17. Mr. Hamlin had 360 acres of land, and sold 33% of it, how many acres remained? Ans. 240 acres. 18. The silver coin of the United States contains 10% of alloy; how much pure silver is there in 16 oz. of silver coin? Ans. 15 oz. 19. A land agent bought 1016 acres of land, and sold 12%. to Mr. Chase and 37% of the remainder to Mr. Dunn ; how much remained? Ans. 555 acres. 20. How much linseed oil can be extracted from 1 cwt. 27 lb. of flaxseed, if flaxseed contains 11% of oil, and a pint of oil weighs of a pound? Ans. 2 gal. 1.31.qt. 21. A clerk's salary is $2000 a year; he spends 10% of it the first quarter, 15% the second, 6% the third, and 4% the fourth; how much did he save? Ans. $1300. 22. Mr. Walton's income is $2500 a year, of which he spends 30% for board, 124% for clothes and books, and 10% for incidentals; what does he save in a year? Ans. $1187.50. 23. A man owning of a machine shop worth $10,000, sold 16% of his share to his brother; what part of the whole shop did he still retain, and what was its value? CASE II. Ans. ; value, $6250. 386. Given, the rate and the percentage or proceeds, to find the base. MENTAL EXERCISES. 1. Twenty-four is 20% of what number? SOLUTION.-If 24 is 20 per cent. of some number, it is %, or of that number; if 24 is of some number, , or the number, equals 5 times or 120. Of what number is 2. 16 25% ? 3. 19 163% ? 4. 27 334%? 5. 1.5 50% ? 6. 4 lb. 6% ? 7. 2 bu. 12% ? 8. 8 A. 66%? 9. £7.5 75% ? 10. Thirty is 25% more than what number? 50% more than what number? 100% more than what number? 11. Sixty is 25% less than what number? 50% less than what number? 100% less than what number? 12. The population of a certain village is 2700, which is 12% more than it was 5 years ago; what was its yearly gain? 13. Mr. A. paid a tax of $60, which was % of the value of his property; what was the value of his property? 14. A gentleman gave his daughter $50 as a Christmas present, which is 62% of what he gave to his wife; what did he give his wife? 15. On a certain day there were present at a graded school 160 pupils, which was 113% less than were registered; how many were registered? WRITTEN EXERCISES. 1. 60 is 5% of what number? What number, increased by 20% of itself, equals 360? SOLUTION.-If 60 is 5% of some number, then .05 times some number equals 60; if .05 times some number equals 60, the number equals 60.05, which is 1200. SOLUTION.-A number increased by 20%, or .20 of itself, equals 1.20 times the number; and if 1.20 times a number equals 360, the number equals 3601.20, or 300. OPERATION. 60.051200 OPERATION. 3601.20300 Rule I.-Divide the percentage by the rate, to find the base. Rule II.-Divide the amount by 1 plus the rate, or the difference by 1 minus the rate, to find the base. 10. What number increased by 40% of itself equals 1694! Ans. 1210. 11. What number diminished by 20% of itself equals 468! Ans. 585. 12. What fraction increased by 16% of itself equals ? Ans. 13. What fraction diminished by 36% of itself equals ? 14. 42 A. 112 P. is 16% of how much land? Ans. Ans. 256 A. 32 P. 18. 14 lb. 10 oz. 16 pwt. is 331% more than what number? Ans. 11 lb. 2 oz. 2 pwt. 16. A bookkeeper spends $600 per year, which is 24% of nis salary; required his salary. Ans. $2500 17. A young farmer owns 320 acres of land, which is 15% of what his father owns; how much has the father? Ans. 21331 A. 18. A newsboy earned $15, which was 30% of what he then had in bank; how much had he in bank? Ans. $50. 19. A teacher spends 24% of his salary, and can thus save $760 a year; what was his salary? Ans. $1000. 20. Mr. Hays drew 35% of his bank deposit to pay a debt of $4788.56; what was his deposit? Ans. $13681.60. 