OPERATION. 7x7= 49; } } = ; 49 - £= 481 Ans. 13. Multiply 84 by 9.1. Ans. 80%. 14. Multiply 113 by 123. Ans. 1431. 15. Multiply 191 by 20.1. Ans. 3991. 16. Multiply 892 by 903. Ans. 80993 Note. — If the fractional parts of the numbers approach within a }, d, or b, &c., of the larger number, the principle is the same. 17. What is the product of 4 multiplied by 51. Ans. 245. OPERATION. 5 x 5=25'; }x}= $; 25 — = 243 Ans. 18. Multiply 7 by 84. Ans. 6315. 19. Multiply 94 by 103. Ans. 9934 20. Multiply 81 by 9%. Ans. 8076 21. Multiply 19% by 2016. Ans. 399935. To find the product of two numbers, one of which is as much less than either 20, 30, 40, &c., as the other is more than either of these numbers. RULE 4. — Multiply the 20, 30, or 40, as the case may be, by itself, and subtract from the product the square of half the difference of the two numbers to be multiplied, and the result will be the product. 22. Multiply 28 by 32. Ans. 896. We find that 28 is as much less than 30 as 32 is more than 30; we, therefore multiply 30 by 30 = 900, and from this product we subtract the square of 2=4; 900 —4= 896 Ans. 23. What is the product of 75 by 85 ? Ans. 6375. 24. What is the product of 83 by 77 ? Ans. 6391. 25. What is the product of 97 by 103 ? Ans. 9991. 26. What is the product of 17 by 23 ? Ans. 391. 27. What cost 18cwt. of steel, at $22 per cwt. ? Ans. $ 396. 28. What cost 27 tons of hay, at $ 33 per ton ? Ans. $ 891. 29. What cost 64 gallons of oil, at $ 0.56 per gallon ? Ans. $35.84. 30. What cost 28 tons of hay, at $ 32 per ton ? Ans. $ 896. 31. What cost 49 tons of iron, at $51 per ton? Ans. $2499. Section XXXVI. QUESTIONS TO BE PERFORMED BY ANALYSIS. 1. If a man travel 48 miles in 12 hours, how far will he travel in 17 hours ? Ans. 68 miles. [The following is the most obvious solution of this question. If he travel 48 miles in 12 hours, in 1 hour he will travel iż of 48 miles, which is 4 miles. Then if he travel 4 miles in 1 hour, he will in 17 hours travel 17 times as far, which is 68 miles, the answer.] 2. If 72 pounds of beef cost $ 6.48, what will 1 pound cost ? what will 675 pounds cost ? Ans. $ 60.75. 3. If of a dollar buy 1 pound of sugar, how much may be bought for $ 1 ? how much for $ 297 ? Ans. 2391b. 4. If a hogshead of wine cost $ 73.50, what is the value of 1 gallon ? what cost 17hhd. 45 gallons ? Ans. $ 1302.00. 5. Bought 11 bushels of rye for $ 9.00 ; what cost 25 bushels ? Ans. $ 20.45 -T. 6. If a crew of 15 hands consume in 3 months 1620 pounds of beef, how much would be sufficient for 27 hands for the same time? Ans. 29161b. 7. Bought 9 yards of flannel for $ 7.00; what would be the value of 3711 yards ? Ans. $29.311. 8. If a certain field will pasture 8 horses nine weeks, how long will it pasture 23 horses ? Ans. 3,5 weeks. 9. If 73 dozen of hats cost $ 318.50, what will 191 dozen cost ? Ans. $ 874.9585. 10. If 1 ton of hay cost $ 25.00, what will 17 tons 13cwt. 19 pounds cost ? Ans. $ 441.46+. 11. What part of 92 is 25 ? Ans. 23. 12. What part of 25 is 92 ? Ans. 13. If $ 25 will pay for 7 yards of broadcloth, what would be the price of 97 yards ? Ans. $ 328.813. 14. If $ 47.25 will pay for the keeping of 7 horses 2 months, what would it cost to keep 43 horses for the same time ? Ans. $ 290.25. 15. If 71 yards of cloth a yard wide is sufficient to make a cloak, how many yards would it take if the cloth was lk yards wide ? . Ans. 4 yards. 16. If a barrel of beer will last 10 men a week, how long would it last 1 man? how long 37 men ? Ans. 13 days. 17. If 5 calves are worth 9 sheer, how many calves will purchase 108 sheep ? Ans. 60 calves. 18. If 11 yards of cotton 3 quarters wide are sufficient to line a garment, how many yards would it require that were 5 quarters wide ? Ans. 6 yards. 19. If 7 pairs of shoes will purchase 2 pairs of boots, how many pairs of shoes would it take to buy 18 pairs of boots ? Ans. 63 pairs. 20. If four gallons of vinegar be worth 7 gallons of cider, what quantity of vinegar would it take to buy 47 gallons of cider? Ans. 264 gallons. 21. If a man travel 377 miles in 15 days, how far would he travel in 1 day ? how far in 100 days ? Ans. 2513} miles. 22. If 12 men can dig a ditch 50 feet long, 4 feet wide,and 3 feet deep, in 30 days, how long would it take 1 man ? how long 47 men? Ans. 731 days. 23. If 5 barrels of flour cost $ 25.75, what will 39 barrels cost ? Ans. $ 200.85. 24. Bought 17 acres of land for $791.01 ; what would 98 acres 3 roods and 14 perches cost? Ans. $ 4598.90,8%. 25. Bought 973 yards of cloth for $275.20; what is the price of 7 yards? Ans. $ 19.78+. 