17. What quantity of cloth, at 10 dollars a yard, ought I to have for 503 dollars? The divisor being 10 we omit the 3 in the right of the dividend, 503, and thus find 10 in 503, 50 times, with remainder 3. The quotient is therefore 50%. The 50 times 10 in 503 gives 50 yards, and the 3 dollars over will buy of a yard. Ans. 50,3 yards. 18. At 3 dollars per cord, what quantity of wood might be bought for 175 dollars? Ans. 58cords. 19. At the rate of 7 miles an hour, how many hours would a stage coach be in running 975 miles? Ans. 139 hours. 20. Allowing a workman to build 9 rods of fence in a day, how many days would he require to build 1603 rods? 21. How many tons of hay, at 1 purchased for 3071 dollars? 22. How many acres of land, at 40 bought for 7309 dollars? 23. How many tons of steel, at 120 bought for the sum of 1577 dollars? Ans. 178 days. dollars per ton, may be Ans. 279 tons. dollars per acre, may be Ans. 182 acres. dollars per ton, may be Ans. 13 tons. 24. Allowing 30 days to make a month, how many months would there be in 200 days+177 days? Ans. 127 months. 25. A has 2345 dollars, and B 3000 dollars. What quantity of land can the two together purchase, at the rate of 50 dollars per acre? Ans. 1065 acres. 26. A farmer sold beef for 130 dollars, and pork for 200 dollars. With the proceeds of these sales, he wishes to purchase corn at 3 dollars per barrel; what quantity can he buy? Ans. 110 barrels. 27. A merchant sold cloth for 423 dollars, cotton for 125 dollars, and silk for 300 dollars; and invested the proceeds in sugar at 12 dollars per barrel. How many barrels of sugar did he buy? Ans. 70 barrels. 28. If 5 acres of ground sell for 163 dollars, what is the price per acre? One acre being of 5 acres, is worth is 163 dollars-5 (§ 51 and 54). of 163 dollars; which Ans. 32 dollars. 29. If a man travels 200 miles in 6 days, at what rate does he travel per day? Ans. 33 miles. 30. If 7 head of horses sell for 850 dollars, what will be the` average sum received for each? Ans. 1213 dollars. 31. Allowing 1703 acres of land to be divided into 8 farms of equal size, what will be the number of acres in each? Ans. 212 acres. 32. If 100 yards of li en cost 57 dollars, what is the price per yard? One yard costs of 57 dollars, or 57 dollars÷÷100; which is, Ans. of a dollar. 57 of a dollar (§ 47 and 51). 100 57 33. If 50 bushels of corn sell for 13 dollars, what is the selling price per bushel? 13 Ans. of a dollar. 34. If 3 plantations of equal value sell for 8491 dollars, what sum would be received for each? Ans. 2830 dollars. 35. If 8 yards of Irish linen amount to 7 dollars, at what price per yard does the linen sell? Ans. of a dollar. 36. If the construction of 4 bridges on a turnpike road, cost 14803 dollars, what is the average cost of each? Ans. 3700 dollars. 37. Allowing 600 acres of ground to produce 24000 bushels of wheat, what would be the produce per acre? Ans. 40 bushels. 38. Allowing 900 barrels of flour to sell for 9900 dollars, what would be the selling price per barrel? Ans. 11 dollars. 39. A capital stock of 225000 dollars is held in 1000 equal shares. What is the amount of each share? Ans. 225 dollars. 40. A farmer has 70 acres of land worth 2450 dollars, and 110 acres worth 4500 dollars. What is the whole worth, and what is each tract worth per acre? The whole, 6950 dollars; Ans. 00 The 1st, 35 dollars, and (The 2d, 40 dolls. per acre. 41. A drover bought 54 head of cattle at one time, and 66 head at another time, the whole amounting to 1800 dollars. What was the average cost per head? Ans. 15 dollars. 42. A planter bought 7 mules at 35 dollars apiece, 4 at 40 dollars apiece, and 9 at 37 dollars apiece. What sum was paid for all, and what was the average sum paid for each? Ans. 738 dollars for all; and 3618 for each. 43. In how many days could 10 men accomplish the same amount of work that one man could do in 349 days? 10 men could do the work in of the time in which 1 man would do it; that is, in 1 of 349 days. Ans. 34 days. 10 44. In how many days ought 7 masons to build a wall which one mason could build in 175 days? Ans. 25 days. 45. How long ought 20 men to subsist on a stock of provisions which would suffice one man 433 days? Ans. 2113 days. 46. How long ought 12 horses to be fed on a quantity of oats which would be sufficient for 1 horse 185 days? Ans. 15,5 days. 47. How long might 30 workmen be employed for a sum of money which would pay 1 workman for 401 days? Ans. 13 days. 48. In how many days could 10 men accomplish the same amount of work that 13 men could do in 349 days? 1 man would do the work in 13 times 349 days, and 10 men would do it in of the time in which 1 man would do it. 10 Ans. 453 days. 49. If 34 men can raise the walls of a fortification in 27 days, in how many days could 20 men do the same ? Ans. 45 days. 50. How long should 12 teams be employed in doing an amount of hauling which 23 teams could accomplish in 65 Ans. 124 days. days? 51. Allowing that 75 laborers could pave a street in 123 days, in how many days could 120 laborers pave the street? Ans. 76 days. 52. A merchant bought 20 yards of cloth for 143 dollars; and, at another time, 30 yards for 165 dollars. At what price per yard was each purchase made? Ans. (The 1st, 73, and The 2d, 5 dollars. 