divide the product by 9, and note the remainder; then divide the whole product by 9, and if the remainder is the same as the last, the work is right. Instead of dividing by 9, the figures of each number may be added, and their sum be divided by 9, as in Art. XXI., (and for the same reason) and the remainders will be the same as if the numbers themselves were divided. In the above example, say 7 and 3 and 4 are 14, which, divided by 9, leaves a remainder 5; then 5 and 8 are 13, which, divided by 9, leaves a remainder 4. Then 4 times 5 are 20, which, divided by 9, leaves a remainder 2. Then adding the figures of the product, 5 and 4 and 1 and 7 and 3 are 20, which being divided by 9 leaves 2, as the other. Instead of dividing 14 and 13 by 9, these figures may be added together, thus 4 and 1 are 5; 3 and 1 are 4. Since in division the quotient multiplied by the divisor produces the dividend; if the divisor and quotient be divided by 9 and the remainders multiplied together, and this product divided by 9, and the remainder noted; and then the dividend be divided by 9; this last remainder must agree with the other. . N. B. If there is a remainder after division, it must be subtracted from the dividend before proving it. Miscellaneous Examples. 1. If 2 lbs. of figs cost 2s. 8d., what is that per b. ? 2. If 2 bushels of corn cost 8s. 6d., what is that per bushel ? 3. If 2 lbs of raisins cost 1s. 10d., what is that per lb. ? 4. If 3 bushels of potatoes cost 9s. 6d., what is that per bushel ? 5. If 4 gals. of gin cost 12s. 8d., what is that per gal. ? 6. If 2 barrels of flour cost 3. 4s., what is that per barrel? 7. If 2 gallons of wine cost 1£. 10s. 4d., what is that per gallon? 8. If 2 barrels of beer cost 1. 15s. 8d., what is that per barrel? 9. If 4 gallons of gin cost 17s. 8d., what is that per gallon? 10. I 5 yards of cloth cost 6£. 10s. 5d.; what is that per yard? 11. If 7 barrels of flour cost 17. 8s. 7d., what is that per barrel? 12. If 8 yards of cloth cost 20£. 18s. 5., what is that per yard? 13. A man had 4 cwt. 3 qrs. 14 lbs. of tobacco, which he put into 2 boxes, of it in each; how much did he put in each box? 14. Divide 13£. 8s. 5d. equally among 5 men. 15. Divide 8 cwt. 3 qrs. 17 lbs. into 3 equal parts. 16. Divide 16 cwt. 1 qr-11 lbs. of flour equally among 7 men; how much will each have? 17. Divide 3 hhds. 42 gals. 2 qts. into 5 equal parts. 18. If 12 yards, 3 qrs. 2 nls. of cloth will make 7 coats, how much will make 1 coat? How much will make 13 coats? 19. If 5 yards of cloth cost 19£. 3s. 4d., what cost 17 yards? 20. What is of 45£. 9s. 7d. ?. 21. If 18 cwt. of sugar cost 56£. 13s. 8d. what will 53 cwt. cost? 22. If of a ship is worth 943€. 7s. 8d., what is the whole ship worth? 23. If 84 cows cost 453£. 14s. 8d., how much is that apiece? 24. If 34 cwt. of sugar cost 9£. 15s. 9d., what is that per cwt.? 25. If 9 barrels of flour cost 21£. 3s. 8d., what cost 173 barrels ? 26. If a staff 4 feet long cast a shade on level ground 6 ft. 8 in., what is the height of a steeple which casts a shade 173 feet at the same time? 27. If 57 gallons of water in one hour run into a cistern containing 258 gallons, and by another cock 42 gallons run out in an hour, in what time will it be filled? 28. A and B depart from the same place, and travel the same road; but A starts 6 days before B, and travels at the rate of 28 miles a day; B follows at the rate of 43 miles a day. In how many days will B overtake A? 29. A sets out from Boston to New-York, at 20 min. past in the morning, and travels at the rate of 5 miles an hour; and B sets out from New-York to Boston at 3 o'clock in the afternoon of the same day, and travels at the rate of 61⁄2 miles per hour. The distance is 250 miles. Supposing them to travel constantly until they meet, at what time will they meet, and at what distance from each place? 30. The distance from New-York to Baltimore is 197 miles. Two travellers set out at the same time in order to meet; A from. New-York towards Baltimore, and B from Baltimore towards New-York. When they met, which was at the end of 6 days, A had travelled 3 miles a day more than B. How many miles did each travel per day? 31. If when wheat is 7s. 6d. per bushel, the penny-loaf weighs 9 oz., what ought it to weigh when wheat is 6s. per bushel ? 32. Suppose 650 men are in a garrison, and have provisions sufficient to last them two months; how many men must leave the garrison in order to have the provisions last those who remain five months? 33. If 8 boarders will drink a barrel of cider in 15 days, how long will it last if 4 more boarders come among them? 34. A ship's crew of 18 men is supposed to have provision sufficient to last the voyage, if each man is allowed 23 oz. per day, when they pick up a crew of 8 persons. What must then be the daily allowance of each person? 