26. If a pole 7 feet long cast a shadow of 5 feet, how high is that steeple whose shadow is 97 feet? Ans. 1356 feet. 27. Gave 3 cwt. of sugar, at $ 9, for 17 of an acre of land ; how much sugar would it have required to purchase an acre ? Ans. 54cwt. 28. If a vessel sail 473 miles in 3 hours, how far would it sail in 1 week ? Ans. 24252 m. 29. James can mow a field in 7 days, by laboring 10 hours a day; how many days would it take him to perform the work by laboring 12 hours a day? Ans. 55 days. 30. If of a lot of land is worth $ 42.12, what is the value of 4 of it? Ans. $ 29.415. 31. If a man can earn $ 10.27 in of a week, how much would he earn in a month ? Ans. $71.89. 32. If 18 men can reap 72 acres in 5 days, how long would it take 6 men to perform the labor ? Ans. 15 days. 33. If 19 gallons of wine can be bought for $ 25, how many gallons will $ 71.25 buy? Ans. 542 gallons. 34. If a penny loaf weighs 8 ounces when wheat is $ 1 a bushel, what should it weigh when wheat is sold for $ 1.25 a bushel ? Ans. 6 ounces. 35. If a basket which contains 14 bushels must be filled with apples 7 times to make one barrel of cider, how many barrels may be made by its being filled 126 times? Ans. 18bbl. 36. If a cloak can be made of 4; yards of cloth that is 13 yards wide, how many yards would it take of cloth that is ! of a yard wide ? Ans. Gyd. Iqr. 3 na. 37. If a box 4 feet long, 2 feet wide, 1} feet high, contains 300 pounds of sugar, how much wiil a box that is 8 feet long, 4 feet wide, and 3 feet high, contain ? Ans. 24001b. 38. How much in length, that is 124 rods in breadth, will make an acre ? Ans. 12-8-rd. 39. Sound, uninterrupted, moves 1142 feet in a second ; how long, after a cannon's being discharged at Boston, is the time before it is heard at Bradford, the nearest distance being 253 miles ? Ans. 2 minutes. 40. Bought I of a ton of potash, and sold it of it for $ 46.70; what was the value of a ton ? Ans. $ 93.40. 41. If 4 of a lot of land be worth $ 97, what would the whole lot be worth? Ans. $ 266.75. 42. If 19 pounds of salmon be worth 50 pounds of beef, how much salmon would buy 77 pounds of beef ? Ans. 2913lb. 43. What part of 173 is 41 ? Ans. 187. 44. What part of lls. 3d. is 158. ? Ans. . 45. What part of 77 yards is 3 ells English ? Ans. 19. Section XXXVII. SIMPLE INTEREST. INTEREST is the compensation which the borrower of money makes to the lender. PRINCIPAL is the sum lent. PER CENT., a contraction of per centum, is the rate established by law, or that which is agreed on by the parties, and is so much for a hundred dollars for one year. CASE I. GENERAL RULE. — Let the per cent. be considered as a decimal of the place of hundreds, and multiply the principal by it, and the product is the interest for one year. But, if it be required to find the interest for more than one year, multiply the product by the number of years. Note. — The decimal for 6 per cent. is .06; for 7 per cent., .07; for 8 per cent., .08; for 94 per cent., .0925; for 24 per cent., .025, &c. The decimal must be pointed off as in Multiplication of Decimal Fractions. This rule is obvious from the fact that the rate per cent. is such a part of every hundred dollars. Thus 6 per cent, is 760 of the principal. Note. — When no particular per cent. is named, 6 per cent. is to be understood, as it is the legal interest in the New England States. See page 148. 1. What is the interest of $ 144 for 1 year? Ans. $ 8.64. OPERATION. $ 144 There being two places of decimals in the ..06 multiplier, we point off two in the product. $8.64 Ans." 2. What is the interest of $ 78.78 for 3 years ? OPERATION. $ 78.78 .06 There being two places of decimals in the 4.72,68 multiplicand, and two in the multiplier, we point . 3 off four places in the product. $ 14.18,04 Ans. Note. - It is a custom with merchants to reject mills in their computations, but when the decimal of a cent exceeds 5 they add 1 to the number of cents. Thus, they would reckon $81.93,8 to be in value $ 81.94. 3. What is the interest of $ 675 for 1 year? Ans. $ 40.50. 4. What is the interest of $ 1728 for 1 year? Ans. $ 103.68. 5. What is the interest of $ 19.64 for 2 years ? Ans. $ 2.35,6. 6. What is the interest of $ 896.28 for 3 years ? Ans. $ 161.33. 7. What is the interest of $ 349.25 for 10 years ? Ans. $ 209.55. 8. What is the interest of $ 3967.87 for 2 years ? Ans. $ 476.14,4. 9. What is the interest of $ 123.45 for 6 years ? Ans. $ 44.44,2. 10. What is the interest of $ 89.25 for 50 years ? Ans. $267.75. 11. What is the interest of $ 17.25 for 7 years ? Ans. $7.24,5. 12. What is the interest of $ 29.19 for 9 years? Ans. $ 15.76,2. 13. What is the interest of $ 617.56 for 25 years ? Ans. $ 926.34. |