. lNTp:RiibT, Time, Principal, to finu Rate. At what rate per cent, will (i) $700 in 3 yrs., yield $126 interest? (2) $850 in 4 " " $272 (3) $1250 in 4}. " " $225 " (4) $740. JO in 3 yrs. 4 nios., yield 5123.43.^ interest ? (5) $856.75 from' May 3, to July 15, yield $17,135 int.? (6) $786.25 from March 7, to July 31, yield $25. 16 int.? (7) $325.rofrom A'r^ril 3, to July 8, yield $14.64^ int.? (8) $2555 from June 17, to Oct. 30, yield $56.70 int.? (0) $3285 from July 18, to Oct. 5, yield $49.77 int. ? (,10) $1095 from Sept. 12, to Jan. 17, yield $19.05 int.? LITI -INTEREST. Interest, Principal, Rate, to find the Time. In what time will (1) $450 prin., at 6 per cent., yield $81.00 interest? (2) $375 " at 4 " ' " ."Fqooo (3) $360 " at 8 " " $158.40 " (4) $768.40 prin., at 7.', per cent., yield $249.73 ''^t. ? 25.80 (5) $16 (6; $101.60 (7) :Si695.oo 'S) $276.90 (9) $2993 (.'o) $2336 n $187.7799 int.? $3.81 int.? $99.44 int. ? $9.23 int. ? $38.13 int.? $63.00 int. ? I IV.— INTEREST. Questions Invoi vinc; the ter.m A.mount, ^Vhat sum will amount to (i) $613.60 in 3 yrs., at 6 percent.? (2) $990.00 in 4 yrs., at 8 " (3) $864.00 in 32 yrs., at 5.^ " (4) $1212.00 in 4| yrs., at 5f{ " (5) $778.25 in 3i> yrs., at 3^ " (6) $290.79 in 219 days, at 4'f " INTEREST. 65 (7) $1499.62 from March 3, to July 27, at 7| percent? (8) $945.88 from March 17, to Jan. 3, at 8^' " (9^ $1 129.60 from April 4, to Sept. 24, at 6| " (10) $1864,15 from May 11, to Oct. 3, at si " LV. -INTEREST. (t) Find the amount of .'850 for 3 yrs., at 6 per cent. (2) What is the interest on 1^750 for 2^ yrs., at 8 per cent. .'' (3) What should be paid for the use of $450 for 9 mos., at 8 per cent. ? (4) If $500 amounts to $630 irx 4 yrs., what is the rate paid ? (5) At what rate pei cent, will $375 amount to $440 in 3 yrs. 4 mos. ? (6) The simple interest on $900 for a certain time at 6\ per cent, is !li247, find the time ? (7) What principal will amount to $1040.40 in 3^ yrs., at 7 per cent. .'' (8) At what rate per cent, will $144 in 4 mos., earn $2.88 as interest ? (9) The interest paid a banker for the use of $1250, from May 3 to Sept. 26, is $40. Find what he would re- ceive for the use of $950 from Mar. 8 to October 13, at same rate ? (10) Find the amount of $1525 at 6 per cent., from May 6, 1894, to July 8, 1895, simple interest. LV I. INTEREST. (i) $750 was lo .'led on May 7, 1896, at 6 per cent. On what date did it iimount to $786 ? (2) How long will it take $300 to e.irn !|>3C)oas interest at 5 per cent., 8 per cent., 9 per cent., 10 per cent, I2l4. |)er cent. ? (3) How long- will it take $750 to earn $750 as interest It 5 )e; cent., 8 per . nt., 9 per cent., 10 per cent., 12J |)cr c-°nt. .'' ■-- . f 66 ARITHMETIC. (4) How long will it take $450.60 to double itself at 5 per cent., 8 per cent., 9 per cent., 10 per cent., 12J per cent. ? (5) How long will it take any sum of money to double itself at 5 per cent., 8 per cent., 9 per cent., 10 per cent., 12J per cent. ? (6) From the foregoing write your own rule for finding the time necessary for any sum of money to double itself when the rate per cent, is given. (7) In how many years will $950 amount to 3 times itself at 5 per cent., 8 per cent., 9 per cent., 10 per cent., 12 J per cent, ? '(8) On June 5 I borrowed $960, and on Oct. 29, I settled by paying $979.20. What rate per cent, was I paying ? (9) The amount of a certain sum for 3 yrs., at 8 per cent, is $930.00, but at 10 per cent, the amount would be $975.00. Find the principal. (10) The amount of a certain sum for 2% yrs. simple interest is $1080, and for 4 Find principal and rate. yrs. the amount is $115: LVIL— INTEREST. (i) At what rate per cent, will $1500 in 4 yrs. amount to the same sum as $1250 at 6 per cent, for 6 yrs. ? (2) The interest on a certain sum for 5 yrs. is '-^ of the principal. Find the rate. (3) I borrow a sum of iV\oncy for two yrs., agreeing to pay 7 per cent, the first year, and 6 per cent, the second year, simple interest. At the end of two yrs. I discharged the debt with $791. ?^ind the sum borrowed. (4) $750 is the amount of a certain sum borrowed at 8 per cent., while $718.75 is the amount of an e(|ual sum loaned at the same time at 6 per cent. Find the sum lent and the time. (5) In 4J^ yrs. a certain sum of money amounts to $848.36 the rate being 8 per rent. In how many years mofc'wWl it amount to $939.80 ; also, what was the sum ? m INTEREST. 67 e itself at ., 12^ per ■ to double per cent., for finding luble itself to 3 times per cent., Oct. 29, I ent. was I ,, at 8 per t would be y^rs. simple It is $1152. yrs. amount yrs. ? . is I of the agreein}( to the second discharged )or rowed at 1 equal sum nd the sum amounts to many years as the sum ? (6) Find the interest on $275.80 for 91 days at 7 per cent. (7) The amount of a certain principal was $307.20 for 3.^ yrs., and $312 for 3^ yrs. Find the principal and the rate. (8) What sum of money will produce $300 interest in 2^ yrs., .at 6 per cent, simple interest ? (9) At what rate per cent, will any sum of money amount to 3 times itself in 25 yrs. ? (10) What will $1 amount to from March 12, 1803, to October 17, 1896, at 7 J per cent. ? MULTIPLICATION TIME TESTS. 7 For Constant Multiplier. Multiply each of the following numbers, using 7 as a factor 10 times in succession : (0 24679- (2) 62749. (3) 97624. (4) 72649. (5) 29647. (6) 92647. (7) 37658. (8) 56738. (9) 85637. (10)68735- ('0 75368. (12)87563. (13)46789. (14) 94768. (15)67948- (16)86974. (17)67498. (18)98764. (19) 46879. (20) 64897. (21) 87496. (22) 49678. (23) 96748. (24) 74689. (25) 34567. (26) 45637. (27) 74653. (28) 43756. (29) 67435. (30) 57346. (31) 23456. (32) 63254. (33) 46532- (34) 53642. (35) 32645- (36) 64523. {^7) 12345. (38) 23145. (39) 4532r. (40) 34152. (41) 43521. (42)24135. (43)76598. (44)65789. (45)95768. 8 For Constant Multiplier. Multiply each of the following numbers, using 8 as a factor 10 times in succession : (i) 56789. (2) 67895. (3) 7895^'. (4) 57896. (5) 78965. (6) 80657. (7) 96578. (8) 67589. (9) 75896. (10)89654. (11)96548. (12)65489. (13)79568. (14) 95687. (15)56879. (16)86597. (17)78659. (18)97865. (19)75864. (20)58647. (21)86475. (22)79465. (23) ')4657. (24) 46579. (25) 85697. (26) 56978. (27) 69785. CS) 78985. (29) 89857. (30) 98578. (j.) 5«979. (32) '■^9795. (33) 97958. (34) 962 1 5. (35) 62 1 SQ. (36) 2 1 596. (37) 58742. (38) 87425. (39) 74258. (40)92145. (4f) J1459. (42)14592. (43)69124. (.!4) 7ts per lb. s 60 lbs. )f 40 cent 3.60, and o sell the of 25 per F'ind rate much as I laid for a 165^ per 5 raised to I retailed it at 45 >^ cents per lb. making 30 per cent, thereby. Find the number of lbs. bought. (6) )4 of selling price = g of cost price. Find rate of gain. (7) A dealer imported 12 pieces silk average length 28 yds., at 90 cents per yd. The customs duties were 35 per cent, of invoice price. Find proceeds of sale to yield a profit of 25 per cent. (8) A hhd. of PVench wine containing 125 gals, of wine was invoiced at $2.40 per gal. The duties charged on foreign wines was equivalent to 80 per cent. Find how much higher price for the lot must be charged to make 30 per cent, profit, than had there been no duty ? (9) A crate of chinawarc was received, j\j of which was damaged. The invoice price was $120. Find at what rate of profit the remainder must be marked to make a profit of 30 per cent, on the transaction ? (10) Bought 60 gals, of brandy at $3.60 per gal. One- third leaked out. At what pri( e per gal. must the re- mainder be sold to yield 20 per cent, profit ? MULTIPLICATION TIME TESTS. 9 For Constant Multiplier. Multiply each of the following numbers, using 9 as a factor 10 times in succession : (1) 79867. (2) 93219. (3) 89378. (4) 5^'«79- (5) 68759. (6) 89697. (7) 69378. (8) 97S65. (9) 7S695. (10)96859. (11)48973. (12)12345. (13)89376. (14) 793^9. (15)97369. (16)48976. (17)87693. (18)76938. (19) 69387. (20) 93876. (21) 38769. (22) 79386. (23) 12876. (24)28761. (25)87612. (26)56345. (27)63455. (28)34556. (29)34652. (30)46523. (31)65234. (32) 54362. (33)43625. (34)36254. (35)62545. (36)25456. (37)54562. (38)75623. (39)56237. (40)62375. (41) 78654. (42) 86547. (43) 65478. (44) 54768. (45) 64875. 74 AKirilMKI IC. MISCELLANEOUS MULTIPLICATION. Find the '"oUowin^'^ products : (i) 13^792468x4567. (2) 135792468x7654. (3) 13579246;'. .745. (4)135792468x5476. (5) 246813579 X- 4567. (6)246813579x5476. (7)246813579x6745. (8) 987654321 X6754. (9)987654321 X7654. (10) 1 23456789 X- 6745. (u) 9''^7^'5432i X45^'7- (12) 9''^7f'5432i x 5^>''4- (13) 123456789x4567. (14) 123456789x7654. (15) 123456789x5476. (16)874325687x8967. (17)817641358- X 45698. Lxv.