ART. 208. CASE II.-To find the cost of a quantity consisting of several denominations. 1. What will be the cost of 4 A. 1 R. 20 P. of land, at $16.40 per A.? OPERATION. Rule for Case II.-Multiply the price by the number of the denomination at which the price is rated, and find the cost of the lower denominations, by taking aliquot parts. Add the different costs; the sum will be the cost of the whole. 15. 16. 3 lb. 13 oz. 15 dr. spice, at $2.56 a lb. 17 A. 3 R. 39 P., at $3.20 per A. $9.91 $57.58 For additional problems, see Ray's Test Examples. REVIEW.-207. What is Case 1? What the Rule for Case I? 208. What is Case 2? What the Rule for Case 2? XVI. PERCENTAGE. ART. 209. Percentage embraces calculations in which reference is made to a hundred as the unit; and, The per cent. or percentage of any number or quantity, is so many hundredths of it. Thus, 1 per cent. is 100; 2 cent. 3 Since 3 per cent. 100 86.02, and so on, (Art. 176), therefore, per cent. may be expressed decimally; thus, .01, 4 per cent. is .04 10 per cent. is .10 9 per cent. is .09 75 per cent. is ..75 100 100 per cent. (188, or the whole,) is 125 per cent. (135, or 25 more than the whole,) is EXAMPLE.-Write 7 per cent. decimally. 41 per ct. 5 per ct. 10 per ct. 371⁄2 per ct. 120 per ct. THE SIGN %, is used in business, instead of the words "per cent. ;" thus, 5 per cent. is written 5%. ART. 210. CASE I.—To find any per cent. of a number. 1. What is 2% (2 per cent.) of $125? SOL. To take 2 per cent. is to take 2 hundredths. Hence, multiply by 2 and divide by 100; or multiply by expressed decimally. 2. What is 7 % of 175 dollars? OPERATION. $125 Ans. 2.50 Ans. $12.25 "IEW.-209. What does Percentage embrace? What is the per cent. aber? Give examples. Rule for Percentage.-Multiply by the rate per cent. expressed decimally; the product will be the per cent. required. Or, by PROPORTION (Art. 203). As 100 is to the rate per cent. so is the given number or quantity to the required per cent. REVIEW.-209. How may per cent. be expressed? What is 100 per cent.? What is 125 per cent.?per cent.? 3 pr cent.? What sign is used for per cent.? Give examples. Give examples. 21. If 81% of $72 be taken from it, how much will remain ? Ans. $65.88 22. I had $800 in bank, and drew out 36% of it: how much had I left? Ans. $512: 23. What is the difference between 131 % of $56, and 143 % of $51 ? Ans. 13 cts. 24. A merchant in expending $1764, paid 23 % for cloth; 31% for calicoes; 9% for linens; 31% for silks; the remainder for muslin: how much did he pay for each? Ans. to last, $595.35 25. A grocer bought 4 bags of coffee, of 75 lb. each: 121 % was lost by waste: what was the rest worth, at 14 cts. per lb. ? Ans. $36.82 26. A flock of 160 sheep increased 35 % in 1 year: how large was it then? 27. I had 320 sheep; 5 % were killed: 25 % of the rest, how many were left? Ans. 216. after selling Ans. 228. 18% for 28. A's salary is $800 a year: he spends rent; 15 % for clothing; 23 % for provisions; 12% for sundries: how much is left? Ans. $256. ART. 211. CASE II. To find what per cent. one number is of another. 1. What % of 8 dollars is $2? SOLUTION.-One per cent. of $8 OPERATION. .08)2.00 Ans. 25 per cent. or, is $8.01.08, (Art. 210); and since $2 contain this 25 times, it must be 25 per cent. of $8. Or thus: the question is the same as to find how 3=1=.25-25 per cent. many hundredths $2 are of $8. Now 2 is 2 of 8, and 2=1=.25= 25 per cent. *2. What % of $15, is $3? Ans. 20. REVIEW.-210. How is the percentage of a number found, Rule? How, when the rate per cent. is a mixed number or a fraction? 211. What is Case 2? What the Rule for Case 2? Rule for Case II.-Divide the number which is considered the percentage, by 1 per cent. of the other number; the quotient will be the required rate per cent. Or, by PROPORTION.-As the given number is to the percentage, so is 100 to the required rate per cent. Ans. Ans. . 11. What % of $2, is 2 mills? 12. What % of $3532, is $13.245? 13. A man had $300, and spent $25: what % was that of the whole? Ans. 8. 14. A man owed $500, and paid $75 of it: what % of the whole debt did he pay ? 15. What % of any number is of it? 16. A miller takes for toll, 6qt. from grain ground: what % does he get? Ans. 15. Ans. 60. every 5 bu. of Ans. 33. For additional problems, see Ray's Test Examples. APPLICATIONS OF PERCENTAGE. ART. 212. The principal applications of percentage are in Commission, Insurance, Stocks, Brokerage, Interest, Discount, Profit and Loss, Duties, and Taxes. ART. 213. COMMISSION Is the sum allowed to Agents for buying, selling, or transacting other business. Those who transact business for others, are Agents, Commission Merchants, Factors, or Correspondents. |