The selling price, $6, divided by 1+.20, which is 1.20, gives $5 as the prime cost. EXAMPLES. 11. A farmer sold wood at $5.40 per cord, and gained 8 per cent. What was the prime cost? 12. A farmer sold hay at $14 per ton, and gained 25 per cent. What was the prime cost? 13. A merchant sold nails at 5 cents per pound, and lost 10 per cent. What was the prime cost? 14. If 20 per cent. be gained on raisins, at $2.75 per box, what is the prime cost? 15. If 15 per cent. be gained on rice, at 4 cents per pound, what is the prime cost? 16. If 12 per cent. be gained on potatoes, at 48 cents per bushel, what is the prime cost? 17. If 9 per cent. be gained on cheese, at 10 cents per pound, what is the prime cost? What 18. A merchant sold sugar at 62 cents per pound, which was 10 per cent. less than it cost him. was the prime cost? 19. A gentleman sold land at $175 per acre, which was 25 per cent. less than it cost him. What was the prime cost? 20. A merchant sold coal at $5 8 per cent. less than it cost him. cost? per ton, which was What was the prime 211. To find at what price goods must be sold, in order to gain or lose a certain per cent., RULE. Find the required per cent. of the prime cost, and add this per cent. to it, if there is to be a gain; but subtract this per cent. from the prime cost, if there is to be a loss. What is the rule for finding the selling price to gain a certain per cent.? 21. Bought flour at $4 per barrel. At what price must it be sold to gain 20 per cent. ? 4 x .20 = .80. .80 + 4 = 4.80. 20 per cent. of $4 is 80 cents, which, added to $4, gives $4.80, the selling price. EXAMPLES. 22. A merchant bought cloth at $5.00 per yard. At what price must it be sold, to gain 25 per cent. ? 23. A merchant bought sugar at 73 cents per pound. At what price must it be sold, to gain 15 per cent. ? 24. A merchant bought molasses at 28 cents per gallon. At what price must it be sold, to gain 12 per cent. ? 25. A merchant bought cotton at 9 cents per pound. At what price must it be sold, to lose 20 per cent. ? 26. A farmer bought apples at 42 cents per bushel. At what price must they be sold, to lose 25 per cent.? 27. Bought cotton at $275 per bale. For how much must it be sold per bale, to gain 30 per cent.? 28. A merchant bought flour at $4.50 per barrel. At what price must it be sold per barrel, to lose 15 per cent.? 29. Bought molasses at 28 cents per gallon. At what price must it be sold per gallon, to lose 12 per cent. ? 212. To find the gain or loss per cent. at any proposed price, when the selling price and the gain or loss per cent. is known, RULE. First find the prime cost, and then the gain or loss per cent. at the proposed price. What is the rule for finding the gain or loss per cent. at any proposed price, when the selling price and the gain and loss are known? EXAMPLES. 30. A merchant sold sugar at 8 cents per pound, and gained 10 per cent. What per cent. would he have gained if he had sold it at 9 cents per pound? 31. A farmer sold corn at 65 cents per bushel, and gained 5 per cent. What per cent. would he have gained if he had sold the corn at 70 cents per bushel? 32. A farmer sold rye at 95 cents per bushel, and gained 8 per cent. What would he have gained or lost per cent. if he had sold the rye at 80 cents per bushel? 33. A man sold his farm for $4560, which was 10 per cent. more than it cost him. What would he have gained or lost per cent. if he had sold it for $4000 ? 34. A farmer sold land at 5 cents per foot, and gained 25 per cent. more than it cost him. What would he have gained or lost per cent. if he had sold it at 3 cents per foot? 35. A grocer sold tea at 45 cents per pound, and gained 10 per cent. What would he have gained per cent. if he had sold it at 50 cents per pound? 36. A merchant sold broadcloth at $4.75 per yard, and gained 12 per cent. What would he have gained per cent. if he had sold it at $5.25 per yard? 37. A farmer sold oats at 37 cents per bushel, and lost 14 per cent. What would he have gained or lost per cent. if he had sold them at 48 cents per bushel? 38. A merchant sold coffee at 11 cents per pound, and gained 10 per cent. What would he have gained per cent. if he had sold it at 12 cents per pound? 39. A farmer sold potatoes at 35 cents per bushel, and lost 12 per cent. What would he have gained or lost per cent. if he had sold them at 40 cents per bushel? N* PRACTICAL QUESTIONS. 40. A man bought 12 acres of land at 3 cents per foot, and after keeping it 10 years, sells it at 20 per cent. advance. Allowing money to be worth 6 per cent., does he gain or lose, and how much? 41. A merchant bought 500 barrels of flour in Chicago, at $4 per barrel; he paid for freight to Boston 65 cents, and for truckage, 7 cents per barrel; he sold it in Boston at $5 per barrel. How much did he gain per cent.? 42. A merchant bought at New Orleans 500 bales of cotton, of 300 pounds each, at 64 cents per pound; he paid for freight to Liverpool 14 cents per pound; for wharfage and truckage, $50; he sold the cotton for 9 cents per pound. Did he gain or lose, and how much per cent. ? 43. A merchant bought in Maine 150,000 feet of lumber, at $9 per 1000 feet; he paid for freight, truckage, and wharfage, $4860. At what price per foot must he sell the lumber, to gain 20 per cent. ? 44. A merchant bought in Vermont 6000 bales of wool, of 100 pounds each, at 40 cents per pound; he paid for freight and truckage to Boston 65 cents per bale. At what price per pound must he sell the wool, to gain 25 per cent. ? 45. A merchant sold flour at $5 per barrel, and thereby gained 12 per cent. What would he have gained per cent. had he sold the flour at $6 per barrel? 46. A grocer bought 10 boxes of Havana sugar, of 400 pounds each, at 64 cents per pound; he paid for freight, truckage, &c., $1.75 per box; he gained 2 per cent. on the weight of the sugar; he sells it at 7 cents per pound. How much does he gain per cent.? 47. A merchant sold tea at 45 cents per pound, and gained 12 per cent. What would he have gained per cent. if he had sold the tea at 54 cents per pound? RATIO. SECTION XVIII. 213. RATIO is the relation which one quantity bears to another of the same kind with respect to magnitude. 214. The ratio of two numbers is the quotient resulting from dividing the first by the second. Thus the ratio of 12 to 4 is 3; the ratio of 30 to 5 is 6 since 12 divided by 4 is 2-3, and 30 divided by 5 is 30-6. ; 215. The two numbers are called the terms of the ratio. The first is called the antecedent, the second, the consequent, and may either be expressed in the form of a fraction, the antecedent for the numerator, and the consequent for the denominator, -as 12, or by placing two points between them, as 12: 4. Both of the numbers must either be abstract numbers or of the same kind. : 216. If both terms of the ratio be multiplied or divided by the same number, the ratio will not be changed. Thus 12 4 is the same ratio as 6: 2, 24: 8, and 36: 12. This is evident from the fact, that the terms of a ratio are the terms of a fraction, which may be multiplied or divided without changing its value, (ART. 84.) 217. An inverse or reciprocal ratio is the ratio of the consequent to the antecedent, and is expressed by changing the order of the terms, or by inverting the fraction. Thus the ratio of 3 to 6, or , is a direct ratio; the ratio of 6: 3, or f, is an inverse or recipro What is ratio? What is the ratio of two numbers? What are the numbers called? How may a ratio be expressed? What is an inverse ratio? |