CHAPTER IX. PERCENTAGE. SECTION I. DEFINITIONS AND PRINCIPLES. 153. Percentage is the name applied to computations in which 100 is the unit or measure. 154. Per cent. is an abbreviation of the Latin phrase per centum, meaning by the hundred. 1. What is ORAL EXERCISE. 50? of 100? ? 100? 100? 100 2. What is of 600? 5 of 600? 15 of 1200? 3. How many hundredths of $100 are $7 ? $20? $25? NOTE.- of any number is 1 per cent. of it; To is 2 per cent., and, in general, any number of one-hundredths of a number is so many per cent. of it. 4. How many hundreths of a number is 6 per cent. of it? 10 per cent. of it? 25 per cent. of it? 60 per cent. of it? 5. How many hundredths of a number is 51 per cent. of it? 120 per cent. of it? 400 per cent. of it? of 1 per cent. of it? 100 6. What per cent. of a number is 15 of it? 1% of it? .16 of it? .37 of it? .005 of it? 1.125 of it? Per cent. is usually written %; thus, 20% is read “twenty per cent.' 7. How many hundredths is 40% ? 60%? 62% ? 125%? 81% ? 18% ? 561% ? 8. What per cent. of a number is of it? NOTE.-is, or 25%. 9. What per cent. of a number is of it??? ? ? ? ? ? ? ? ? ? 11? 15 10. What fractional part of a number is 20% of it? = ANALYSIS.-20% 20%, or ; hence, 20% of a number is of it. 11. What fractional part of a number is 10%? 30%? 60%? 75%? 121% ? 12%? 311%? 331%? 66% ? 871%? 551% ? 12. What part of a number is % of it ANALYSIS.-% = 1 of 180=200. 13. What part of a number is 1% of it? %? %% ? %? WRITTEN EXERCISE. Express decimally the following: 1. 1%; 12%; 70%; 95%; 60%; 50%; 87%. 2. 12%; 37%; 561%; 51%; 91%; 220%. Change to expressions having the per cent. (%) sign the following: 3. .16; .125; .875; .331; .621; .005; .183. 4. .311; .87; .002; 15; 3; §. PRINCIPLES AND DEFINITIONS. 155. The Rate is the number of hundredths. Thus, in 3%, or 8, 3 is the rate, and itself the rate per cent. 156. The Rate per cent. is the fraction which denotes how many hundredths are taken. 157. The Base is the number of which the per cent. is taken. 158. The Percentage is the result of taking a per cent. of the base. 159. The Amount is the base added to the percentage. 160. The Difference is the remainder found by subtracting the percentage from the base. In computation, any per cent. less than 100 may be expressed as a decimal; as 16% = .16; 45% = .45; 7% = .07, etc. Any per cent. greater than 100 may be expressed as a whole number and a decimal; as 125% = 1.25; 1874% = 1.87, etc. SECTION II. GENERAL CASES IN PERCENTAGE. CASE I. The Base and the Rate given, to find the Percentage. 1. What is 15% of 160? SOLUTION.-15% is 10%, or 2%; 2% of 160 is 24. 2. What is 5% of 60? 5. What is 6% of 300? 8. What is 33% of 15 sheep? 9. What is 561% of 120 cents? 10. What is 871% of 96 yd. of cloth? 11. What is 3% of 90 bu. of corn? 12. A farmer had 50 sheep, and bought 20% of his number more: how many had he then? 13. A laborer who received $60 a month, had his salary diminished 10% how much did he get then? 14. Bought a knife for $2, and sold it at a gain of 25% : what did I get for it? 15. A man had a flock of chickens consisting of 75; they increased during the summer 120%: how many had he at the close of the summer? 16. Bought goods at $36, and gained on them 16% what was the selling price? 17. Having $80, I expended 15% of it for bread, 30% for clothes and 25% in travelling: how much did I spend for each, and how much have I remaining? 18. A has $40, and B has 4 times as much; B gives 25% of his money to A: how much has each then? 19. 15% of $700 is him at a gain of 12% 20. Two men, C and of what I paid for a horse; I sold what did I get for him? D, owned a store worth $16500; C owned as much as D; D bought 20% of C's: how much did each then own? WRITTEN PROBLEMS. 1. What is 27% of $6723? SOLUTION. $6723 .27 47061 13446 $1815.21 Explanation. Since 27% equals .27, the required percentage is .27 of $6723, or $1815.21. From the foregoing solution and explanation we derive the following RULE. Multiply the base by the rate per cent.; the result is the percentage. 5. What is 66% of $186.50? 6. What is % of $100? 2. What is 63% of 127 A.? of 71% of $647 ? 8. What is 6% of $140+9% of $160+23% of $175? Ans. $63.05. 9. Find the value of 11% of $180+22% of $160+92% of $63. 10. Find the value of 7% of $6.50+12% of $12.50 +25% of $19.64. 11. Find the value of 12% of 25 £ 6 s. 6 d. Ans. $112.96. Ans. $6.865. Ans. 3 £9.36 d. 12. Find the value of 25% of 6 yd. 2 ft. 6 in. Ans. 1 yd. 2 ft. 1 in. 13. What is the value of of 44% of T.? Ans. 9 lb. 6 oz. 14. What is the value of 24 times 1% of 66 gal.? Ans. 1 qt. 1 pt. 32 gi. 15. If iron ore yields 63% of pure much iron is there in 16 T. of ore? metal to the ton, how Ans. 10 T. 160 lb. 16. How much silver in 26 T. of ore that yields 21% of metal to the ton? Ans. 1300 lb. 17. An operator mined 12600 T. of coal; he paid 20% for mining and 25% for transportation: how much did he have remaining? Ans. 6930 T. 18. A and B each invest $3300 in business; at the end of a year A has gained 12%, and B has lost 51% how much has each ? Ans. A, $3696; B, $3126.75. 19. A man has an annual income of $2550; he spends 15% in travelling, 20% for board and 61% for clothing: how much does he save? Ans. $1491.75. 20. If a man have a yearly income of $2500, and spend the first year 25% of it, the second 35% of it, and the third 421% of it, how much does he save in three years? CASE II. Ans. $4937.50. The Base and the Percentage being given, to find the Rate. 1. What per cent. of 40 is 10? ANALYSIS.-10 is of 40; it is therefore of 100% of 40, or 25% of 40. 2. What per cent. of $25 is $5? Of 40 cows is 4 cows? 3. What per cent. of 75 yd. is 15 yd.? Of 72 sheep is 9 sheep? 14. From a barrel containing 36 gal. of vinegar a grocer draws 20 gal: what per cent. of the vinegar remains? 15. A boy having 90 cents, spent 60 cents: what per cent. of his money did he spend, and what per cent. has he remaining? 16. Bought 4 doz. of eggs, but found that 6 of the eggs were not good what per cent. were good? : 17. of $25 is what per cent. of † of $96? 18. of 20% is what per cent. of 24 times 12% ? |