— connissioN and insurance. (1) Sold 30 bales of cotton, each of 480 lbs., at i2>2C. per lb. on a commission of zyz per cent. Find the amount of commission. (2) On a sale of 3600 bushels of wheat made at 60c. per bushel, my commission was .'548.60. P'nd the rate of commission charged. (3) A shipment of 560 hogs, averaging 180 lbs., was sent to Montreal for sale. The price realized was ^}i cents per lb. Find the commission at 2)^ per cent. (4) An insurance for $18000 was effected at }i per cent. Find premium charged. (5) On my house worth $6000 there is a policy for ~/i of its value. Find my loss after paying five premiums of \ per cent, each, in case my house were destroyed by fire. (6) My commission on a sale of wheat at 75c. per bushel on a commission of 2% per cent, is $94.50. Find the number of bushels. (7) Find the cost of insurance to a business man who held policies on his property as follows : (a) Phoenix Co., $3000 at I per cent. ; (b) Gait Mutual, $5000 at % per cent.; (c) Liverpool and (ilobe, $3000 at | per cent.; (d) The Imperial, $3000 at % per cent. (8) A tax collector is paid lyi per cent, commission on all taxes he collects. If his share is $214.65, find how much the town receives. LOSS AND CAIN. 7$ (9) In a town where the collector is paid a commission of $2 per cent, for collecting the taxes, the council desire to raise $17493 for the buildin},^ of a waterworks system. How much did the collector ^,'ather in? (10) What is the preniiuiu for insuring a cargo valued .It $35620 at 2} per cent.? LXVI.— MISCELLANEOUS PERCENTAGE. (i) By selling tweed at $2.60 a yd., it was found that there was a gain of ()2}4 per cent. ; wiiat selling price per yd. would have given a gain of 70 per cent. ? (2) A grocer gained 20 per cent, by selling 10 lbs. sugar for $r. He then raised the price giving only 9 lbs. for $1. What rate per cent, did he make at the new |; ce ? (3) By selling tea at 60 cents per lb. a grocer losr . 20 jicrccnt. At what price should he sell to gain 2c per cent. ? (4) IJought oranges at the rate of 10 cents per dozen and sold them at the rate of 5 for 11 cents. Find rate per cent, of gain ; also gain on 1 1 boxes, each containing 20 dozens ? (5) Find the duty on 8 hhds. of sugar, each weighing 1 200 lbs. gross, at i^ cents per lb., 16 per cent, being allowed off for packages. (6) Mow much water must be added to 92 gals, brandy \k'orth J4.60 a gal., in order that there may be a gain of 25 per cent, when the mixture is sold for $4.50 per gal. ? (7) A merchant buys suyjar at $7. 50 i)cr cwt. At what price per lb. must he sell to gain 10 per cent. ? (8) A man who lost 33>^ per cent, of his fortune one year, and 28* per cent, of the remainder next year, finds he has $900 left. What had he at first ? (9) A dealer sold a coat for $8.10 and lost 10 per cent. At what price would he have made 10 per cent. ? (10) A dishonest grocer used a weight o{ i^'A ounces for I lb. What gain per cent, does he make by his dis- honesty ? 76 ARllH.MKTIC. LXVIl— niSCELLANEOUS PERCENTAGE. (1) A man sold 2 farms for $3600 ciuli. On one he gained 20 per cent., and 011 ihe other he lost 20 per cent. Find gain or loss on whole. (2) A merchant soKl a i)ie(e of cloth for $24 and lost 25 per cent. What per cent, would he have gained had he bold it for $34 ? (3) Water in freezing expands 10 ])er cent. A cu1)ic foot of water weighs luoo o/. l-'ind the weight of a cubic fool of ice. (4) A merchant bought 1000 yds. of carpet at 60 cents a yd., and sold 'j of it at a profit of 30 ])er cent. ; I2 at a protit of 2CJ per cent, and the remainder at a loss of 20 per cent How nuu h did he receive for the i ar|)et .'' (5) A house and lot are together worth 52100; 25 per cent, of the value of the house is equal to 33.^ per cent, of the value of a lot. Find the value of each. (6) If in a certain town 3'3093.75 was raised from a ^4 per cent, tax, what was the value of the property in town? (7) A man having lost 20 percent, of his capital now has just as much as another who has gained 1 5 per cent, of his ca])ital. The second man's capital was originally Jyooo. What was the first man's capital ? (8) A bushel of potatoes weighs 60 lbs. If a grocer buys a ton of ])otatoes for $15 and sells them for 15 cents a peck, find gain \)cr cent. (9) A town whose population was loooo increased 10 per cent, each year for 3 years ; what was its population at the end of that period ? (10) If for $7 I can have tjie use of S35 for 3 years 4 months, what rate am I paying .'' LXVI 1 1. -MISCELLANEOUS PERCENTAGE. (1) A fruit merchant bought a qua.itity of apples for $144 ; he sold lialf of them for $82.80, thereby gaining I2c. on each bushel. Find how many bushels were bought, also the gain per cent. MISCELLANEOUS PERCENTAGE. 11 AQE. one he )tr cent. jind lost lied had A cul)ir t'a cubic 60 cents >2 .'It a of 20 per ; 25 i)er r cent, of rom a V ■ in town? )ital now per cent, ariginally a grocer • 1 5 cents eased 10 opuhitictn 5 years 4 (2) A sold a town lot to B, and gained f2>^ percent. \\ sold it to C for $306, and lost 15 percent. How much did the lot cost A ? (3) Brown purchased ./jv of a mill property for $4064.55, and Smith ])un hased .jV, of the same property at a rate 5 per cent, higher. \\ hat did Smith's part cost him ? (4) A farmer whose pioperty is assessed $(/)Oo, pays on the dollar 1 '4' 'I'il's foi' township rales; i '+ mills for county rates ; i^zniills for railway bonus, and 2 'j mills for scliool rates. How much does he pay in all .'* (5) A pcrstm sold A 75 per cent, of his land, \\ '.r cord. (2) A ; lot of ground 240 it. x 120 ft. is piled with wood to the height of 12 ft. What is its value at $4.50 per cord .'' (3) A lot containing half an acre is piled 8 ft. high with cord wood worth $3 50 per cord. Kind its value. Ui dianii (') the fo cter 4' 5' 3" ; (2) (.t)ir 127392- 1 visor lo 13) 5916- ?9 1 44704. 5380703- 36.S. livisor lo 02. (23) 1 2802060- 32898613. ;o) 16198- divisor 10 760. (33) 6 1 1 7966 1 - )23I32!6o 40) 84778- divisor 10 '819. (43) 5) 311634- p6 1 28 172- 370687723- lonj;, 12 ft. with wood $4.50 per :. high with uc. CIRCLES. 79 (4) A barn 80 ft. long and 60 ft. wide, is built on a lot 308 ft. long and 204 ft. wide. The rest of the lot is covered with cord wood to the depth of 8 ft. How many cords of wooci were there ? (5) A fanner lelivers to a merchant a pile of wood 88 ft. long, 12 ft. wide and 8 ft. high, worth $3.50 per cord, and takes a carpet 27 in. wide to fit a room 18 ft. wide and 24 ft. long, costing $1.25 per yard, and takes up a note owing ^o the merchant for $120, bearing interest at 8 per rent, for one ye;' r, and from 15th March to Aug. 8th following. The rest he got in cash. Find that amount. (6) Wood covering a quarter acre lot to the heigh*^ of 8 feet is transferred to another lot 120 ft. by 121 ft. low high is the wood piled in the second lot .'' (7) A load of wood 10 ft. long, 3 ft. 8 inches wide, and 3 ft. high was sold for $3. What was the price per cord, and at $4 ])er cord, what would the load be worth .'' (8) How many bricks 9 inches long, 4 '3 inches wide, and 4 inches ♦ lick will he required for a wall 60 ft. long, 17 ft. high and 4 ft. thick, allowing that the mortar increases the brick ^\ in bulk ? (9) There is a pile of solid bricks long, 16 ft. 6 inches wide, and 14 ft. 6 contains 122496 bricks of uniform size, inches long and 4,5^ inches wide. Find its thickness. (10) A brick wall is to be built 90 feet long, 17 feet high and 4 feet thick. Each brick is 9"x 4>^"x 2>^". How many bricks will be re>.[uired .'' LXX -CIRCLES. Unless otherwise instructed, always assume that the diameter multiplied by 3I -= circumference of any circle. (i) Find the circumference of the circle which has the following dime/isions : (a) diameter 7 feet ; (b) diam- eter 4' 8' ; (c) diameter 8' 2" ; (d) radius 3' 6" ; (e) radius 5' 3" ; (f) radius 4' i". (2) Find the diameter when the circ umfcrencc is : (a) u'; (b) 12' 10"; (c) 20' 2". which is 36 feet inches high, and Each brick is 9 8o ARITHMETIC. (3) Find the area when (a) radius — 7' ; (1)) radius = 154' ; (c) radius = 9' 4". (4) Find the area when (a) circumference— 14' 8' ; (b) diameter = 3' 6" ; (c) circumfeicnce = 22'. (5) The wheel of a wheelbarrow is 20' in diameter. How many times '»ill it turn in goinj( a mile? (6) The fore-wlicel of a carriage turns 420 i.nes more thai, the hind one does in j,'^oinj^ a distance of tiiree miles. If diameter of smaller wheel be 3', find circumference of larger. (7) The len},nh of the minute hand of a fire-hall dork is 42". Find the distance travelled by the extreme point of the hand in a year of 365 days. (H) The hour hand of the same clock is but 28" lonj^. Find how much farther tin; extreme point of the minute hand travels in a year of 365 days than does the extreme point of the hour hand, (9) A bicyclist ridinj^ a wheel of 26" diameter counts 168 revolutions per minute. Find distance travelled in one hour. (10) A horse in trottinj,' takes i.So steps ju-r minute, each 5' 6" long. Find h(nv many times the hind wheel (5 feet in diameter) of the buggy will turn in one hour. LXXI. -CIRCLES. (i) A circular plot of ground 120' diameter has a walk 10' wide on the inside. Find the cost of constructmg such a walk at 31 '2 cents |)er sc|uare yard. (2) The interior of the plot referred to in No. i above is sodded at the rate of 6,'Jj cents per square yard. Find the cost of th.c sodding. (3) A boy turns a grindstone of 15' radius 24 times per minute. If a chalk mark were made on the stone 4K"fiomthe outer edge, find in yards the distance it would travel in the course of 15 minutes' turning. (4) The diameters of the fore and hind wheels of a carriage arc respectively 4' 4^'<" and 5' 3". How far has the carriage gone when the hind wheel has made 768 revolutions less than the fri>nt one ? (I) F cylinder (a) (b) (c) (d) (e) (0 (g) (h) fi) < (2): (.1) : (b) (c) CYLINLERS. 