510. The base and rate being given to find the percentage. ORAL EXERCISES. 1. What is 10% of 140? ANALYSIS.-10% is 10%, and of 140 is 14. Hence 10% of 140 is 14. What is = How much is 16. A farmer had 150 sheep, and sold 20% of them. How many had he left? 17. A mechanic who received $20 a week had his salary increased 8%. What were his daily wages then? 18. From a hhd. of molasses containing 63 gal. 331% was drawn. How many gallons remained? 19. A grocer bought 150 dozen eggs, and found 16% of them bad or broken. How many were salable? 20. A train of cars running 25 miles an hour increases its speed 124%. How far does it then run in an hour? 511. PRINCIPLE.-The percentage of any number is the same part of that number as the given rate is of 100%. OPERATION. $4957 .17 WRITTEN EXERCISES. 512. 1. What is 17% of $4957 ? ANALYSIS.-Since 17% is .17, the required percentage is .17 of $4957, or $4957 × .17, which is $842.69. RULE.-Multiply the base by the rate. Or, take such a part of the base as the rate is of 100%. This rule may be briefly expressed by the following What Find 13. 84% of 254 bu. 8. Is 41% of 312.8 rd.? 9. Is 105% of $5728? 10. Is $3140.75 +11%? 11. Is 2 mi. +71% ? 12. Is 400 ft. - 31%? 18. The bread made from a barrel of flour weighs 35% more than the flour. What is the weight of the bread? 19. A man having a yearly income of $4550 spends 20% of it the first year, 25% of it the second year, and 371% of it the third year. How much does he save in 3 years? 20. A man receives a salary of $1600 a year. He pays 18% of it for board, 84% for clothing, and 16% for incidentals. What are his yearly expenses, and what does he save? 21. A man owning of a cotton-mill, sold 35% of his share for $24640. What part of the whole mill did he still own, and what was its value? 22. Smith had $5420 in bank. He drew out 15% of it, then 20% of the remainder, and afterward deposited 121% of what he had drawn. How much had he then in bank? 513. The base and percentage being given to find the rate. ORAL EXERCISES. 1. What per cent. of 25 is 3? ANALYSIS. Since 3 is of 25, it is of 100%, or 12%. Hence, 3 is 12% of 25. What per cent. 2. Of 24 is 18? 3. Of $16 are $4 ? 25 4. Of 200 figs are 20 figs? 5. Of 40 lb. are 15 lb. ? 6. Of 12 bu. are 2 bu.? What per cent. 9. Are 64 mi. of 12 mi.? 10. Are 18 qt. of 30 qt.? 11. Are 16 cents of $1 ? 12. Is $1 of $25 ? 13. Is of ? sq. rd.? 14. ls of 21? 7. Of 2 A. are 80 15. Is 2 of 3? 16. of an acre is what per cent. of it? 17. of a cargo is what per cent. of it? 18. 24 times a number is what per cent. of it? 19. If $6 are paid for the use of $30 for a year, what is the rate per cent.? 20. If a milkman adds 1 pint of water to every gallon of milk he sells, what per cent. does he add? 514. PRINCIPLE.-The rate is the number of hundredths which the percentage is of the base. WRITTEN EXERCISES. 515. 1. What per cent. of 72 is 48 ? OPERATION. 4872.66} = 66% Or, 4; 100% x = 66% × ANALYSIS.-Since the percentage is the product of the base and rate, the rate is the quotient found by dividing the percentage by the base; and 48 divided by 72 is 43 = = .663; hence the rate is 66%. Or, Since 48, the percentage, is of the base, the rate is of 100%, or 66%. RULE.-Divide the percentage by the base. Or, take such a part of 100% as the percentage is of the base. 20. A grocer sold from a hogshead containing 600 lb. of sugar, of it at one time, and of the remainder at another time. What per cent. of the whole remained? 21. A merchant owes $15120, and his assets are $9828. What per cent. of his debts can he pay? 516. The rate and percentage being given to find the base. ORAL EXERCISES. 1. 18 is 3% of what number? ANALYSIS. Since 3%, or 180, of a certain number is 18, TOT is 1 of 18, or 6, and 188 is 600. Hence 18 is 3% of 600. 10. 124% of 96 is 334% of what number? 517. PRINCIPLE.-The base is as many times the per centage as 100% is times the rate. WRITTEN EXERCISES. 518. 1. 144 is 75% of what number? OPERATION. 144.75 192 Or, 100 75 100 = $ 144 x = 192 ANALYSIS. Since the percentage is the product of the base by the rate, the base is equal to the percentage divided by the rate; and 144.75 is 192. Or, Since the rate is .75, the per centage is, or of the base; hence the base is of the percent age, and of 144 is 192. 2. $54 are 15% of what? 3. $18.75 are 24% of what? 1 4. 4.56 A. are 5% of what? 5. 39.6 lb. are 71% of what? RULE.-Divide the percentage by the rate. Or, take as many times the percentage as 100% is times the rate. FORMULA.-Base = Percentage ÷ Rate. |