The following per cents., with their fractional equivalents, are so frequently used that they should be committed to 154. Percentage is that process of computation in which the basis of operation is a hundred. The Base is the number of which the per cent. is taken. The Rate is the number of hundredths of the base taken. The Percentage is the result obtained by taking as many hundredths of the base as are indicated by the rate. Thus, 10% of $40 = ten hundredths of $40 $4. In this problem $40 is the base, 10% is the rate, and $4 is the percentage. The base plus the percentage is the Amount. The base minus the percentage is the Difference. CASE I. 155. Given the base and rate, to find the percentage. ORAL EXERCISES. 1. What is 10% of 60? 10% of 60 equals 10%, or fo, of 60, which is 6, Ans. 2. What is 163% of 60? 163% = (see table). of 60 is 10, Ans. .24 92 46 $5.52, Ans. 24% of $23 equals .24 times $23, which by multiplication is $5.52. NOTE.-The method of Ex. 21 should be used in all written work when the per cent. can be readily expressed as a pure decimal. The method of Ex. 1 and 22 should be used in all other cases. 23. A owned 750 acres of land, and sold 15% of it; how much did he sell? 24. A merchant bought goods for $520, and sold them at a gain of 22%; how much did he gain? 25. A farmer raised 4280 bushels of grain, and sold 20% of it; how much did he sell? 26. A house was bought for $5240, and sold at a gain of 25%; what was the selling price? 27. A farm was bought for $10,500, and was sold at a loss of 20%; required the selling price. 28. A merchant failed in business, and was able to pay only 35% of his debts; how much would A lose, to whom he owes $4860? 29. A coal-dealer buys coal at $4.25 a ton, and sells it at a gain of 18%; what is the selling price? 30. A man whose salary is $4500 pays 121% for board and 17% for current expenses; how much does he save? 31. A store was sold for $10,800: 41% of the price was paid in cash; how much remained unpaid? 32. Mr. Bitner had $8600 in bank: he drew out 44% of it to purchase a library, and 15% of the remainder for living expenses; how much remained in bank? 33. M bought a horse for $200: he sold him to N at an advance of 35%, and N sold him to P at a loss of 223%; what did the horse cost P? CASE II. 156. Given the rate and percentage, to find the base. ORAL EXERCISES. 1. 40 is 25% of what number? If 40 is 25%, or, of some number, of that number is 4 times 40, or 160, Ans. PROCESS. .31)$17.36 155 186 186 If $17.36 is 31% of some number, then .31 times that number equals $17.36, hence the number is $17.36.31, which is $56. If of the number is 120, that number is of 120, or 135, Ans. RULE. Divide the percentage by the rate. FORMULA.-P ÷ R = B. 22. A farm was sold for $425 less than cost, which was at a loss of 20%; what was the cost of the farm? 23. B owns 420 acres of land, which is 25% of what C owns; how much land has C? 24. A merchant lost $340, which was 17% of all his money; how much money had he? 25. Mr. Noble gained $175 by selling his horse and carriage at a gain of 314%; required the selling price. 26. A miller lost 12% by selling a quantity of flour for $616; required the cost of the flour. SUGGESTION. The difference + (1 - rate) = base. 27. An army lost 20% of its men in battle, and 25% of the remainder were discharged; how many men were there in the army at first, if there were 33,240 men remaining? 28. A gained 15% of his capital, and then had $4830; what was his capital? SUGGESTION.-The amount ÷ (1 + rate) = base. 29. By selling my horse for $207 I gained 15%; how much would I have received for him if I had sold him at a loss of 15%? 30. A speculator lost $660 by selling goods at 411% below cost; required the selling price. 31. A merchant clears $1240 by selling goods for 51% more than cost; required the selling price. 32. What must I ask for a farm worth $6000, so that I may fall 4% on my asking price and still gain 20%? 33. 40% of the inhabitants of an Asiatic city perished from cholera, leaving 7560 alive; what was the original population? 34. I paid $300, which was 163% of my indebtedness; how much did I then owe? CASE III. 157. Given the base and percentage, to find the rate. ORAL EXERCISES. 1. 15 is what per cent. of 60? 15 is of 60. equals .25, or 25%. |