8l ■adius = ^14' 8'; iameter. les more :;e miles, rcncc of all clork lie point 28" long. t minute exlreiue T counts veiled in • minute, 11(1 wheel ! hour. (5) ^. man trundling a wheelban-ow takes on an aver- age 60 steps of 2' 6" each per minute. How many limes does the wheel 14" in diameter turn in an hour? (6) I have a plot of ground 28 feet sruare. Centrally in it I place a circular flower bed 28 feet in diameter. Find area I shall have to sod around the margin of the bed. (7) The fore wheel of a carriage is 4' in diameter, while the hind one is 5'. Find difference in number of revolutions in a drive of 20 miles. (8) A goat is tethered in a pasture lot with a rope 126 feet long. Find area she can graze over in square yards. (9) A woman rolls her pastry for cakes into a square of 28 inches to a side. She uses a cake-cutter 4" in diamtiter. After cutting all the cakes she can, find the area of the pastry left. (10) I have bunting 22" wide, with which I desire to cover the four posts of my verandah. The posts are 7" in diameter and 12' high. Find the cost of the bunting necessary at 40 cents per yard. LXXII.-CYLINDERS. as a walk istructmg I. I above rd. Find ; 24 times the stone listance it neels of a w far has made 768 (i) Find the cubic inches in each of the following cylinders : (a) 3 in. radius, 6 in. height. (b) 6 " " 10 " (c) 4 " " 12 " (d) 10 " diameter, 4 in. (e) 12 " " 8 " (f) 14 " " 10 " (g) 44 " circumference, 8 in. height, (h) 22 " " 6 '• " 'a) 66 " " 7 " " (2) Find the diameter of the following cylinder? : (a) 1232 cubic inches contents, and 8 in. heiglu. (b) 1540 " " " 10 " (c) I13[-? " " " 10 " It 82 ARITHMETIC. (3) Find the radius of each of the following cylinders : (a) contents 2425 X cubic inches, height 7 in. (b) " 231 " " 6 " (c) « 905^ " " 8 " (4) Find the number of cubic inches in a wooden cylinder 18 in. high and 6 in. diameter. (5) How many gallons in a cylindrical cistern 4 ft. diameter and 8 ft. deep (i cubic ft. =6)4 gals.)? (6) How many bbls. of water '-. a cistern 6 ft. diameter and 14 ft. deep (i cubic ft. =6X gals.)? (7) I have cylindrical oil r,ans 12 in. high and 6 in. diameter. How many of these could I fill from a cylin- drical tank 36 in. diameter and 8 ft. long ? (8) Find the weight of a circulai piece of lead 4 in. diameter and 6 in. thir.k, allowing lead to be ii>^ times as heavy as water. (9) A wooden cylinder 24 in. high and 8 in. diameter is reduced to a diameter of 6 in. Find the number of cubic inches thus removed. (10) A circular piece of lead is 2 in. in thickness and 10 in. in diameter. A piece of 3 in. radius is cut from it. Find the weight of the circular ring left, allowmg lead to weigh io>^ times as much as water. LXXIIL— niSCELLANEOUS PROBLEMS. (1) Simplify- 10I of 7'i 19/1-4/- 4t 3 + 3iix8f 9^-4 24X73 (2) The long'tude of Ottawa is 75° 45' west, and that of Tokio, Japan, is 149' 15' east. Find time at Tokio when it is 12 o'clock noon on Monday at Ottawa. (3) My gain was at the rate of 20% when I sold tweed at $1.50 per yard. Find the gain on a sale of 875 yards made at $1.75 per yard. (4) A can do a piece of work in li of a day, B could do the same V ' r! in yIj of a day. Find the time thev would take to do .61 of the work. (5) A years, am rate per c (6) W price per (7) A of his wh( a lo-acre (8) Sil .1794870 (9) Tl thick. A many gall ft. = 6Xg (10) A 3/ in. thic long. F'v. LXXI (I) Si (2)T] if 1920 so sovereign (3) TI simple in (4) Six ni Two Hull eij^ht })cr On Ja settle the (5) A ions will i (6) A ■ii ^;J cei MISCKLLANEOUS PROULEMS, 83 blinders : wooden tern 4 ft. diameter md 6 in. 1 a cylin- ;ad 4 in. \yi times diameter umber of cness and It from it. ig lejid to EMS. , and that at Tokio a. old tweed B75 yards , B could time they (5) A certain sum of money amounts to $750 in 4 years, and to $843.75 in 7 years. Find the sum and the rate per cent. (6) When 2460 lbs of hay costs $21,525, what is the price per ton } (7) A farmer sows 6^^ oz. of v.heat on 1 1 square yards of his wheat field. P'ind the value of the grain sown on a lo-acre field at $.73 per bushel. (8) Silver is worth $1.17 per oz. Find the value of .179487 of a pound of the metal. (9) The ice on a pond containing 5 acres is 1 1 inches thick. Allowing water to expand -^^ in freezing, find how many gallons of water the melted ice would give (i cubic ft. = 6X gallons). (10) A plate of copper 5 ft. 6 in. long, 3 ft. wide and 3/ in. thick is rolled into a sheet 4 ft. 6 in. wide and 6 ft. long. Find its thickness. LXXIV. -niSCELLANEOUS PROBLEnS. (i) Simpl ^ Xo 5 X .006 ofUx(.^)2) / "f^^d)'^ 1. 6 X. 627 (2) The Avoir, pound contains 7000 Troy grains, and if 1920 sovereigns weigh 40 lbs. Troy, find the number of sovereigns coined from an ounce Avoir. (3) The amount of a certain sum for 6 years at z\%i simple interest, is $907.50. Find the principal. (4) Toronto, July 2, 1896. Six months after date I promise to pay J. K. Smith Two Hundred and Seventy I'lve Dollars with mterest at eight per cent. Value received. T. L. Loom IS. On Jan'y 5, 1897, $120 was paid. Find what sum will settle the debt on July 2, 1897. (5) A cubical cistern is 5 feet deep. How many gal- lons will it contain ? i gallon — 277.274 cub. ins. (6) A produce merchant exchanged 48'i bush, of oats at 3q| cents, and 13J bbls. of apples at $3.85 for butter at >!il M ARITHMKTIC. 37| cents per pound. How many pounds of butter did he receive ? (7) Find the L.C.M. of 7, 9, 11, 14, 15, 22, 27, 35, 44, 45. 54- (8) Add together 154.2125, .5421, .0001235, 74i-2o6, .03, and 4567.0004. (9) The difference between 82,610 and the product of two numbers is 70,300,000. One of the numbers is 9,402. Find the other. (10) After spending ^^^ of my money and $26, I found I had still 1^ of my money and $26 left. Find my money. LXXV.— niSCELLANEOUS PROBLEMS. (1) Simplify ?(|-i;^;v|inT|ofAx.7?)^sV (2) At whit time between 6 and 7 o'clock will the| hands of a watrh be i" minute spaces apart? (3) Find the amount of the following bill in dollars! and cents, the shilling being worth 24 !j cents : 1 15 yards Hnisscls carpet at 5s. lod. per yard ; 95 yards Dutch fililli at 2s. 7d. ; 84 yards Kidderminster nt p. jd.; 7j| yards drugget at 2s. 8d.; 10 doz. stair rods at 5s. M. (4) Find the greatest number of which 853554 andj 1 1 28894 are multiples, and tho least number of which 26, 33, 39 and 44 are divisors. (5"> What per cent, is Um by miil-kiliM goods 16?^ perl cent, above cost, and then giving a discount of i6i^ perl cent. ? (6) A and H had the same sum of money. A lost iiil the course of a year $225, while 11 int reased his moiieyl by J of his original sum. A's money is now ■^■)^ of 15'- Find the shares at first. (7) A sells a horse which cost him $120 at a gain ot| 20 per cer^*. t') li. B, in turn, sells to Catanadvan of / 5 per cent, on his cost. Had A sold directly to l,| find A's rate of profit. (8) A's farm contains 100.46875 acres, which lacks! .28125 acres of being X ^s large as B's. B's farm c\\ Lxx^ (1) Si (2) If !;o X 24 X ; (3) If apples an^ of each. (4) Fi (5) I^i may have together, (6) 60 8 tiays' W( necessary (7) Tl O.C.M. is (8) A \vas wort I |)i r lb. (9) L)i nuich as . (10) ( cial fonn, ^ kegs 3 ^~^' pkgs. 4^^^ lbs. st MISCELLANEOUS I'ROULEMS. 8: ( c-eds six times C's by 5.725 acres. Find the extent of tlic three farms. (9) A farmer bought 50 animals, sheep, lambs and pigs, for $324. There are three times as many lambs as siieep, and twice as many pigs as lambs. A sheep costs twice as much as a lamb, and a lamb i % times as much as a pig. Find the numbers and prices of each. (10) A purse and its contents are worth $10.50, and thirteen times the value of the purse is equal to twice the value of the contents. Find the respective values. LXXVI.- MISCELLANEOUS PROBLEMS. 1^1 of Hi .i (5 7 8-' (1) Simplifyjf-Jof, J.., (2) If 16 X 10 X 14 X 40x65 X 18x84x45 be divided by 50 X 24 X 70 X 26 X 7 X 12, find the quotient. (3) If 6 apples and 7 apricots cost 4s. 4|d. ; and 10 iipples and 8 apricots cost 5s. i lid., what is the cost of one of each. (4) Find theG.C.M. and L.C.M. of 49. 