PART SECOND. PERCENTAGE. ART. 68. Per cent. is a contraction of the Latin phrase per centum, which signifies by the hundred. Percentage includes all those operations in which 100 is the basis of computation. The rate per cent. is the number of hundredths. Hence, any per cent. of a number is so many hundredths of it. Thus, 5 per cent. of a number is 5 hundredths of it. Note. Instead of the words " per cent.," it is now customary to use the character: thus, 12 per cent. is written 12%; 21 per cent., 21%. ART. 69. The rate per cent. may be expressed decimally by writing it as so many hundredths. Thus, 1 per cent. is written .01 7 per cent. is written .07 5 per cent. is written .05; or .055 15 per cent. is written .15 100 per cent. is written 1.00 per cent. is written .001; or .005 per cent. is written 2 per cent. is written per cent. is written .001; or .0025 .021 .00%; or .0005 2 ART. 70. To find a given per cent. of any number or quantity. Ex. 1. Sold a house and lot, which cost me $1450.75, at a gain of 15%. What was the gain ? 1450.75 .15 $217.6125 Explanation.-Since 15% is .15, the gain was 15 hundredths of $1450.75. Some persons prefer, and it is sometimes more convenient, to find the percentage as follows: $14.5075 15 $217.6125 Explanation.-1 per cent. of any number is .01 of it (which is found by removing the decimal point two places to the left), and 15 per cent. is 15 times as much as 1 per cent. RULE, Multiply the given number by the rate per cent. EXPRESSED DECIMALLY. Or, Remove the decimal point Two places to the left, and multiply by the rate per cent. AS A WHOLE NUMBER, Examples. 2. What is 8 per cent. of 500 miles? 3. What is 6 per cent. of $72.371 ? Ans. $4.3425. 4. Find 32 per cent. of 1200 men. 5. Find 25 per cent. of 12 hours 30 minutes. 6. What is 1000 per cent. of $1000 ? 7. What is per cent. of $320 ? Ans. 3 h. 7 m. 30 s. Ans. $10000. Note. The second rule is most convenient in solving such examples as the above. Thus, of $3.20=$1.20. 8. What is per cent. of $15.80 ? 9. What is 1 10. Find per cent. of 134500 bushels. per cent. of 1050 sheep? Ans. 14 sheep. Ans. 67 bu. 11. 33 per cent of any number is what part of it? Ans.. 12. What is 33 per cent. of 252 cattle? Ans. 84 cattle. Note. When the rate per cent. is a convenient part of 100, take the same part of the given number. of 252 is of 252-84. 13 13. What is 163 per cent. of 1200 hogs? 14. Find 663 per cent. of 660 men. 15. Find 75 per cent. (3) of 4852. Thus, 33 per cent. Ans. 200 hogs. Ans. 440 men. Ans. 3639. 16. Find 15 per cent. of 25 per cent. of $13.60. Ans. $0.51. 17. Find 87 per cent. () of 1632 feet. Ans. 1428 feet. 18. A merchant failing was able to pay his creditors but 40 per cent. He owes A $3500, B $1200, C $1134, D $650. What will each receive? Ans. A $1400, B $480, C $453.60, D $260. 19. A person at his death leaves an estate worth $1500; 12 per cent. of which he received from his wife; 20 per cent. from speculation; 30 per cent. from rise of property; 25 per cent. from the estate of an uncle; and the remainder from his father. How much did he receive from each source? Ans. to last, $195. 20. A has an income of $1100 per year; he pays 10 per cent. of it for board; per cent. for washing; 2 per cent. for incidentals; 15 per cent. for clothing; 9 per cent, for other expenses. What does each item cost, and how much has he left ? Ans. He has left $698.50. CASE II. ART. 71. To find what per cent. one number is of another. Ex. 1. 6 is what per cent. of 25 ? Explanation.—6 is, of 25, which changed to a decimal (Art.) equals 24 hundredths; or 24 per cent. Ex. 2. 12 cents is what per cent. of $3? Explanation.-Since only quantities of the same denomination can be compared, reduce $3 to cents, and proceed as above. RULE. Reduce the numbers to the same denomination. Annex two ciphers to the number which is to be the rate per cent., and divide the result by the other number. Examples. 3. What per cent. of $40 is $12 ? Ans. 30%. 4. What per cent. of 120 yards is 20 per cent. of 90 yards? 5. 2 dimes is what per cent. of $5? 6. 40 men is what per cent. of 150 men ? 7. 150 men is what per cent. of 40 men ? Ans. 5. 8. The cent (new coinage) contains 22 parts copper and 3 parts nickle; what per cent. of it is copper and what per cent. nickle ? Ans. Copper 88% 9. 15 per cent. is what per cent. of 60 per cent. ? Ans. 25%. 10. A person whose annual income is $450 pays $125 for board, $140 for clothing, $25 for books, and $30 for sundries; what per cent. of his income is each item, and what per cent. remains ? Ans. to last, 283%11. A merchant failing owes $3500; his property is valued at $2100. What per cent. of his indebtedness can he pay ? Ans. 60%. CASE III. ART. 72. To find a number when a certain per cent. of it is given, Ex. 1. A merchant sells 40 per cent. of his stock for $3500; what is the value of his whole stock at this rate : $3500 40 ×100=$8750, Ans. 40 per cent. of his stock, 1 per cent. is of $3500, or $87.50, and 100 per cent., or the whole stock, 100 times $87.50, or $8750. Ex. 2. A person pays $13.50 a month for board, which is 30 per cent. of his salary, what is his salary? Divide the given number by the given rate per cent. and multiply the quotient by 100. Or, Annex two ciphers to the given number, and divide the result by the rate per cent. Note. When the given number contains cents (see Ex. 2, above), remove decimal point two places to the left, instead of annexing two ciphers. Examples. 3. 45 is 10 per cent, of what number? 4. $3.60 is 15 per cent, of what number? 5. $5.62 is 12 per cent. of what number? Ans. $45. 6. Sold cloth for $3.50 per yard, which was 70 per cent, of its cost; what was the cost of the cloth per yard? Ans. $5. 7. A boy spent 60 per cent. of his money for toys, and 25 per cent. for candies, and had 15 cents remaining; how many cents had he at first? Ans. $1.00. 8. The assets of a merchant are $45000, which is 60 per cent, of his indebtedness; what is his indebtedness? Ans. $75000. 9. The deaths in a certain city, during the year, are 980, which is 3 per cent. of the population; what is the number of inhabitants? Ans. 28000. |