? 16% ? $10.35 2500 cd. ? ? 365 da. $16,200 $10,800 ? 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 5760 gr. 7000 gr. ? 91 ? ? ? ? ? 328285 ? ? ? 872 ? ? ? 을 8 gt. 24 111 300 196 lb. ? ? ? ? 10,318 $29.24 ? 11 17 18 19 20 21 371 1 bu. ? ? 2 645 REVIEW PROBLEMS. 1. If a merchant sells of an article for what of it cost, what is his gain per cent.? Suggestion : Find the value of P. and use Formula 2. 2. If I buy a farm for $5950, for what must I sell it to gain 5%? Suggestion: Use Formula 4. 3. I received for my horse $164, and thereby lost 18% of his value? What was his value ? ? 4. If I buy boots at $3.25 a pair and sell them at $3.871 a pair, what per cent. do I gain ? 5. In a school, 77 pupils are present, which is 871% of the number enrolled. Find the number enrolled. 6. & is % of what number? 7. A man sold flour at $11 per bbl., by which he gained 371% of the cost. He raised the price to $13.50. What does he gain per cent. by this advance ? 8. If the bread made from a barrel of flour weighs 331% more than the flour, what is the weight of the bread ? 9. A regiment lost in a campaign 400 men out of 965. What was the rate per cent. of loss ? 10. I shall be obliged to use to-day 533% of my money to pay a note for $8620. How much money have I ? 11. In a certain school, during 1895, the attendance of pupils was 824, which was 3% more than in 1894. What was the attendance in 1894? 12. In 1897 I gained in business $9207, which was 7% less than I gained in 1896. How much did I gain in 1896 ? 13. In a mixture of copper and zinc, the copper is 11 times the zinc. Find the percentage of each ingredient in the mixture. 14. What per cent. of a pound troy is a pound avoirdupois ? 15. A piece of land is bought for $3600, and a man who owns of it sells į of his share for $800. What rate per cent. does he gain? COMMERCIAL DISCOUNT. 1. Commercial Discount means deduction from the price of merchandise or from the amount of a bil, and is computed at some rate per cent. 2. When two or more discounts are allowed, the first is counted off, and the second from the remainder, and so on. 3. (1.) The Price or Bill is the Base. (2.) The Rate per cent. is the Rate. (3.) The Discount is the Percentage. (4.) The Price or Bill - the Discount = the Net Price or Net Amount the Difference. Hence formulæ 1 and 5 on page 218 become : : 1. Discount= Price or Bill X Rate. 2. Net Price or Net Amount Price or Bill x (1 – R.). = PROBLEMS. 1. What is the net amount of a bill of $500 discounted at 20%? By Formulæ. x = $500 X (1 — .20)= $500 x .80 = $400. By Analysis. Brief Process. 20% = 5/500 t of $500 = $100. 100 $500 – $100 = $400. 1400 2. What is the net amount of a bill of $500 with 33} and 121 off ? Analysis. Brief Process. 331% = }; 121% = }; ; 3,500.00 3 of $500 = $166.663 ; 166.663 $500 – $166.663 = $333.33}; 8 333.33} of $333.33} = $41.663 ; 41.663 $333.33} -$41.663 = $288.663. 288.663 = 3. A bicycle marked $90 was sold at a discount of 121%. Find the discount and selling price. 4. An agent sold a book, price $5.50, at 20% discount. What did he get for it? 5. A piano was marked $650, but was sold at a discount of 20 and 8. Find the selling price. 6. Is 50 off $2000 the same as 25 and 25 off ? Find the difference, if any. 7. A merchant bought $850 worth of goods and received 25 and 10 off. What was the net amount of his bill ? 8. What is the cash value of a bill of goods amounting to $2157.25 at 15 and 3 off? 9. Valentines marked $18 were sold at 20, 15, and 5 off. What was the selling price ? 10. A bill of goods amounted to $3268.36. What was the net value if 15 and 3 were counted off ? 11. A bill of envelopes amounted to $86.40. On a credit of 30 da. the reduction was à and 5 off; for cash 21 off. With all rates off, what was paid ? 12. Find the net amount of a bill for $762 subject to the following discounts : 40, 5, and 10. 13. What is the discount on a bill of goods, if 20%, 15%, and 5% are successively made? 14. Find the net cost of 20,000 bags at $4.50 per M., with 60, 10, and 5 off. 15. Which is the better discount for the buyer, 40 and 10 off, or 30 and 20 off ? 16. After getting 25% off, a book cost me $4.50. What was the mark price of the book ? 17. What single discount is equal to the following double discounts ? 1. 30 and 10%. 3. 50, 5, and 5%. 18. What must a merchant ask for an article which cost $40, so that he may deduct 20% and still gain 10% ? 19. A bill of $670 is subject to the following discounts: 20, 15, 10, 5. Find the net amount of the bill. 20. What must I ask for an article that cost me $3.60, so that I may deduct 121% and still make a profit of 16% % ? GAIN AND LOSS. 1. Gain or Loss in business is computed at some rate per cent. of the cost. 2. (1.) The Cost is the Base. (2.) The Rate per cent. is the Rate. (3.) The Gain or Loss is the Percentage. (4.) The Selling Price (Cost + Gain) is the Amount. (5.) The Selling Price (Cost — Loss) is the Difference. 3. Hence the formulæ on page 218 become: NOTE.—Let the pupil derive formulæ for S. P. from formulæ 4 and 5. EXERCISES. 1. I bought corn at 40 cents a bushel, and sold it at a gain of 121%. How much did I get for it? By Formula. By Analysis. 12% = G.= C. X R. 121% : &, cost, + , g G. = 40 X = 5. š 5 gain, = f, selling price. 40 + 5 = 45, selling 5 p=40; } 5; g = 45, price. selling price. 2. I bought sugar at 5 cts. per pound, and sold it at 51 cts. per pound. What was my gain per cent. ? 8 |