383and. 142569. (5) Divide J3975 among A, 15, C", and D so that 15 may have ^23 more than A ; C $45 more than A and B together, and D 129 less than B and C together. (6) 60 men can do a piece of work in 24 days. After 8 days' work 12 of the men leave. Find length of time necessary to finish the work. (7) The product of two numbers is 31671 ; their G.C.M. is 9. Find tiie L.C.M. (8) A dealer sells 210 lbs. tea for $142.50. Part of it was worth 73 cents per lb., and the remainder 6( cents per lb. Find tlie number of pounds of each. (9) Divide $59.13 among A, B, and C, giving A '\ as much as B, and giving B only | of C's share. (10) (ci) Make out the following bill in good commer- cial form, supplying names, date, and place : 5 kegs 3-inch nails, 75 lbs. each, at 4J cents per lb. 2H pkgs. copper rivets, 1 lb. 4 oz. each, at \z\ cents per lb. 48 lbs. steel % inch boUs at 36.25 per cwt. 86 ARITHMETIC. 13 doz. table knives and forks at J3.50 per doz. 2 kegs, 62 lbs. each, gunpowder, at 30 cents per lb. 6 barrels millers' lubricant, 31^ gals, each, at 25 cents per gal. {h) The customer pays cash for the bill, and is allowed a discount of 10%. Receipt the bill, you signing for the proprietor. LXXVII.— niSCELLANEOUS PROBLEHS. (i) Simplify 1-5 3-25 , 1-875 3-5 .075 I A 2.1 3.75 (2) A train travels 19 miles in 20 minutes, and a pigeon flies at a uniform rate of 12 miles in 6,5^ minutes. Express as a decimal the rate of the train as compared with the rate of the pigeon. (3) A coal dealer bouglit a quantity of coal for $484. 50 ; he sold 72 tons at $5.25 per ton, and the remainder at 31 cents per cwt. He gained .$153.90 on his bargain. How many tons did he buy .'' .(4) The product of three numbers is 8937992 ; the third is double of the second, and the sum of the second and the third is 906. Find the first. (5) Add together 4840, 478 and 982 ; divide the sum by 140; from the quotient subtract 18, and multiply the remainder by 409. (6) A dealer sold 103 yards of silk and velvet for $105.03. The silk sold for $1.15, and the velvet for $.93. Find the number of yards of each. (7) A grocer bought 6 cwt. of sugar for $52.10; he set aside 65 ll)s. for his own use, and sold the rest so as to make a profit of i}i cents per pound on the whole quantity. How much per pound did he sell it for? (8) I bought a bush farm, 180 rods by 96 rods, at $12.50 per acre. The clearing cost $14.75 per acre, and I paid Si 35 per rod for enclosing the whole farm. The wood was sold for $1 160, and the ashes realized $17.20. Find the net cost per acre. lb: 25 cents allowed for the .Ens. es, and a minutes. compared r $484. 50; ider at 31 tin. How 7992 ; the he second e the sum jltiply the velvet for ;t for $.93. 552.10 ; he rest so as the whole for? j6 rods, at r acre, and arm. The ed $17.20, MISCELLANEOUS PROBLEMS. 87 (9) A note of $360 drawn April 20, 1896, is paid on July 2, 1897, with interest at 7^^ percent, per annum. Find the amount paid. (10) Express as a fraction of an acre the sum of the following : h of ^ of \^ of an acre ; 5 of if of f ^ of ico sq. rods, and ^f of 2J times 605 sq. yards. LXXVIIL— MISCELLANEOUS PROBLEMS. (i) An old lady on counting her eggs found she had an exact number of dozens, but when she counted them by 5's or 7's she always had 3 over. How many eggs had she ? (2) A merchant received a case of goods invoiced as follows : 12 pieces silk, 48 yards each, at 5s. 3d. per yd. ; 15 pieces cotton, 60 yards each, at 6Xd. per yd. ; 20 pieces cotton, 56 yards each, at 4^d. per yd. ; 14 pieces linen, 40 yards each, at is. 3>^d. per yd. Supposing the shilling to be worth 24)^ cents, find the amount of the above bill of goods. (3) A and B together can do a piece of work in ^ of a day, B and C in =^^ of a day, and A and C in y^ of a day. In what time could all working together do the work ? (4) Find the G.C.M. of 68590142 and 85044059. (5) For a voyage of 17 weeks a ship takes provisions to the amount of 17 tons, 12 cwt., i qr., 6 lbs. 10 ozs. Supposing there are 73 men aboard, how much may be allowed each man per day ? (6) A dealer bought 8 carloads of lumber each con- taining 9870 feet at $13.50 per M. He retailed it at Si. 43 per 100 feet. Find gain on the whole lot. (7) If 4 men t'r 6 boys can do a piece of work in 8 days, how long will it take 8 men and 4 boys to do such a piece of work ? (8) Reduce 75.0125 cwts. to ounces. (9) A horse worth $170 and 3 cows worth $36 each were exchanged for 14 calves and $82. Find the value of a calf. 88 ARITHMETIC. (lo) Divide $82.60 among 27 men and yi boys, so that each man may have 3 times as much as each boy. LXXIX.— niSCELLANEOUS PROBLEflS. (i) a. Which is the heavier a lb. of feathers or a lb. of gold ? b. By how much docs an ounce of gold exceed in weight an ounce of feathers ? (2) What sum will amount to $2646.70 in 3X years at "jYz per cent. ? (3) How can you tell without actual division whether a number is divisible, (a) by 2 ; (b) by 3; (c) by 4; (d) by 5 ; (e)by9; (f) by 10.^ (4) A man can cover a 220 yard race in 22 seconds. At that rate how far would a bicycle rider go m 3 hrs., 30 min., 15 sees. ? (5) A map is drawn to a scale of %, an inch to a mile. Find the area represented by a square inch of the map. (6) A druggist buys borax for 5 cents per lb., and sells 3 lbs. for 25 cents. Find rate of profit. (7) By selling 12 lbs. sugar for $1, a profit of 25 per cent, is made. Find what amount of profit a grocer makes by selling 13 lbs. for $1. (8) A cube of silver of one inch side is rolled into a sheet of 4 ft. by 3 ft. Find its thickness correct to 6 places of decimals. (9) A dealer gives ir lbs. 4 oz. sugar for $1. At that rate, find his proceeds from the sale of i ton. (10) A class-room 32 ft. long, 24 ft. wide and 12 ft. high has accommodation for 48 pupils. How much air space is allowed for each ? , LXXX.— niSCELLANEOUS PROBLEMS, ' (,\^- vf ^'^^_ 3H + 4/ 2^5 ^3 22 (i) Simplih'^ rr^ + +7of — x — - ^ ^ '' ' 3h 9 ^^ ''. 25, • (2) Find the difference between .428571 of a guinea and ]\ of a sovereign. C3) Find the smallest sum of money with which I MISCELLANEOUS PROBLEMS. 89 At that could buy chickens at 34 cents, ducks at 85 cents, geese Ht $1.19, and turkeys at $1.87. (4) IJy seUing hats at $2.21 each we make a gain of .625 of cost. Find seUing price per doz. to make a gain of 50 per cent. (5) Divide $258 among 12 men, 15 women and 20 boys, giving a man $3 for every $2 paid a woman, while a boy was paid at just half the rate given a woman. (6) How many cords of wood on a lot 120 feet wide and 180 feet long, and piled 10 feet high, allowing a roadway 12 feet wide through the middle runn-ng the long way ? (7) The population of India is roughly placed at 280,000,000. Allowing each person the 30 inche? allowed a soldier, what length of line would they form if placed side by side ? (8) A man borrows $500 for 3 years at a certain rate, and $400 for 1% years at 1^2 per cent, more, both at simple interest. His total interest charge is $177^. Find the rates. (9) What will it cost to carpet a room 18 feet h^ \^)i feet, strips laid lengthwise, at $1.20 per yard for 27 inch carpet ? (10) A dealer bought 240 bbls. of flour, and sold yi of it at a gain of 33 per cent., 80 bbls. he sold at a gain of 25 per cent., and the remainder was disposed of at an advanrp of 40 per cent, on cost. His total gain was $35 \. 1 md cost price per bbl. % LXXXl.— niSCELLANEOUS PROBLEnS. (i) In walking 2 miles, A takes 4224 steps, whereas P), in walking the same distance, will require 3520 steps. Find difference in the length of their steps. (2) In what time will $3850 at 4X per cent, amount to $4369.75.? (3) A block of ice is 3 ft. by 4 ft. by 6 ft. What quan- tity of water, in gallons, will it furnish when melted, water expanding 10 per cent, in freezing ? IMAGE EVALUATION TEST TARGET (MT-3) 1.0 I.I 11.25 Li|28 |25 |50 *^" »■ U lii |22 *- .. m 1.4 mil 1.6 <^ /: *^ -V ^v '>' o / /A Photograpnic Sciences Corporation 23 WEST MAIN STREET WEBSTER, N.Y. M5S0 (716) 872-4503 ^.V 90 ARITHMETIC. (4) % of A's money =^ of B's, and ^ of B's=^ of C's. Together they have $899. Find share of each. (5) In an election contest A's vote is to B's as 5 to 7. B is elected by a majority of 192. If the total names on the list were 1 260, how many did not vote ? (6) A mixture of wine and water, in which there is 120 gallons of wine, is worth $1 .00 per gallon. If the wine be $1.25 per gallon, how much water is there in the mixture? (7) At what time after six o'clock are the hour and minute hands first 10 minute spaces apart ? (8) f of a quantity of goods was sold for what f of the goods cost. Find the rate of gain. (9) Divide $103.75 among three persons, so the first has $10 less than the second, but has double the third man. (10) I have $30000 invested in mortgages, which yield an income of 6 per cent., but after paying an income tax on the whole mcome, I find I have for my own use $1771.20. Find the rate charged. LXXXIL— niSCELLANEOUS PROBLEnS. (!) S.mphfy -iyj:.