PROMISCUOUS EXAMPLES. 1. What cost 12 cords of wood @ $4.87? Ans. $61.54-+. 2. At $.37 per bushel, how many barrels of potatoes, each containing 2 bushels, can be purchased for $33.75? Ans. 36. 3. If 36 boxes of raisins, each containing 36 pounds, can be bought for $97.20, what is the price per pound? Ans. $.075. 4. If .625 of a barrel of flour be worth $5.35, what is a barrei worth? Ans. $8.56. 5. What is the difference between of a hundredth, and of a tenth? Ans. .025. 6. What is the product of 814,9% × 2615 correct to 2 decimal places? 99 200 7. A drover bought 5 head of cattle @ $75, and 12 head @ $68; at what price per head must he sell them to gain $118 on the whole? Ans. $77. 8. If 1 pound of tea be worth $.62, what is .8 of a pound worth? the tea @ Ans. $.5. 9. A person having $27.96, was desirous of purchasing an equal number of pounds of tea, coffee, and sugar; $.87, the coffee @ $.181, and the sugar @ $.101. pounds of each could he buy? How many 10. If a man travel 13543.47 miles in 365 days, how far does he travel in of a day? Ans. 32.445 miles. 11. Bought 100 barrels of flour @ $5.12, and 250 bushels of wheat @ $1.061. Having sold 75 barrels of the flour @ $61, and all the wheat @ $13, at what price per barrel must the remainder of the flour be sold, to gain $221.87 on the whole investment? Ans. $6.75. 12. If 114.45 acres of land produce 4580.289 bushels of potatoes, how many acres will be required to produce 120.06 bushels? Ans. 3. 13. Divide .017217 by .031, and obtain a quotient true to 4 decimal places. Ans. .5625. Ans. 600. 14. Divide 13.5 by 24 hundredths. 15. A man agreed to build 59.5 rods of wall; having built 8.5 rods in 5 days, how many days will be required to finish the wall at the same rate? Ans. 30 days. 16. A farmer exchanged 28 bushels of oats worth $.37 per bushel, and 453 pounds of mill feed worth $.75 per hundred, for 12520 pounds of plaster; how much was the plaster worth per ton? Ans. $2.25. 17. A farmer sold to a merchant 3 loads of hay weighing respectively 1826, 1478, and 1921 pounds, at $8.80 per ton, and 281 pounds of pork at $5.25 per hundred. He received in exchange 31 yards of sheeting @ $.09, 63 yards of cloth @ $4.50, and the balance in money; how much money did he receive? 18. If 35 yards of cloth cost $122.50, what will be the cost of 29 yards? Ans. $101.50. 19. A speculator bought 1200 bushels of corn @ $.564. He sold 375 bushels @ $.60. At what price must he sell the remainder, to gain $168.675 on the whole? 20. If a load of plaster weighing 1680 pounds cost $2.856, how much will a ton of 2000 pounds cost? Ans. $3.40. 21. If .125 of an acre of land is worth $157, how much are 25.42 acres worth? 22. A farmer had 150 acres of land, which he could have sold at one time for $100 an acre, and thereby have gained $3900; but after keeping it for some time he was obliged to sell it at a loss of $2250. How much an acre did the land cost him, and how much an acre did he sell it for? 23. A lumber dealer bought 212500 feet of lumber at $14.375 per M, and retailed it out at $1.75 per C; how much was his whole gain? 24. If 10 acres of land can be bought for $545, how many acres can be bought for $17712.50? Ans. 325. 25. How much is the half of the fourth part of 7 times 224.56? Ans. 196.49. 26. Sold 10450 feet of timber for $169.8125, and gained thereby $39.183; how much did it cost per C? Ans. $1.25. 27. If $6.975 be paid for .93 of a hundred pounds of pork, how much will 1 hundred pounds cost? 28. Three hundred seventy-five thousandths of a lot of dry goods, valued at $1000, was destroyed by fire; how much would a firm lose who owned .12 of the entire lot? 13 29. Reduce 44 2)× of to a decimal. 21 Ans. $180. Ans. .15. 30. If 7.5 tons of hay are worth 375 bushels of potatoes, and 1 bushel of potatoes is worth $.331, how much is 1 ton of hay worth? Ans. $16.663. 31. A person invested a certain sum of money in trade; at the end of 5 years he had gained a sum equal to 84 hundredths of it, and in 5 years more he had doubled this entire amount. How many times the sum first invested had he at the end of the 10 years? Ans. 3.68 times. 32. A miller paid $54 for grain, 3% of it being barley at $.62 per bushel, and of it wheat at $1.87 per bushel; the balance of the money, he expended for oats at $.37 per bushel. How many bushels of grain did he purchase? Ans. 40. 33. A merchant tailor bought 27 pieces of broadcloth, each piece containing 193 yards, at $4.31 a yard; and sold it so as to gain $381.87, after deducting $9.62 for freight. How much was the cloth sold for per yard? Ans. $5.06. 34. Bought 1356 bushels of wheat @ $1.183, and 736 bushels of oats @ $.41; I had 870 bushels of the wheat floured, and disposed of it at a profit of $235.871, and I sold 528 bushels of the oats at a loss of $13.621. I afterward sold the remainder of the wheat at $1.12 per bushel, and the remainder of the oats at $.31 per bushel; did I gain or lose, and how much? 116 Ans. I gained $171.07. 35. The sum of two fractions is 125, and their difference is 41; what are the fractions? 704 36. A manufacturer carried on business for 3 years. The first year he gained a sum equal to of his original capital; the second year he lost of what he had at the end of the first year; the third year he gained 3 of what he had at the end of the second year, and he then had $28585.70. How much had he gained in the 3 years? Ans. $10594.70. CONTINUED FRACTIONS. 268. If we take any fraction in its lowest terms, as 3, and divide both terms by the numerator, we shall obtain a complex fraction, thus: Reducing, the fractional part of the denominator, in the same manner, we have, Expressions in this form are called continued fractions. Hence, 269. A Continued Fraction is a fraction whose numerator is 1, and whose denominator is a whole number plus a fraction whose numerator is also 1, and whose denominator is a similar fraction, and so on. 270. The Terms of a continued fraction are the several simple fractions which form the parts of the continued fraction. Thus, the terms of the continued fraction given above are, , k, and. CASE I. 271. To reduce any fraction to a continued fraction. 1. Reduce to a continued fraction. 339 OPERATION. 109 1 = 339 3+1 9+1 12 ANALYSIS. We divide the denominator, 339, by the numerator, 109, and obtain 3 for the denominator of the first term of the continued fraction. Then in the same manner we divide the last divisor, 109, by the remainder, 12, and obtain 9 for the de nominator of the second term of the continued fraction. In like manner we obtain 12 for the denominator of the final term. Hence the following RULE. I. Divide the greater term by the less, and the last divisor by the last remainder, and so on, till there is no remainder. |