Of $840? Of $784? Of 500 ft.? Of 600 ft.? Of 63 gals.? Of 94 gals.? Of $500 ? 7. What is 120% of $250? 8. What is 100% of 87 ft.? 9. What is 210% of 40 gals.? 10. What is 60% of $60? 11. What is % of $1,000? Of $8,000? Of $6,000? 233. To find the Amount, when the Base and Rate are given. See Principle 2, Art. 231. EXAMPLES. 150 lbs. x 1.10 1. What is the amount of 150 lbs. increased by 10% of itself? Ans. 165 lbs. 2. What is the amount of $300 increased by 35%? 3. What is the amount of 610 yds. increased by 16%? 4. What is the amount of 76 acres increased by 15% ? 5. What is the amount of $218 increased by 9%? 6. What is the amount of 48 tons increased by 80% ? 234. To find the Difference, when the Base and Rate are given. See Principle 3, Art. 231. EXAMPLES. 1. What is the difference between $108 and 30% of itself? $108 × .70 = $75.60, Ans. 2. What is the difference between 160 rods and 80% of itself? 3. Diminish $540 by 30% of itself. 235. To find the Rate, when the Base and Percentage are given. See Principle 4, Art. 231. EXAMPLES. 1. The percentage is $90.24, and the base is $752; what is the rate? $90.24 ÷ 752 = .12 = 12 per cent, Ans. 2. What is the rate, when the percentage is $7 and the base is $100? What, when the base is $500 ? 3. Find the rate, when the base is $400 and the percentage is $20. 4. What is the rate, when the percentage is 60 lbs. and the base is 300 lbs. ? 5. Given the base $2,000, and the percentage $200; what is the rate? 6. A gentleman in Cleveland sends to his friend in New York $50,000, asking him to take out $500 for his services, and invest the balance in New York Central R. R. stock; what rate per cent of the money sent does for the services of his friend? What rate per cent he pay of the money invested does he pay? 236. To find the Base, when the Rate and Percentage are given. See Principle 5, Art. 231. EXAMPLES. 1. 960 is 25 per cent of what number? SOLUTION. 960.25 Ans. 3,840. 2. 74 is 621 per cent of what number? 3. 450 is 112 per cent of what number? 4. Of what number is 66, 2 per cent? 5. In a school 100 pupils are present; this number is 80 per cent of the pupils on the roll; what is the number on the roll? MISCELLANEOUS PROBLEMS. 1. The population of a town in 1860 was 3,750, and in 10 years it increased 30%; what was the population in 1870 ? 2. A merchant bought goods to the amount of $3,150 and paid 15% on their first cost for transportation and insurance; what was their final cost? 3. A man has 50 geese, 40% more of chickens than geese, and 60% more of ducks than chickens; how many chickens has he, and how many ducks? 4. A cask of wine contained 44 gals., but 18% of it leaked out; how much remained ? 5. A man has a capital of $20,000, of which he loses 35%; how much has he remaining? . Define per cent. What is percentage? What is the base? What is the rate? Illustrate. What is the amount? What the difference? Repeat the 5 principles of percentage. Write an example that will illustrate each principle. COMMISSION. 237. Commission is a percentage paid to an agent for transacting business. 238. An Agent is one who transacts business for another. If he buys and sells merchandise, he is called a Commission Merchant, or Factor; if he buys and sells stocks, exchange, real estate and the like, he is called a Broker; if he collects debts, taxes, and the like, he is called a Collector. 239. A Consignment is a quantity of merchandise sent to an agent for sale. The party that sends the goods is called the Consignor; and the party to whom they are sent is called the Consignee. 240. An Account of Sales is an account rendered by the Consignee to the Consignor. 241. The Net Proceeds is the remainder after deducting commission and other expenses. All problems in Commission are solved by the principles of percentage. The base in Commission is generally what the agent expends or collects; but in buying and selling stocks, and the like, the commission is based on the par value. EXAMPLES. 1. A commission merchant received a consignment of wheat which he sold for $2,850; what was his commission at the rate of 4% ? Ans. $114. 2. A commission merchant purchased cotton for a manufacturer to the amount of $5,140; what was his commission at 2% ? Ans. $102.80. 3. A broker sells a house for $13,400; what is his commission at 11% ? Ans. $150.75. 4. A broker buys 6 lots of land for $8,490; what is his commission at 3% ? 5. A cotton broker sells 40 bales of cotton, each weighing 450 lbs., for 15 cts. per pound; what is his commission at 14% ? 6. My agent purchased goods for me to the amount of $7,850, on which I agreed to pay 21% commission; how much must I pay him? 7. An architect builds a house which costs $13,710, and charges 21% for his services; what is his bill? 8. A broker sold 70 shares of stock whose par value was $100 per share; what was his commission at 1% ? 9. What commission should a broker receive for selling 100 shares of stock whose par value is $100, at 1% ? 10. Find the net proceeds of the following account of sales: Sales on account of JOHN R. BENSON, Rochester, N. Y. What is commission? What is an agent? A commission merchant? A broker? A collector? A consignment? A consignor ? A consignee? What is the net proceeds? How do you solve problems in commission? What is the base? What is account of sales? NOTE.-For a more extended treatment of Commission, see Davies & Peck's Complete Arithmetic. |