^_ g|- -^x^x,x2| (2) When the dealer's gain was 14^ per cent, of the selling price his gain was $378. Find the sum for which he sold the goods. (3) 15 geese and 12 turkeys cost $22.20. The turkeys were worth 50 cents each more than the geese. Find the value of 8 geese and 5 turkeys. (4) Divide $144 among A, B, and C, giving A ^ of B's share, and B ^ of C's share. (5) A capitalist has $67,718 which he divides into 2 shares, so that the interest on the ist sum for 8 years at 5 per cent, is equal to the interest on the 2nd sum for 5 years at 6 per cent., simple interest in both cases. Find the two sums. (6) Resolve 180 1800 and 540540 into their prime MISCELLANEOUS PROBLEMS. 9t ch. 5 to 7- mes on e is I20 wine be fixture ? our and ^ of the the first he third lich yield :ome tax own use Ens. It. of the for which le turkeys Find the r A H °^ des into 3 5 years at 5 sum for 5 ses. Find heir prime factors ; from these factors find their L.C.M. and G. CM. and divide the former by the latter. (7) The wages of A alone for 36 days will pay the wages of A and B together for i6ff days. For how long would the same sum pay the wages of B alone ? (8) A Montreal commission merchant sold a consign- ment of 240 hogs, average weight 180 lbs., for $4.75 per cwt. Find his commission at 2)4 per cent. (9) A grass plot having its sides in the ratio of 2 to 3, contains 2400 square yards. Find the cost of an orna- mental fence round it, costing 53 cents per foot. (10) What is the total cost of the following : 108 eggs at 13 cents per doz. ; 128 lbs. pork at $6.25 per cwt. ; 1650 lbs. bran at $12 per ton ; 6060 lbs. wheat at 87 cents per bushel ; 375 lbs. sugar at 20 lbs. for $1 ; 963 lbs. oats at 68 cents per bushel ? LXXXIIL— MISCELLANEOUS PROBLEilS. (i) Simplify ?£ ^-«f6-4 .38X .27 .9 (2) A and B can do a piece of work in 4f days when working together ; B can do ^ of the work in 6 days. Find A's daily wages if $18 were paid for the whole job. (^) In an 80 gallon mixture of wine and water the wine was § of the whole. How much water added will make the mixture, half-and-half ? (4) A sailor had a rope 140 feet long, which he cut so that I of the shorter piece is just the length of ^ of the longer. Find the lengths. (5) A farm worth $7200 is rated at ^ of its value. Find Mr. A's taxes when we know the rate to be ii>^ mills on the dollar. (6) Bought ^ of 4j cords of wood for | of § of $30 ; find value of 26 cords at same price. (7) If we increase a quantity by }4 of itself, and that result by y^ of itself, what part of the original number shall we now have ? ' 92 ARITHMETIC. LXXXIV.— ENTRANCE, 1895. (i) (a) Make out the following bill neatly, accurately and in proper form. All fractions are to be retained : John Wilson bought from you to-day : 7)^ lbs. cheese, at I2>^ cents per lb.; 6>^ lbs. butter, at 23 cents per lb.; 2}4 lbs. tea, at 55 cents per lb.; 27 lbs. sugar, at $1.00 for 12 lbs. (b) He paid you cash, and you allowed him a discount of 5 per cent, (c) Receipt the account. (2) Find the simple interest on $912.50 at 8 per cent, from 13th February, 1893, to 19th December, 1894. (i year =365 days.) (3) A farmer sold a load of barley weighing 2712 lbs., when barley was 40 cents per bushel. In weighing the gram, the dealer made a mistake and took it as rye, paying for it at 49 cents per bushel. How much did the farmer gain or lose by the result ? (4) A cord of wood and 100 bushels of grain fill equal spaces. A cubic bin whose edge is 12 feet contains 45900 lbs. of grain. Find the weight of one bushel of this grain. (5) Find the expense of sodding a plot of ground which is 40 yards long and 100 feet wide, with sods each a yard in length and a foot in breadth, the sods, when laid, costing 75 cents per hundred. (6) A can walk 3^ miles in 50 minutes, and B can walk 2)4 miles in 36 minutes. How many yards will A be ahead of B when A has gone 6 miles, if they start together? (7) A can do a piece ot work in § of a day, and B in i of a day. In what time can both together do it? If $1.40 is paid for the work, how much should A receive? . (8) (a) Simplify Sl + ^^^-^xs of 3*-^, and (b) Divide 6 by .000725 correct to four decimal places. LXXXV.— ENTRANCE, 1896. (i) How many boxes, each holding |^ of a quart, will be required to hold 12 bushels, 3 pk., i gal., 2 qt. of straw- berries ? oats avera bushc (8 (i (ii (ii (v (vi (vi nine. ENTRANCE. 93 urately :ained : :ese, at jer lb.; Lt $i.oo ed him er cent. r, 1894- 712 lbs., ing the as rye, did the ill equal contains ushel of ground )ds each ds, when d B can s will A ley start and B in o it? If receive ? decimal [uart, will ofstraw- (2) a. Reduce to its simplest form : i-jfof - Hi 1 b. Simplify the following without reducing to vulgar fractions: .0476x4.2-;-. 014. (3) Toronto, Jan. 8th, 1894. One year after date, I promise to pay Gilroy & Wiseman, or order, one thousand dollars, with interest at six per cent. Value received. John Wilson. This note was paid in full on Jan. 25th, 1895. Find amount. (4) At $15.00 per M., board measure, what will be the cost of 2-inch plank for a 4-foot sidewalk, half-a-mile long? (5) A man earns $280 in 2J months. If he spend in 4j months what he earns in ^Ji months, how much will he save in a year? (6) An apple buyer paid $198.00 for I26bbls. of apples consisting of Northern Spies and Wagners ; there were % as many Spies as Wagners, and the latter costing 25 cents per bbl. less than the former. Find i'le cost of each kind per barrel. (7) On Monday, a grain dealer bought 932 >ushels of oats at 2 1 cents per bushel ; on Tuesday, 080 L jshels at 20 cents ; Wednesday 836 bushels at 20 cents ; Thursday 675 bushels at 21 cents ; Friday 765 bushels at 22 cents ; Saturday 751 ^bushels at 22 cents. He then sold the entire week's purchase at 2 cents per bushel above the average cost per bushel. Find (a) The average cost per bushel, (b) His whole gain, (c) His gain per cent. (8) Find the sum of the following numbers : (\) Nine millions, five hundred and three, (ii) Eight hundred thousand and four. (iii) Five hundred and seventy millions and two. (iv) Three hund'-ed and fifty-three thousand, (v) Two thousand and four, (vi) Fifty-eight thousand and nfty-eight. (vii) Four millions, fifty thousand, three hundred and nine. 94 ARITHMETIC. (viii) Three hundred and six millions, forty thousand and ten. Give the result both in figures and in words. LXXXVL— ENTRANCE, I897. (i) The equatorial diameter of the earth is 13948880 yards, and the polar diameter 2527760 rods. By how many miles and rods is the equatorial diameter greater than the polar ? (2) If $2.o6X buy 7% lbs. of tea, how many lbs. can bebought for $3.71 X? (3) Find the simple interest on $1387 at 1% per cent, per annum from March 21st, 1896, to June 29th, 1897. (4) A farmer sold a load of four-foot wood, 7 ft, long by 4 ft. high, to a grocer, at the rate of $3.60 per cord, • receiving in exchange 3 lbs. tea at 37.J cents per lb.; 5 lbs. rice at 5. J cents per lb., and the remainder of the price in granulated sugar at the r.\te of 22 lbs. for one dollar. How many lbs. of sugar did he receive ? (5) A produce dealer bought 833 lbs. oats at 24 cents per bushel ; 1572 lbs. barley at 36 cents per bushel ; 1995 lbs. peas at 44 cents per bushel. He mixed them, and had the mixture ground into feed without loss of weight at a cost of 5 cents per cwt., and then retailed the feed at $24.50 per ton. Find his entire gain. (6) Find the cost of gilding the entire outside surface of a covered box, 3 ft. long, 2 ft. 6 in. wide, and i ft. 9 in. deep*, at $1.20 per square foot. (7) A retail dealer sold a suit of clothes for $29.40, making a profit of 20 per cent. If the cloth and trim- mings cost six times as much as the making, find how i^uch the tailor who made the suit received. (8) (a) Find the G.C.M. of 1573 and 689. , Divide .7^6064 by .0052. Multiply .0362 by 5.23. Simplifyiof|^ix§-(-H^. e: times. 465. (b) (c) (4) >usand Answers for Fourth Book Classes. 1948880 Jy how greater bs. can er cent. 1897- ft. long er cord, erlb.; 5 r of the for one 24 cents lel ; 1995 lem, and »f weight le feed at surface id I ft. 9 )r $29.40> ind trim- find how (2) 396^. (3) (6) 297. (7) 373- EXERCISE I.— No answers. EXERCISE II.— (i) 38(^% miles. (2) 7 miles, 213 rods, 4 yards, i foot, 6 inches. (3) $2380. (4) 42. (5) 7200 metres. (6) 26880 acres. (7)145. (8) $837.31. (9) 73 cents. (10) $20.10. EXERCISE III.— (i) $6.72. (2) $317.52. <3)$8.58. (4) $28. (5) 66 feet. (6) $102.20. (7) 400,820 bushels (8) 90 cents. (9) 23^^^ bbls. (10) $29250. EXERCISE IV.