35. How many yards of flannel that is 14 yard wide will line a cloak, containing 9 yards, that is yard wide? 36. A garrison of 1800 men have provisions sufficient to last them 12 months; but at the end of 3 months, the garrison was reinforced by 600 men, and 2 months after that, a second reinforcement of 400 men was sent to the garrison. How long did the provisions last in the whole? 37. A regiment of soldiers, consisting of 1000, are to be new clothed; each coat to contain 2 yards of cloth 14 yard wide, and to be lined with flannel of yard wide. How many yards of flannel will line them? 38. I borrowed 185 quarters of corn, when the price was 19s. per quarter; how much must I pay to indemnify the lender when the price is 17s. 4d. ? 39. If 7 men can reap 84 acres of wheat in 12 days, how many men can reap 100 acres in 5 days? 40. If 7 men can build 36 rods of wall in 3 days, how many rods can 20 men build in 14 days? 41. If 20 bushels of wheat are sufficient for a family of 15 persons 3 months, how much will be sufficient for 4 persons 11 months? 42. If it cost $23.84 to carry 17 cwt. 3 qrs. 14 lb. 85 iniles, how much must be paid for carrying 53 cwt. 2 qrs. 150 miles ? 43. If 18 men can build a wall 40 rods long, 5 feet high, and 4 feet thick in 15 days; in what time will 20 men build one 87 rods long, 8 feet high, and 5 feet thick ? C 44. If a family of 9 persons spend $305 in 4 months, how many dollars would maintain them 8 months, if 5 persons more were added to the family? 45. If a regiment consisting of 1878 soldiers, consume 702 quarters of wheat in 336 days; how many quarters will an army of 22536 soldiers consume in 112 days? 46. If 12 tailors can finish 13 suits of clothes in 7 days, how many tailors can finish the clothes of a regiment consisting of 494 soldiers, in 19 days of the same length? 47. If 24 measures of wine, at 3s. 4d. serve 16 men for 6 days, how many measures, at 2s. 8d., will serve 48 men 4 days? 48 How many tiles 8 inches square, will cover a hearth 12 feet wide and 16 feet long? 49. How many bricks 9 in. long, 41 in. wide, and 2 in. thick, will build a wall 6 feet high and 13 in. thick, round a garden, each side of which is 280 feet on the outside of the wall? 50. There is a house 40 feet in length, and 30 feet rafters; how many shingles will it take to cover the roof, supposing each shingle to be 4 inches wide, and each course to be 6 inches ? 51. A man built a house consisting of 4 stories; in the lower story there were 16 windows, each containing 12 panes of glass, each pane 16 in. long 12 in. wide; the second and third stories contained 18 windows, each of the same size; the fourth story contained 18 windows, each window 6 panes 18 by 12. How many square feet of glass were there in the whole house? 52. A merchant sold a piece of cloth for $40, and by so doing lost 10 per cent. He ought in trading to have gained 15 per cent. For how much ought he to have sold the cloth? 53. Bought a hogshead of molasses for $25, but 12 gallons having leaked out, I desire to sell the remainder, so as to For how much per gal 54. Bought a hogshead of brandy, for $93 on 6 months' credit, and sold it for $103 ready money. How much did I gain, allowing money to be worth 6 per cent. a year? 55. Bought 3 hhds. of wine for $320 ready money, and sold it at $1.87 per gal. on 6 months' credit. What did I gain, allowing money to be worth 6 per cent. per year? Note. To answer this question, it will be necessary to compute the interest on $320 for 6 months, and add it to * $320. gain 3 per cent. on the whole cost. lon must I sell it? 56. Bought a quantity of goods for $437.45 and hired the money to pay for it, for which I paid at the rate of 8 per cent. a year. Having kept it on hand 3 months and 17 days, I so.d it for $470, on 4 months' credit. What per cent. did I gain? 57. Bought 5 hhds. of rum at 1 dollar per gal., ready money, and having kept it 3 months and 23 days, I sold it at $1.20 per gallon, on 5 months' credit; 16 gals. had leaked out while in my possession. How much did I gain? * When a debtor keeps money longer than a year, the interest is considered as due to the creditor at the end of the year, and he has a right to demand it. If the interest is not paid at the end of the year, the creditor sometimes requires the interest for the year to be added to the principal, and considered a part of the debt, and consequently interest paid upon it for the rest of the time, and so on at the end of every year. In this way the principal increases every year by the interest of the last year. This may seem just, but it is not allowed by law. This is called compound interest. 58. What will $143.17 amount to in 3 years and 4 months, at 6 per cent. compound interest? The most convenient method is, to find the amount of 15 dollar for the time, and then multiply it by the number of dollars in the question. |