21. A man bought some flour and sold 25% of it to A, and 333% of the remainder to C; how much did he buy if he sold C 640 barrels? Ans. 2560 bar. 22. Mr. Herr drew 62% of his money from the bank, and paid 33% of it for a house worth $4500; how much money had he remaining in bank? Ans. $8100. 23. A lady invested 90% of her money in bank stock, and some time after sold 333% of the stock, and still had $4500 invested; required the whole amount of her money. CASE III. Ans. $7500. 387. Given, the base and the percentage or the proceeds, to find the rate. MENTAL EXERCISES. 1. 12 is what per cent. of 48? SOLUTION.-48 is 100 per cent. of 48, and 12, which is of 48, is of 00 per cent., or 25 per cent. of 48. What per cent. 2. Of 75 is 15? 3. Of $12 are $3? 4. Of 81 is 27? 5. Of 16 qt. are 5 qt.? 6. Of is 8. Of 75% is 25% ? 9. Of 2.5% is 1.5% ? 10. From a hogshead of wine containing 90 gallons, 12 gallons leaked out; what per cent. was lost? 11. It a man's income is $2000 a year and he saves $300; what per cent. does he spend? 12. The standard for gold and silver coin in the United States ia 9 parts pure to 1 of alloy; what % of pure metal is there? 13. A merchant having put $5000 into a certain speculation, finds on settling up the business that he has received $5250; what % diɑ he gain? WRITTEN EXERCISES. 1. 20 is what per cent. of 80? SOLUTION.-If 20 is some per cent. of 80, then 80 multiplied by some rate equals 20; if 80 multiplied by some rate equals 20, the rate equals 20 divided by 80, which is .25, or 25%. OPERATION. 20-80=.25 2. 240 yd. being increased by a certain per cent. of itself equals 300 yd.; required the rate. SOLUTION.-300 yd. minus 240 yd. equals 60 yd., which is the percentage. If 240 yd. multiplied by some rate equals 60 yd., the rate equals 60 divided by 240, which is .25, or 25%. OPERATION. 300-240-60 60-240-.25 Rule I.-Divide the percentage by the base, to find the rate. Rule II.—Divide the difference between the proceeds and base by the base, to find the rate. NOTE.-The rate may also be found by dividing the proceeds by the base and taking the difference between 1 and the quotient. 13. The base is $14.10, the percentage $2.35; what is the rate? 14. If a miller takes 10 quarts of every bushel he grinds for toll, what per cent. does he take for toll? Ans. 314%. 15. My income last year was $1800 and my expenses $1356; what % of my income did I expend? Ans. 75%. Ans. 16%. 16. A regiment went into battle with 960 men, and came out with 600 men; what per cent. was lost? 17. A merchant's liabilities are $15760, $7289; what % of his debts can he pay? Ans. 37%. and his assets Ans. 461%. 18. A merchant bought 275 barrels of flour, and after losing 20% of it, he sold 25% of the remainder; what per cent. of the whole remained? Ans. 60%. 19. A put $780 in a savings bank, which was 15% of all his money, and afterward deposited 25% of the rest of his money; what per cent. of all his money had he then in bank? Ans. 36%. 20. A gold eagle of the United States weighs 258 gr. and the alloy in it weighs 25.8 gr.; what per cent. of the coin is alloy? Ans. 10%. 21. 35 per cent. of a regiment being sick, only 637 men were able to enter battle, of whom were killed; how Many did the regiment number, and what per cent. of the whole number were killed? Ans. 980 men; 94%. GENERAL FORMULAS. 388. These methods and rules may all be represented in general formulas as follows: NOTE.-These formulas apply to all the cases in the practical applica tions, and may be used instead of the rules, or with them, as the teacher prefers. APPLICATIONS OF PERCENTAGE. 389. The Applications of Percentage are extensive, owing to the great convenience of reckoning by the hundred in business transactions. 390. These Applications of Percentage are of two |