-(i) 30808063. 23865. (4)^105. (5) 12 lbs. Avoir. (8) 129. (9) $1.25. (10) 137 yards. EXERCISEV.— (i) I3feet. (2) $2520. (3)13.(4) 840 yards. (5) :<-> feet. (6) $36720. (7) 2187. (8) 47 lbs. (9) 113. (10) II inches. EXERCISE VI.-(i) There is no number. (2) 13 times. (3) 7. (4) 72. (5) 45105 and 165. (6) 651 and 465. (7)527554. (8)221. ^9) 4 and I. (10) 13 pecks. EXERCISE VII. -(i) 25t^ miles. (2)87680. (3^ 1980 tons. (4) 63 lbs. (5)56336. (6) 15 acres. (7 $94.50. (8) ^^ fields. (9) $83j. (10) %\ lbs. EXERCISE VIII.— (i) 1280 bushels. (2) 151^ bushels. (3) 46|Hj per cent. (4) 9 lbs. green, 15 lbs. black. (5) $188.75. (6) I ton, 14 cwt., 92 lbs., 14 oz. (7) 2271JI sovs. (8) fV- (9) .06857142. (10) $29j. 96 ARITHMETIC. EXERCISE IX.— (i) $31.50. (2) 3 tons, 6>A cwt. (3) 1 2 j^ cents when bought by cental. (4) 30 bbls. (5) $388.80. (6) 40 gallons, 3 quarts, 1 pint. (7) 8 feet. (8) 72 bottles. (9) $45.00. (10) 6 gallons. EXERCISE X.— (i) $37.65. (2) $61.44. (3) $4.82. (4) $465. (5) $i2.96 + $i3.22 + $24.45 + $66.56 = $ii7.i9. (6) $46.70. (7) $95.50. (8) i6oo lbs. (9) $2280. (10) 56 lbs. EXERCISE XI. — (i) I hour, 49 minutes, 26 seconds. (2) 10. (3) 8 o'clock. (4) 880 hours. (5) .2083. (6) I2:i5-Jp.m. (7) 24 inches. (8) $7.50. (9)$37-73- (10) 220%. EXERCISE XII.— (i) 27 acres. (2) 177 acres, 36 square rods, 17 square yards, 4 square feet, 72 square inches. (3) 26 miles, 226 rods, 4 yards, 2 feet, 8 inches. (4) 14991 7 >^ ounces. (5) $1578.605. (6) 6562 >^ grains. (7) 10042320 seconds. (8) $1 1 52. (9) 4 gallons, 2 quarts, I pt. (i6) $34.56. EXERCISE XIII.-(i) 2489i\ miles. (2) $16000. (3) The latter ; $1.20 in favor of latter. (4) 1960^ bushels. (5) $600. (6) 1980 tons. (7) $189. (8) 225 lbs. (9) $1500. (10) 7 inches. EXERCISE XIV.— (i) 10 feet; 3 feet, 2\iV inches. (2) 3 hours, 24 minutes, 19SIS? seconds. (3) 29, 13, 37. (4) '3- (5) 4 tons, 13 cwt , 22 lbs., 8 oz. (6) 1680 times. (7) $8247.80. (8) 3130 acfes. (9) ^ of field. (10) 5500 miles, <87 rods, 4 yards, i foot, 6 inches. EXERCISE XV.— (i) U. (2) $674. (3) 17 1^ bush- els. (4) (a) o ; (b) o ; (c) A ; (d) ;ft. (5) 43/A miles, and 3(>^^ miles. (6) im, fifg, mi MfS; A. f I I (7) A i%> ?e, i%- (8) M-48. (9) $3790.82. (10) 2^. EXERCISE XVI.— ri) J6300. (4) $24. (5) $10400. (6) $5495. (9) 144 loads. (10) $6339. (2) $15000. (3) $1024. (7) $2484. (8) $5150. e: rods, sq. ft rods. sq. yc yds. rods. (7) rl (10) E^ 7680 acres J 72pai sq. ft.j e: (4) $i (9)$J 6^ cwt. bbls. (5) 7) 8 feet. (3) 54.82. = $117.19. 280. (10) [6 seconds. 2083. (6) 7-73- (10) r acres, 36 72 square t, 8 inches. \2% Stains. -IS, 2 quarts, (2) $16000. 60^ bushels. 25 lbs. (9) 2^^^ inches. () 29, 13, 37- I I 1680 times, p I. (10)5500 ) I7i^bush- 82. (10) 2^. o. (3) $1024. ,. (8) $5 ISO- ANSWERS. 97 EXERCISE XVII.-(i) $3600; $6000. (2) $24.60. (3) $3654. (4) ^ of work. (5) 834 cents. (6) 10500 words. (7) $4.16. (8) $72. (9) $u66. (10) 56 acres. EXERCISE XVIII— (i) $96. turkeys. (4) J of cost. (5) A $28 ; $144. (7) 114. (8) House $1908 ; 4>^ cents. (10) 126 bbls. (2) 444. (3) B $54 ; C $30. contents $1272. 720 (6) (9) EXERCISE XIX. -(i) ^ of cost. (2) 33J cents. (3) 2i days. (4) $44 ; $66 ; $165. (5) 7J hours. (6) 108 feet. (7) $840. (8) i3^Jdays. (9) 20 days. (10) 692 ; 121 1. EXERCISE XX.— (i) $258; $301 ; $215. (2) 4 days. (3) A of cost. (4)584. (5) 45% days. (6) $1085; $217; $434. (7) $396. (8) 8 of each. (9) 180 sheep. (10) ^ of cost. m- , (3) %i- \l' (9) iSf EXERCISE XXI.-(i) ^mih- (4^ li- (5) A- (6) tW- (7) TVa- (10) 3i- EXERCISE XXII —(i) (a) 12 sq. ft. (b) 300 sq. rods, (c) 1225 sq. miles, (d) 2925 sq. miles. (2) (a) 36 sq. ft (b) 1320 sq.ft. (c) 2750 sq. yds. (d) 128000 sq. rods. (3) (a) 67^ sq. ft. (b) 5760 sq. ft. . (c) 6348100 sq. yds. (d) 22303600 sq. yds. (4) (a) 40 yds. (b) 54 yds. (c) 247J ft. (d) 360 ft. (5) (a) 220 yds. (b) 8 rods, (c) 40 rods, (d) 55 yds. (6) 385 yds. by 440 yds. (7) 176 yds. by 220 yds. (8) ^\ acres. (9) 640 acres. (10) 640 acres. EXERCISEXXIII.— ^ cents. (3) $1.17. (4) $i.2a (5) 80 cents. (6) $72.60. (7) $78.40. (8) $96. (9) $12.60. (10) $27. EXERCISE XXXIII.- (i)2i,) $528. ) 5 miles. (6) U of ^62. (10) (2) land, 8640. (5) 8) $34.02. (2) .17 of |C inches. :.68. (10) ^ards. (3) yards, 49 yards, 54 27, $36.75, $73-5o-«- ?5-50- (8) 27 inches. b) 36 feet. 3) 24 feet. 120 yards ; (6) $72.60. (2)(a)32A es; (d) 12 ;(b)2iA minutes ; 32',\ minutes; (t) 38,-, minutes, 491^, minutes; (d) 49j'| minutes ; at 1 1 o'clock. (4) (a) s^'y minutes ; 38^"! minutes ; (b) i6j\ minutes ; 49^^ minutes ; (c) 27^ minutes ; 9 o'clock. (5) (a) S'^^ minutes ; (b) i6|^ min- utes ; (c) 27i\ mins. (6) 32^3 mins. (7) 27^^ mmutes. (8) 8|*j minutes. (9) 32^ minutes past seven ; 43^^^ minutes past seven. (10) 19^^,^ minutes after four ; 24 ninutes after four. EXERCISE XXXIV.— (i) ^ minutes. (2) 30 miles. (3) 218^ miles. (4) 1:48 a.m. Tuesday; 150,'/^ miles from Toronto. (5) 10^ seconds. (6) 6 miles per hour. (7) 125 yards. (8) 120 yards. (9) 99 yards ; 297 yards. (10) 32 miles. EXERCISE XXXV.-(i) (a) 1.286 cents; ^b) 1.706 cents ; (c) 2.331 cents ; (d) 3. 179 cents (2) $55, $109.37!, $194.83.], $3377011. (3) 57JJ cents; $1.36^ J 59.6o; $17.01. (4) Posts $7.20; stnngers $9.90 ; lumber $48.1 if; total $65.2 1 ]J. (5) Lumber $114.12; stringers $31.70; total $145.82. (6) $40.32. (7) $52.44. (8) Sides 3000 feet ; roof 2976 toet ; gables 400 feet ; total 6376 feet ; cost$92.45i. (9) $68.o6X. (10) $390.87. EXERCISE XXXVI.-(i> 60 lbs.; 30 lbs. (2) 45 lbs.; 38 lbs. (3) 73 lbs.; 38 lbs. (4) 15 yards. (5) 188 coins. (6) 60 lbs. ; 40 lbs. (7) $2.40 and $3. (8) Coffee, 36 cents ; chicory, 10 cents. (9) Wheat, 60 cents ; oats, 2j cents. (10) Wheat, 60 cents ; oats, 30 cents. EXERCISE XXXVII.— (i) f. (2) .36. (3)55440 inches. (4) M- (S) 'J times. (6) .583. (7)7. (8) i rood, 32 square rods, 22 square yards. " ' *. (lo) ^, EXERCISE XXXVIII.-(i) i6| yds. (2) A wins by I yd' (3) B wins by 2 yds. (4) 10^ yds. (5) 24 miles. (6) 20 miles. (7) 60 to 79. (8) 293J yds. {9) The first by 5 J inches. (10) 300 leaps. EXERCISE XXXIX.— (i) $1000 ; $250. (2) $424 ; $364; $212. (3) $16.75 ; $13.25. (4) $1468 ; $1398 ; lOO ARITHMETIC. $734- (5) $1373; 51338; J1321. (6) $30.18; $28; $30.98. (7) $2668 ; $933^. (8) $2.10 ; $.70. (9) $1200 ; $900. (10) $13.20 ; $6.60 ; $2.20. EXERCISE XL.— (i) $558 ; '$372 ; $279. (2) 483 acres ; 414 acres ; 368 acres. (3) $2500 ; $3000 ; $4000. (4) $100; $125; $120. (5) $270; $240. (6) $315; $350. (7) 270 ; 240 ; 192. (8) 576 ; 640 ; 600. (9) $227.40 ; $113.70 ; $341.10. (10) $9; $43; $52. EXERCISE XLI.— (i) 30 of each. (2) 30 cows. (3) $143. (4) 300. (5) 12 men. (6) 133 cwt. ; too cwt. ; i3Jcwt. (7) i03i=V lbs. (8) $465.60. (9) 15 of each. (10) 80 of each. V EXERCISE XLIL— (i) 60 cents ; 75 cents. (2) Green 65 cents ; black 75 cents. (3) $19.80. (4) $29.00. (5) 60 lbs. tea ; 40 lbs. coffee. (6) Hlack 35 lbs. ; green 32 lbs. (7) 30 gallons of ist.; 42 gallons of 2nd. (8) 140 gallons. (9) 72 gallons water. (10) 5 brandy to 4 water. . EXERCISE XLIII.— (i) 315 lbs. (2) 60 cents. (3) 144 francs. (4) 34 women. (5) 12 lbs. (6) 11 dozen oranges. (7) 8 J lbs. (8) $19.50. (9) 75 lbs. of each. (10) $10.05, (i) 2|\ days. (2) 7,\ days, j-r uitys. (5) lU days. (6) $11.38; $13.16; $9.87. (7) $6.36; $8.48. (8) $17.35; (9) 26^ days. (10) \o\ days. EXERCISE XLIV. $14.10 $13.88. 3) 2§ days. (4) 4jV days EXERCISE XLV.— (i) 19^} days. (2) 54 days. (3) A \ol\ ; B \zl\ days ; C 19}^ days. (4) 12, 14, 15 days respectively. (5) %^ days, (o) 28^, 36, 48 hours respec- tively. (7) 24 days. (8) A 2 1 days ; B 28 days ; A I48; B $36. (9) i days. (10) 3/0^ works. _;- EXERCISE XLVI.— (i) 10 days. (2) 4 days. (3) No answer. (4) 2f days. (5) Man i».25 ; boy $1.25, (6) 4f days. (7) A $45 ; B $15. (8) 53^ days. (9) 60 days. (10) 2^1^ hours. (4) (9) ANSWKRS. lOl ays. (3) )y $1.25. (9)60 EXERCISE LXV^II.— (i) $8. (2) $20. (3) 180 men. (4) 12 clays. (5) 3lf hours '^^0 Cap. $1.50; wajfcs 6c cents. (7) 56 days. (8) 33[i ' ys, (9) 17-^ clays. (10) I of work. EXERCISE XLVIII.— (i) $68.7^ (2) S126.802?. (3) Mr. Mills owes 80 cents. (4) $31.89^ (5) $75. 4r.!. (6) $3907.02. (7) $93-39'4. (8) $2.80. '(9) $2.20. (16) $29027.84^. EXERCISE XLIX.— (I) .fi525. (2) $90. (3) $12?. (4) $240.50. (5) $187.11. (6) $75.0-2 >i. (7) $160.10. (8) $72.50. (9) $i29.i7j- (10) $223,861%. EXERCISE L.— (i) $25.70. (2) $10.80. (4) $33.69. (5) $51.68. (6) $10.71. (7) $3-98. (9) $9.91. (10) $11.93. EXERCISE LI.- (4) $1302. (5)2212. (9) J332. (10) $203. -(i) $1400. (2) .$250. (6) $526. (7) $1460.25. (3) J6.05. (8) $7.81. (3) J368. (8) $1806. EXERCISE LII.— (1)6%. (5)10%. (6)8%. (7). 178^1%. (2)8%. (3)4%. (4)5%- (8)6%. (9)7%. (10)5%. EXERCISE LIII.— ^ years. (7) $850. (8) 6 per cent. (9) $45.60. (10) $1634.80. EXERCISE LVI.