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 Too; 2 per cent. 180; 3 per cent. 180. = Since 0.01, 8 .01, .02, and so on, (Art. 176), therefore, per cent. may be expressed decimally; thus, 1.25 = of, is .005 .00125 .035 125 per cent. (125, or 25 more than the whole,) is per cent. is a half of 1 per cent., per cent. is of 1 per cent., of, is 3 per cent. is .031,=.035 is = EXAMPLE.-Write 7 per cent. decimally. 4 per ct. 51 101 5 per ct. 10 per ct. 37 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 .02 Ans, 2.50 Ans. $12.25 REVIEW.-209. What does Percentage embrace? What is the per cent. of any number? 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? Give examples. What is 100 per cent.? What is 125 per cent.? per cent. ? 31 per gent.? What sign is used for per cent. 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 13 % 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: 123% 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. 28. A's salary is $800 a year: he spends 18% for rent; 15 % for clothing; 23 % for provisions; 12 % for sundries: how much is left? Ans. $256. ART. 211. CASE II. per cent. one number is of another. To find what 1. What % of 8 dollars is $2? OPERATION. .08)2.00 Ans. 25 per cent. or, SOLUTION.-One per cent. of $8 is $8X.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=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. 3. what % was Ans. 8. 12. What % of $3532, is $13.245? 13. A man had $300, and spent $25: that of the whole? 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. Commission is estimated at a certain rate per cent. on the amount employed in the transaction; it is calculated by the Rule, Art. 210. 1. At 5%, what does an agent receive for selling goods amounting to $240? Ans. $12.00 2. At 21%, what is the commission for selling goods amounting to $460? Ans. $11.50 3. What the commission on sales of $180 at 4%, and on sales of $119 at 3%? Ans. $10.77 4. What the commission on $240 sales at 3%, and on $225 sales at 5%? Ans. $18.45 5. What the commission on sales of $480 at 21%; $275 at 3%; and $216 at 23 %? Ans. $25.36 6. What on sales of $275 at 3%; $341 at 15%; $964 at 25%; and $217 at 24 %? Ans. $305.2825 7. An agent sells 25 bl. of molasses, at $13 each, at 21% commission: what will the agent and owner each receive? Ans. Agent, $8.12; Owner, $316.87 8. A factor sells 15 hhd. sugar, of 1114lb. each, at 8cts. a lb., charging 3% commission: what sum will he pay the owner? Ans. $1293.354 9. A factor sells flour, at $7 each; and his commission is 3% 250 bl. pork, at $15 each; 175 bl. 1456 16. feathers, at 25 cts. a lb.; what sum will he pay the owner? Ans. $5178.83 ART. 214. When an agent invests MONEY, his com mission is computed on the amount he expends. 10. An agent receives $210 to buy goods; after deducting his commission of 5%, what sum must he expend? SOLUTION. For each $1 expended, he receives 5 cts. Hence, for each $1.05, received, he must expend $1; therefore, he must expend as many dollars as $1.05 are contained times in $210: That is,-$210-$1.05 200. Ans. $200. PROOF.-$200 X.05 $10; and $200 + $10-$210. |