180 PROBLEMS-REVIEW 1. What is the cube of each number from 1 to 10? 2. What is meant by the cube root of a number? What is the cube root of 64? Of 125? Of 1,728? 3. A piece of woolen cloth lost 18% of its length in shrinking. The present length is 41 yards. If the cloth cost $60 before shrinking, what was the price per yard? 4. Beef loses about 15% of its weight by boiling and 20% by roasting; how much will a piece of beef, weighing 10 lb. when raw, weigh after having been roasted? Boiled? 5. A straight glass jar, 12 in. high, was filled full of milk. The next day, the cream on top was in. thick. What percentage of the milk poured in was cream? 6. The water surface of Kentucky is 1% of the land surface; the total area is 40,000 sq. mi. Find the area of the land surface of Kentucky; the water surface. 7. The land surface of New Hampshire is about 9,000 sq. mi. The water surface is 33% of the land surface. Find the total area. 8. By passing some soil through sieves, Thomas found that 18% of his sample was coarse gravel, 37% gravelly sand, and 11 oz. fine earth; what was the weight of the sample? 9. When wheat is ground, 771% by weight of the product is fine flour; how many bushels of wheat are required to produce 1,000 barrels of fine flour? 10. The distance from Chicago to Minneapolis is 70% of that from Boston to Toronto. The sum of the two distances is 1,020 miles. Find each. II. A maker of picture-frames is asked the cost of a frame 24 in. by 36 in., outside measure. The molding selected costs him 16¢ per running foot, the glass 404, the back and nails 15¢, labor 254. He wishes to set the price so as to gain 121%. .What price should he set? BUSINESS APPLICATIONS Commission I. A real-estate agent receives for his services 5% of the rents collected. If he collects $25 rent each month, how much does he receive in a year? 2. An agent sold a car-load of fruit for $142. He retained 6% for his services. How much did he remit to the shipper? 3. The percentage received by an agent for handling goods is called his commission. What is the commission in Exercise 2? 4. A real-estate agent sold a 200-acre farm at $75 an If he charged 21%, what was his commission? acre. 5. A commercial traveler receives 7% commission on the orders he takes. In 6 months he sells goods to the amount of $9,800. How much does he earn? 6. An auctioneer received $15 for selling $500 worth of goods; what was his rate of commission? 7. A broker bought 10,000 bu. of wheat for a customer at a commission of of a cent per bushel; what was the amount of his commission? 8. A merchant gave bills aggregating $300 to a collector who succeeded in collecting $240, but reported the rest uncollectable. If the collector charged 8% of the amount collected, how much of the $300 did the merchant lose? What was the percentage of loss? 9. Mr. Jones is an agent for an automobile company that pays him a commission of 10% on his sales. In one month he sold one automobile at $760, and another at $925. How much did he earn? His expenses were $96. How much did he make above expenses? 182 PROBLEMS-COMMISSION 1. A real-estate agent received $125 commission for selling a house at $5,000; how many per cent did he receive? 2. A commission merchant remitted $142.50 to the owner of the goods and retained $7.50 commission; for how much did he sell the goods? What was his rate of commission? 3. An agent sold 6 cottages at $1,000 each for 21% commission; what was his commission per cottage? 4. A real-estate agent sold a house and lot for $3,200. His commission was 21%. How much did the owner receive? 5. Mr. Baker, a cattle broker, paid $1,100 for sheep to stock his ranch. This includes the broker's commission of 10%. What did the sheep cost the broker? PLAN. 1. Let C the cost. 3. 1.10 C = $—. 2. C 10% of C = $1,100. 4. Therefore C = $ 6. A commercial traveler, who receives a commission of 5% on his sales, earned $28 in ten days. Find the amount of the sales. PLAN. 1. Let S the amount of his sales. 2. .05 × S = $—. 3. Therefore S = $—. 7. A real-estate agent collects rents amounting to $400 and remits $384 to the owner; what is his rate of commission? 8. A man sold his house and lot through an agent, who charged a commission of 2% and remitted $9,310. What was the selling price? PLAN. 1. Let S = selling price. 2. S.02 x S = $9,310. 3. Therefore S = $. 9. A merchant gave bills to the amount of $300 to an agency for collection. The agency charged 2% for collecting of the amount, but 5% for collecting the other half, on account of the trouble in collecting. How many dollars did the merchant receive? TRADE DISCOUNT 183 1. A merchant offered a reduction of 5% on purchases at one time amounting to at least $50. A woman bought $65.20 worth of goods. What reduction was made her? When for any reason a reduction is made from a fixed price, such a reduction is called a discount. At the close of a season damaged goods were offered at the following discounts. Find the reduced price: 6. A car-load of fruit valued at $160 was slightly damaged in transit. The buyer agreed to take it at a discount of 25%. What did he pay? If the fruit cost the shipper $135, what was his loss? The price after the discount has been taken off is called the net price. Determine the numbers to fill the blanks : 184 PROBLEMS-TRADE DISCOUNT 1. When goods are sold on 60 days credit, allowing 2% discount if paid for within 10 days, how much is gained by paying a bill of $480 within 10 days? Many articles of merchandise have fixed prices which are published in catalogues and price-lists. as the list price. State orally the numbers to fill the blanks: This price is known LIST DIS- NET PRICE. COUNT. PRICE. 2. Shakespeare (Temple Edition). . $26.00 20% 4. Hawthorne's Works, 8vo. cloth. 5. Poe's Works, 6 vol., cloth. . . . 6. Cooper's Leatherstocking Tales. $2.00 15% $10.00 25% $7.50 20% 25% $3.75 30% $1.05 $4.50 8. Dickens's Works, 12 vol., cloth. $6.00 9. Kipling's Works, 15 vol. . .... $15.00 $10.00 When two or more discounts are quoted, the first discount is taken from the list price, the second discount from the price after the first discount has been taken off, and so on. Thus, if the list price is $9 and the discounts are 20%, 10%, and 5%, what is the net price? PLAN. 1. $9.00 -- $1.80 = $ 2. $7.20 $.72 = $—. 3. $6.48-$.32 = $—, net price. It was 10. A bill of goods amounted to $163 (list-price). bought at 10%, 10%, and 5%, off, and the goods were sold at 10% more than the list price. Find the percentage of profit. II. To what single discounts are the following discounts equivalent: 25% and 10%? and 25%? 40%? 10%? 5%? 12. Compare the net prices of a carriage listed at $330 sold at the following discounts: (a) 30%, 20%, and 10%; (b) 20%, 10%, and 30%; (e) 10%, 30%, and 20%; (d) 10%, 20%, and 30%. What is the similarity in these cases? |