-(i) Februar)' 23, 1897. (2) 20 years ; 12% years ; n^ years ; 10 years ; 8 years. (3) 20 years ; I2>^ years ; 1 1,\ years ; 10 years ; 8 years. (4) 20 years ; 12^ years ; i ig years ; 10 years; 8 years. (5) I02 ARITHMETIC. / 20 years ; I2>^ years ; 11 J years ; 10 years ; 8 years. (6) No answer. (7) 40 years; 25 years; 22$ years ; 20 years ; 16 years. (8) 5 percent. (9) $750. (10) $9(5o ; 5 per cent. tXERCISE LVII.— (1) 3>f^r cent. (2) 7% per cent. (3) $700. (4) 5625 ; 2>4 years. (5) i^ years ; $635. (6) $4.81+. (7) $240 ; 8 per cent. (8) $2000. (9; 8 per cent. (10) f i 27. EXERCISE LVIII.— (i) $39.33. (2) $896. (3) S1480. (4) Gain $878.57. (5) Single dis. by $1.26. (6) $50.60. (7) $318.36. (8) $750. (9) $24.64. (10) $15000. EXERCISE LIX.—(i) $8.40. (2) $15. (3) $110.55. (4) $128.96. (5) $1596.05. (6) $156.25. (7) $126.28. (8) ^ loss. (9) $2672^. (10) ^ of cost. EXERCISE LX.— (i) $862.50. (2) $171.25. (3) $1930. (4) 37^ per cent. (5) $600. (6) i6| per cent. (7) $8.80. (8) 23 per cent. (9) $120. (10) Loss $20. $38.60. (3) $7.40. $3000 ; (b) loss, " $225 ; (b) loss, EXERCISE LXII.— (i) 15^ per cent. (2) 23 per cent. (3) $217.03. (4) $104.80. (5) 118 sheep. (6) $257.16. (7) $39.20. (8) $18.60 per dozen. (9) $2.76. (10) $9.54 loss. EXERCISE LXIII.-ri) 50 lbs. (2) 80 lbs. (3) 14? gals. (4) 24 gals. (5) 5o(^ bushels. (6) 9if^ cents. (7) 30 gals. (8) 20 lbs. (9) 50 lbs. (10) 30 gals. EXERCISE LXIV.— (i) 50 per cent. (2) JiZYz per cent. (3) 33J per cent. (4) 40 per cent. (5) 10 lbs. (6) 6^ per cent. (7) $510.50. (8) $312. (9) 44^ per cent. (10) $6.48. (17) ('9) (21) (23) 10 (25) (27) (29) i: (3') i: (33) (35) I (37 (39 (41) (43) (45 ANSWERS. 107 ars. (6) 3 years ; ; 5 per 7K per years ; CKX>. (9; 96. (3) .26. (6) > $i5cxxj. $110.55. $126.28. 25. (3) per cent. )ss $20. (3) $7.40. (b) loss, (b) loss, (9) 14^ 2) 23 per eep. (6) (9) $2.76. 5. (3)M? f^} cents. jals. ' 33 >^ per 5) 10 lbs. \ per cent. (26^ 5321361. (30) 5366226. (34) 6543103- (38) 6079424. (42) 7560532. (46) 13886347. (50) 7395627. (54) 8699605. (58)8371635. "12) 9279687. (66) 5387645. (70) 758938. Practice (i) 7 times (3) 13 (5) 8 (7. (27) 4984314- (31)6434935- (35)6341198. (39) 6376598. (43) 7459878. (47)7205421. (51)8657407. (55)9765094. (59)8157445- (63) 708675. (67) 6439857. (28) 5137658. (32) 6449234, (36) 5987385. (40)5864231. (44) 8864298. {48)7156036. (52) 8452756. (56) 1 07 1 263 1. (60) 8609233. (64) 9348679. (68) 5397684. (29) 5166336. (33) 5880128. (37)6093241. (41) 14360401. (45) 7592556. (49)7192347. (53) 8569956. (57) 1 1034749. (61) 7967428. (65) 7458967. (69) 579385. IN Subtraction.— Page 50. rem. 789213. (2) :3 times ; rem. " 640997. (4) 10 « 468754. (6> II " 478659. (8) 8 " 844746. (10) 13 " 555555- («2) 12 " 954738. (14) 12 " 893976. (16) 9 " 586749. (18) II " 837594. ('20) II '* 568794. (22) 10 " 222222. (24) 12 " 495876. (26 1 2 " 586578. (28) 13 " 999999. (30) 7 " 1045876. (32) 8 ♦' 758649. (34) 10 « 648956. (36) 13 " 787694. (38) 10 " 546213. Uo) 9 " 687965. (42) 13 •' 378927. (44) II " 578946. (I (C 645758 648997 745689 874956 968754 947856 935478 49786s 467895 794685 568794 IIIIII 597864 758679 498776 186754 859678 568749 798654 123456 569786 479656 (43) 13 (45) 9 Time Tests in Multiplication.— 5 For Constant Multiplier. — Page 60 — (i) 240917480468750. (2) 192- 785400390625. (3)241126463843750. (4)111520751953- io8 ARITHMETIC. 125. (5) 19273828 I 2 50000. (6) 165985839843750. (7) 1938 14697265625. (8) 24090454 loi 5625. (9) 177831- 298828125. (10) 167218505859375. (11) 141 572021484- 375. (12) 2267561035 1 5625. (13) 1 19545 1 6601 5625. (14) 201840087890625. (15) 144698974609375. (16) 166741455078125. (17) 72941650390625. (18) 17545'- 416015625. (19)93822509765625. (20)193526611328125. (21) 84674560546875. (22) 19445385742 1 875. (23) 202- 13061 5234375. (24) 52646240234375. (25) 1151 18408- 203125. (26) 151081298828325. (27) 192819580078125. (28) 175274658203125. (29) 164911376953125. (30) loi 554443359375. (31) 58210205978125. (32)40831737- 109375- (33) 163922607421875. (34) 226737548828125. (35) 158185791015625. (36) 139884521484375. (37) 150226806640625. (38) 71407470703125. (39) 178537- 353515625. (40)101788818359375. (41)95184814453125. (42) 127392333984375. (43) 211976806640625. (44) 532141 1 1328125. (45) 241127197265625. Time Tests in Multiplication.— 6 For Constant Multiplier. — Page 60.— (i) 4696286957568. (2) 5361354- 427392. (3) 4037810300928. (4) 3355207640064. (5) 3553536697344- (6)4217394843648. (7)4628625306624. (8) 47 1 01 94 178048. (9) 5434397568000. (10) 5916978- 118656. (11)4156807735296. (12)4471352782848. (13) 5374717452288. (14)4624815937536. (15)5320237427712. (16)4496083448832. (17)2653134870528. (18)4465306- 165248. (19)5434397568000. (20)4646644227072. (21) 5849866063296. (22) 4648579144704. (23) 4111034840- 064. (24) 5840307007488. (25) 4647672152064. (26) 5984579303424- (27) 4646402362368. (28) 2761973987^ 328. (29) 5233166134272. (30) 5374112790528. (31) 4104141696000. (32)4647853550592. (33)5367401044992. (34 4070824833024. (35) 6046557133834- (36) 6033859- 236864. (37) 5380703603712. (38) 4709649982464. (39) 40 1 846 1 124608. (40) 3487628565504. (41) 4589140893- 696. (42) 3439255624704. (43) 2751 150541824. (44) 4702877770752. (45) 2265546682368. Time Tests IN Multiplication. — 7 For Constant Multiplier. — Page 67. — (i) 697i2o6!S7oo7i. (2) 17725- 039399 (5) 837 926842. 1 94 1 59 228187. (15) ^91 5IV357C (/u) i8j cic54i98 (25) 97( 6247635 (30) 161 6894002, (35) 922 1 569489< (40) 964 5401346 I (45) 270 Time Multiplit 701 1404? (5) 8478 ^378782 (10) 962( 3182783 913088. (17) 84 4583497 230400. (24) 500 66164787 (29) 9648 21903766 (34) 1033 52843 1 10 963200, (41) 2304 32984217 Time Multiplie '50- (7) 177831- '2021484- J6015625. '5- 06) ) I7545I- 11328125. (23) 202- 151 18408- 80078125. 25- (3o) 40831737- 48828125. 75- (37) ;) 178537- 1I4453I25- •25. (44) r Constant ) S361354- 3064. (5) 625306624. ) 5916978- 2848. (13) 237427712. }) 4465306- 7072. (21) 111034840- 064. (26) 761973987- .528. (31) 401044992. 3) 6033859- 82464. (39) .589140893- 824. (44) )r Constant (2) 17725- ANSWERS. 109 039399501- (3) 27576363708376. (4) 2052i5443646:)i. (5) 8374543707103. (6) 261/0484394103. (7) 10637452- 926842. C8) 16027080677762, (9)24190332898613. (10) 1941 59^624001 5. (11) 21289594566632. (12) 24734380- 228187. (13) I 32 I 673442 546 I. (14) 26769614397232. (15)19193628219052. (16)24568002306526. (17)19066- 511357002. (18)27898385492236. (19)13242157197871. (-/O) 18331796234353. (21) 24715454386504. (2'2) 14032- 605419822. (23)27328914890252. (24)21097793872561. (25) 9764321932183. (26) 12891322938613. (27) 21087- 624763597. (28) 12359986995244. (29) 19048718416315. (30) I6198825629154. (31) 6625739440544. (32) 17867- 689400246. (33) 13144138286468. (34) 15152537306858. (35) 9221404503605. (36; 18226150491227. (37) 3487- 156948905. (38) 6537889638105. (39) 12802060759929. (40)9647094703848. (41) 12293605311729. (42)6817- 540134615. (43)21637039122902. (44)18583764156461. (45) 27052089646232. Time Tests in Multiplication.— 8 For Constant MultipJier.— Page 67.— (1) 60976724443136. (2) 72901- 701140480. (3)84778359455744- (4)62165356642304. (5)84788023132160. (6)96268470714368. (7)103699- 837878272. (8)72573136142336. (9)81492709474304. (10) 96265249488896. (11) 103667625623552. (12) 70- 31827831 1936. (13) 85435489452032. (14) 102743133- 913088. (15) 61073361207296. (16) 92982820732928. (17) 84459458x34016. (18) 105081743605760. (19) 81- 458349735936 (20) 62971736752128. (21) 92851824- 230400. (22)' 85324894044160. (23) 101637 1 79834368. (24)50013820420096. (25)92016453091328. (26)61179- 661647872. (27)74931073187840. (28)84809497968640. (29)96483219079168. (30)105847321526272. (31)63328- 219037666. (32)96416647086080. (33)105181601595392. (34)103310069596160. (35) 667427 iA»58o 16. (36)23188- 528431 104. (37) 63073742225408. (38) 93871878- 963200. (39) 79733920366592. <4o) 98939940372480. (41)23041425801216. (42) i5668o4^>(6958o8. (43)74221- 329842176. (44)84788023132160. (45)53016002560000. Time Tests In Multiplication.— 9 For Constant Multiplier.— Page 73-— (0 278479009754667. (2) 325034- ^lO ARITHMETIC. 555076819. (3)311641816192578. (4)198324809944479. (5)239747808628359. (6)312754100416497. (7)241906- 128172578. (8)341234155403865. (9)274392498436695. (10)337726450296459. (11)170758292470173. (12)43044- 353430345- (13) 31 '634842623776. (14)276801866457- 786. (15)339504710340969. (16)170768752823^76. (17) 305766584476893. (18)268266218244138. (19)241937- 509232187. (20) 327325372428276. (21) I35179144442- 369. (22)276801866457786. (23)44895835947276. (24) IO0283406157161. (25) 305484 1 549404 1 2. (26) 196462- 867074345, (27) 221253904165455. (28) I20489321760- 956. (29) 120824053063452. (30) 162215670687723. (31) 227456893614834. (32) 189548573607162. (33) 152:10- 969493625. (34) 126409881673854. (35) 218080930360- 545. (36)88759583711856. (37)190245930487362.