53. A farmer sold his farm containing 273 acres, at 35 dollars per acre, and immediately invested the proceeds in another farm at 50 dollars per acre. How many acres did he buy? Ans. 191 acres. 54. A plantation containing 1200 acres, was exchanged for another containing 1000 acres, and worth 53 dollars per acre. At what price per acre was the first plantation rated? Ans. 44,200 dollars. 55. A gentleman having on hand 5000 dollars, took 2300 dollars to purchase bank stock, at 100 dollars a share, and divided the remainder equally among three benevolent institutions. How many shares of stock did he purchase, and what sum did each institution receive? Ans. 23 shares; and each inst'n rec'd 900 dollars. 437630-9. 873007-11. Ans. 486255. Ans. 79364. 703687-20. Ans. 35184. 8526-3 110. 56. Find the Quotient of 57. Find the Quotient of 58. Find the Quotient of 59. Find the Quotient of 60. Find the Quotient of 61. Find the Quotient of 3800370-300. 62. Find the Quotient of 70307600÷700. Ans. 10043908 937863 110. Ans. 6403,17 120 Ans. 12667378. $40. To Divide by any Number exceeding 12, and containing two or more SIGNIFICANT FIGURES. 1. Take figures enough in the left of the dividend to contain the divisor, and on the right set the number of times the divisor goes therein. 2. Multiply the divisor by the quotient figure, and subtract the product from those figures of the dividend which were taken in dividing. 3. Bring down the next figure of the dividend, annexing it to the remainder, if any. Divide into the number so obtained, and set the quotient figure on the right of the first one; if the divisor will not go in the number, set a 0 in the quotient, and bring down the next figure of the dividend. 4. Multiply the divisor by the last quotient figure-subtract the product from the number last divided,-bring down the next figure of the dividend, and so on. 5. Ciphers in the right of the divisor, and the final remainder, are to be treated as directed in RULE VII. Omitting the 0 in the right of the divisor, and one figure in the right of the dividend, we say 69 in 210, 3 times, and set the 3 on the right; multiplying the 69 by 3, we get 207; subtracting 207 from 210, the remainder is 3; annexing the 4 from the dividend to the remainder 3, we say 69 in 34, 0 time; annexing the 9 from the dividend, we say 69 in 349, 5 times; multiplying 69 by 5, we get 345; subtracting 345 from 349, the remainder is 4, to which annexing the 0 omitted in the dividend, the remainder becomes 40. Under the remainder setting the given divisor 690, we have to annex to the quotient. 590 40 690 The quotient 305 shows that the dividend contains the divisor 305 times, and of the divisor, besides. It is also 6 of the dividend (§ 51). In dividing by this method, observe that the product of the divisor and any quotient figure, must be less than the number from which it is to be subtracted; and that the remainder must always be less than the divisor. This Rule differs from RULE VII, only in requiring the products and remainders to be written down. By Rule VII, the divisor being a small number, the multiplication and subtraction are carried on mentally. Both Rules depend on the same principles. Proof by Addition. § 61. The operation by the last Rule may be proved, most readily, by adding up the remainder, if any, and the several products of the divisor and quotient figures, in the order in which they stand. The Sum must be equal to the dividend. For the preceding example the proof may be presented thus: Ans. 302 460 3220* Ans. 1598.492 69. Find the Quotient of 973100 3220. 5473 Ans. 29878 2174 Ans. 3290 90933503 10700° 25414136 53601 74. At the rate of 32 miles per day, how many days would a person be employed in walking 3968 miles?. The number of days will be the number of times 32 in 3968. Ans. 124 days. 75. If 45 acres of ground sell for 1039 dollars, what is the price per acre? The price per acre is of 1039 dollars. Ans. 23 dollars |