(38) 263681096756823. (39) 196086294359037. (40) 217488- 1770I2375. (41)274249540276254. (42)301770729553347. (43) 228307669008678. (44) 190964208073968. (45) 226- 205 1 3801 4875, Miscellaneous Practice in Multiplication.— Page 74-— (i) 620164201356. (2) 1039355550072. (3) 915920196660. (4)743599554768. (5)1127197615293. (6)1351551158604. (7)1664757590355- (8)6670617284- 034. (9)7559506172934- (10)832716041805. (11)4510- 617284007. (12) 5603950617354. (13) 5638'"' T 55363. (14)944938263006. (15)676049376564. (16^7040078- 435329- (17) 37364574777884. Time Tests in DivisioN.-Page 77-8.-(i) 986745. (2) 579879. (3) 826737. (4)718649. (5)346827. (6)618829. (7)238429. (8)928717. (9)731289. (10)521799. (11) 66778. (12) 89876 with a remainder. (13)97856. (14) 73848. (15)76879. (16)76864. (17)67875. (18)88987. (19) 57679. (20) 37468, (21) 53642. (22) 67498. (23) 72649. (24)43756. (25)45321. (26)65789. (27)85637. (28) 46789- (29) 87496. (30) 57346. (31)96758- (32) 97865. (33)58742. (34)96548. (35)56978. (36)58979. (37) 78965- (38) 58647- (39) 2H59- (40) 78956. (41) 34556. (42)93219. (43)62545. (44)64875. (45)89376 (46) 79386. (47) 69378. (48) 62375. (49) 46523. (50) 7693^ EJ yds. 1680. e: 603? ;| 2425*. (c) 6^' bbls. Uo) si ANSWERS. 103 $09944479- 7) 241906- ^98436695. ;i2) 43044- Boi 866457- 3376. (17) 9) 241937- 1 79 1 44442- 7276. (24) [6) 196462- 1489321760- 87723- (31) 33) 152^0- 1080930360- 87362. (38) 40) 217488- 0729553347- 1. (45)226- LICATION.— 50072. (3) 7 1 976 1 5293- 6670617284- . (11)4510- ,3?-TT 55363. 16; / 040078- 986745- (2) (6) 618829. 121799- (/») 97856. (14) . (18)88987. 67498. (23) : (27) 85637- 96758. (32) . (36)58979. ) 78956. (40 . (45)89376. I 46523- (50) EXERCISE LXV.— (1) $45. (2) 2% percent. (3) $n5.24. (4) $135. (5) $2120. (6) 5600 bushels. (7) $101.25. (8) $8371.35- (9) $17850. (10) $783.64. EXERCISE LXVI.-(i) $2.72. (2) 33* per cent. (3) 90 cents. (4) 164 per cent.; $36.08. (5) $110.88. (6) 25f gals. (7) 8J cents. (8) $1890. (9) $9.90. (10) 3^ percent. ._, _..--- r. . EXERCISE LXVII.— (1) $300 loss. (2) 6} per cent. (3) 909^ oz. (4) $720. (5) House, $1200; Lot, $900. l6) $412500. (7) $12937.50. (8) 33J per cent. (9) 13310. (10) 6 per cent. , EXERCISE LXVIII.— (i) 180 bushels; 15 percent. 2) $320. (3) $4076. i6,V (4) $67.20. (5) 100 acres. 6) 44 per cent. (7) $368. (8) $32 ; 4o| per cent. (9) 1209.50. (10) 6^ per cent. ; $4. EXERCISE LXIX.— (i) $336. (2) $12150. (3) S4764H. (4) 3627 cords. (5) $17.56. (6) 6 feet. (7) $3-49tV ; $3-43^ (8) 40960 bricks. (9) 3 inches. (10) 104448 bricks. EXERCISE LXX.— (i) (a) 22'; (b) 14' 8"; (c) 25' 8"; (d) 22'; (e) 33'; (f) 25' 8". (2) (a) s/^'i (b) 4V"; (c) 6' 5". (3) (a) 154 sq. ft.; (b) 74536 sq. ft.; (c) 273.7 sq. ft. (4) (a) 2464 sq. inches ; (b) 1386 sq. inches ; (c) 38)^ sq. ft. (5) 1008 times. (6) I2f feet. (7) 36;^ miles. (8) 34JJ miles. (9) 13 miles. (10) 3780 times. I EXERCISE LXXI.— (1) $121 yds 1680. (8) 5544 sq. yds. ... (2) $;5. (4) 12 miles. (5) 2454y^j times. (6) 168 sq. ft. (7) (3) 660 .ft. (7) (9) 168 sq. inthes. (20) $6.40^ EXERCISE LXXII.— (0 (a) 169^ ; (b) 1131^; (c) 603?; (d)3l4^;(e)905f ; (f) 1540 ; (g) 1232 ; (h) 231 ; (i) 2425*. (2) (a) 14"; (b) 14"; (c) 12". (3) (a) lor (b) 3I"; (c) 6 . (4) 5091 cubic inches. (5) 628* gals. (6) 78^ bbls. (7) 288 cans. (10) 383V lbs. {S) 3iv^'vk lbs. (9) 528 cubic inches. 104 ARITHMETIC. EXERCISE LXXIIL— (1} 4. (2) 3 o'clock a.m. Tuesday. We omit one day when we cross meridian 180°. (3) i437.5o- (4) T^V ^^y^- ^5) $625 ; 5 per cent. (6) J17.50. (7) $21.90. (8) $2.52. (9) 1134375 gals. (10) IJ mches. EXERCISE LXXIV.— (i) \^^. (2) 3 sovereigns. (3) $750. (4) $172.75. (5) 779-OI gals. (6) 190^ lbs. (7)41580- (8)5462.9911235. (9)7485^*?- (io)$225j. EXERCISE LXXV.-(i) 5. (2) 19/^ mins. after 6 ; 45Tl»iy mins. after 6. (3) $356.30iV- U) 27534, 1716. (5)2^ per cent. (6) $900. (7) 38 per cent. (8) 569 acres, 2 roods, 29 sq. rods. (9) 5 sheep, 1 5 lambs, 30 pigs ; $14.40, $7.20, $4.80. (10} $1.40; $9.10. EXERCISE LXXVI.— (1) 4- (2) 2160. (3) Apple 3M'd. ; apricot ^%d.\ (4) G.C.M. .000279; L.C.M. 25234.713. (5) A $546 ; B $569 ; C$1160; D $1700. (6) 20 days. (7) L.C.M. 3519. (8)120 lbs. ; 90 lbs. (9) A $15.33 ; B $20.44 ; C $23.36. (10) $153.58; $138.22. EXERCISE LXXVIL— 44.16. (2) .514583. (3) 114 tons. (4) 49. (5) 1 1043. (6) 42 yds. silk; 61 yds. velvet. (7) II cents. (8) $23X. (9) $392.40. (10) ^ acres. EXERCISE ,XXVIII.-(i)io8eggs. (2)$ii33.793V (3) m day. (4) 9187. (5) 4.12 lbs. (6) $63.i6|. (7) 3 days. (8) 120020 ozs. (9) $14. (10) $2.10; $.70. EXERCISE f-XXIX.— ^ cents, (8) .000578+ ins. (9) $1775. (10) 192 cubic feet. EXERCISE LXXX.-ri) i^^A. (2) 1,^ d. (3) $130.90. (4) $24.48 per dozen. (5) $9, $6, $3. (6) I5i8f cords. (7) i32575§| miles. (8) 6)4 per cent. ; 8 per cent. (9) $50.40. (10) $4.52. HHPI ANSWERS. 105 ck a.m. neridian )er cent. 75 gals. ^ereigns. )) $225J. after 6 ; S. (5)4 acres, 2 JO pigs; 3) Apple L.C.M. 3 $i7. lbs. (9) 5138.22. 83. (3) 61 yds. (10) 7A 1 33793V 6|. (7) $.70. . (b)42* :4) 7 1 Hi («^ cents. iet. d. (3) (6)i5i8i t. ; 8 per EXERCISE LXXXI.— (i) 6 ins. (2) 3 years. (3) 409TJr gals. (4) $335^ ; $298^ ; J265}. (5) 108. (6) 30 gals. (7) 2i,\ minutes after 6. (8) 25 per cent. (9) $37-5°; $47-50; $18.75. ('o) if percent. EXERCISE LXXXI I.— (i) 3M. (2) $2646. (3) $10.30. (4) $36, $48, $60. (5) $29022, $38696. (6) L.C.M. 5405400; G.C.M. 1 801 80 ; quotient 30. (7) 32 days. (8) $51.30. (9) $318. (10) $144.95. EXERCISE LXXXIIL— (i) 2^. (2) $2.25. (3) 20 gals. (4) 60 feet; 80 feet. (5) $55.20. (6) $120. (7) Double the original number. EXERCISE LXXXIV.-(i) $5.70. (2) $134.80. (3) $1.13. .'4} 34 lbs. (5) $30. (6) 660 yds. (7) ^ day ; 60 cents. (8) (a) i^f ; (b, 8275.8620 + . EXERCISE LXXXV.— U) 552 boxes. (2) (a) yj^ ; (b) 14.28. (3) $1062.79. Simple interest only ; the law will not collect compound interest in such cases. (4) $316.80. (5) $230.40. (6) Spies $1.75; Wagners $1.50. (7) (a) 21 cents; (b) $92.78; (c) 9^1^ per cent. (8) 890303890. EXERCISE LXXXVL— (i) 26 miles' 80 rods. (2) i3Klbs. (3) J97.18X. (4)38>^lbs. (5) $i9-4o. (6) $41.10. (7) $3.50. (8) (a) 13 ; (b) 147.32 ; (c) .189326 ; Time Tests and Mechanical Work. Time Tests in Addition.— Page 10.— (i) 91 5621. (2) 923244. (3) 923226. (4) 965193. (5) 901455- (6) 934233- (7)963204. (8)932127. (9)921354. (10)913623. (11)936312. (12)912354. (13)923622. (14)936303- (15)963114. (16)9^227. (17)930147. (18)901554. Time Tests in Addition.— Page 14. — (i) 956292. (2) 963006. (3) 931227. (4) 905046. (5) 943233- (6) 932415- (7)924234- (8)942423. (9)924315.00)942414. io6 ARITHMETIC. (ii) 924225. (12) 942333- (13) 923415- ('4) 956466. (15) 964745- («6) 947547. (17) 975555- («8) 955638. Time Tests in Addition.— Page 22.— (i) 1008561. (2)985701. (3)957099- (4)971076. (5) 1010847. (6) 989859. (7)998681. (8)986880. (9)968889. (10)988977. (11) 965637. (12) 956457- (13) 964656. (14) 946647. (15) 966555. (16) 913980. (17) 939882. (18) 898905. Weekly Mail Statement.— Page 28.— Vertical Totals : 24829, 24554, 26643, 27543, 27793, 32924- Hori- zontal Totals: 52060, 4124, 10846, 2988, 1562, 92706. Aggregate : 164286. Religious Population.— P^ge 29.— Vertical Totals : 17374, 1 1 131, 14169,9192, 7364,7108. Horizontal Totals : 13519, 15419, 11964, 10494, 10717, 4225. Aggregate: 66338. • School Attendance.— Page 29.— Vertical Totals : 9357, 8949, 8639, 9027, 9650, 9552. Horizontal Totals : 6074, 6814, 7172, 7241, 6753, 7251, 6868, 7001. Aggregate : 55i::4. Sales Statement. — Page 35.— First Week.— Daily Totals, $136.27, $184.90, $180.06, $197.61, $166.55, $306.02. Clerk's Totals, $204.71, $192.66, $171.03, $21 1.35, $195.21, $196.45. Aggregate, $1171.41. Second Week. — Daily Totals, $404.22, $463.95, $431.22, $449.91, $432.09, $467.39. Clerk's Totals. $480.25, $385.16, $397-94i $488.54, $419-95. $476.94. Aggregate, $2648.78. Third Week.— Daily Totals, $326.01, $362.61, $379.58, $448.1 1, $280.89, $416.47. Clerk's Totals,$338.6i, $332.06, $460.04, $321.86, $399.16, $361.74. Aggregate, $2213.47. Practice in Subtraction.— Page 43.— (1) 3209009. 2) 2901798. (3) 3209606. (4) 3011596. (5) 3191016. (6)3115985. (7)2682089. (8)2818598. (9)3011868. .10)2915974. (11)4132004. (12)4301225. (13)4287719. ^14)4212716. ^15)4132127. (16)4212711. (17)4270615. (18) 3922651. (19) 3572089. (20) 4316547. (21) 5431761 (22)4518315. (23)4540815. (24)5119814. (25)5365816. 956466. 955638. ic»856i. 847. (6) ) 988977- I 946647. 898905. -Vertical [. Hori- 2, 92706. il Totals: il Totals : jgregate : il Totals : 1 Totals: g^gregate : c. — Daily ;, $306.02. ;, $195.21, 5, J43I-22* 5, $385-16, , $2648.78. I, $379-58, I, $332.06, $2213.47. ) 3209009. ) 3191016. I 301 1868. ) 4287719. ) 4270615. ) 543 1 761. ) 5365816. 44 SCHOOL HELPS" SERIES CANAAUN HISTORY NOTES, fbr 3rd, 4th, and 6th Classes By G. E. 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