Solution. 6 times; for 2 equals §, and is contained in just as many times as 1 apple is contained in 6 apples, or as 1 is contained in 6. 3. How many times in 2? Solution. 3 times; for is contained in just as many times as 2 in 6. Or, since is contained 6 times in is contained of 6 times, viz., 3 times, in §. 4. A boy having 3 oranges, gave of an orange apiece to several of his companions; to how many could he give them? 5. How many times in 3? 3 in 3? 6. If of a pound of butter will last a family 1 day, how many days will 4 pounds last the same fimily? How many days will 6 pounds last? 7 pounds? 7. How many times in 4? In 6? In 7? 8. If of a barrel of apples will supply a family for a week, for how many weeks will 6 barrels supply the same family? For how many weeks will 6 barrels supply them, if they use of a barrel a week? If they use? ?? ? 9. In 6 how many times 10. If a family consumes of a barrel of flour in a month, how long will 33 barrels last them? 93 barrels? 81? 11. How many times 3 in 33? In 93? 81? 12. How long will 9 pounds of butter last a family, if they use 1 pounds per week? 13. How many times 1, or in 9? 14. How many soldiers will 83 pounds of bread supply, if each soldier is allowed 13 pounds? 15. In 83 how many times 13? 16. How many garments will 20 yards of cloth make, if each garment requires 24 yards? 17. In 201 how many times 24 ? 18. When raisins cost of a dollar a pound, how many pounds can you buy for 3 of a dollar? 19 How many times is contained in ? equals 11⁄2; † times. of a dollar a Solution. are the same as, and in 1, 4 times; therefore, & in 3, 4 20. When cream of tartar costs pound, how many pounds may be bought for $1? How many for $23? 21. How many times in 1? In 23? 22. At of a dollar per pound, how many pounds of tea can I buy for $24? For $34? 23. How many times in 2? In 34? 24. If coffee costs of a dollar a pound, how many pounds may be bought for $1? For $2%? 25. How many times in 13? In 23? 26. At $1 per bushel, how much wheat can I buy for $34? For $51? 27. How many times 1 in 34? In 5? 1st Ans. 11 = 4; 31 = 13; 13÷§=13=27. 28. At $24 a box, how many boxes of raisins can you buy for $63? For $93? 29. How many times 24 in 63? In 93? 30. At 8 cents a pound, how many pounds of sugar can I buy for 12 cents? For 334 cents ? 31. How many times 83 in 121? 32. How many times 61 in 37? In 334? In 871? 34. If 3 barrels of flour cost $20%, what will 63 barrels cost? Suggestion. 6 is twice 3%. 35. If 5 barrels of apples cost $114, what will 283 barrels cost? 36. If 23 acres of land are worth $26, what are 10% acres worth? 57. If 7 acres of land cost $288, what will 53 acres cost? Suggestion. 73 in 288, 4 times. 38. If 23 pounds of veal cost 242 cents, what will 5 pounds cost? 10 pounds? 21 pounds? 7} pounds? SECTION EIGHTH. LESSON I. REMARKS. 1. Per centum, or per cent., is an expression which means by the hundred; thus, 5 per cent. of any number is 150 or of that number; 25 per cent. is or; 3 per cent. is 18, etc. 2. Gains and losses, interest on money, commissions of agents, increase or decrease of population, etc., are usually computed at some given per cent. on the sum or number considered. 3. The following rates, being readily reduced to convenient fractional forms, are easily computed : 2 per cent. is 4 5 66 12 per cent. is 2616 66 1 16 1.333 To 50 Ex. 1. A farmer having 80 sheep, lost 25 per cent. of them; how many sheep did he lose? Solution. He lost or of his flock; 4 of 80 is 20; therefore, he lost 20 sheep. 2. The number of inhabitants in the town of B on the 1st of May, 1860, was 2500; in a year the population increased 20 per cent.; what was the increase of population in the year? What was the population of B on the 1st of May, 1861 ? 3. An agent sells $500 worth of goods for his employer, and receives a commission, or compensation, of 4 per cent. for transacting the business; how many dollars does he receive for his services? How many dollars does he pay over to his employer? 4. In one town in Wisconsin 16000 bushels of wheat grew in 1863; what will be the number of bushels in 1864, if there shall be a decrease of 12 per cent.? 5. A physician having bills against his patients to the amount of $72, paid 163 per cent. for their collection; what did the agent receive for collecting the money? What did he pay over to the physician? 6. Suppose the number of deaths in New York dur ing the 1st week of March was 500, and that the decrease during the 1st week of June was 10 per cent.; how many less deaths were there in the city during the latter week? What was the number of deaths during the latter week? 7. The American Insurance Company has insured $4000 on my house, at a premium of 2 per cent.; what is the premium, or sum paid for the insurance? 8. What is 64 per cent. of $64 ? 9. What is 333 per cent. of 45 bushels of corn? 10. What is 5 per cent. of 80 peaches? 11. What is 83 per cent. of 48 boys? 12. What is 50 per cent. of 36 horses? 13. A physician having bills against his patients to the amount of $80, paid $20 for collecting them; what per cent. did he pay? Solution. $80 is 100 per cent., or the whole sum collected, and $20 is 8 or 4 of the whole sum; of 100 per cent. is 25 per cent.; therefore, etc. 14. In a lot of 60 barrels of apples, 12 barrels are spoiled and the rest are good; what per cent. of them are spoiled? What per cent. are good? 15. From a cask of 63 gallons of molasses, a grocer has drawn 21 gallons; what per cent. of the molasses has he drawn out? What per cent. of it remains in? 16. What per cent. do I gain by buying hats at $4, and selling them at $5, apiece? 17. What per cent. do I lose by buying hats at $5, and selling them at $1, apiece? 18. Twenty is what per cent. of 50? 19. A gentleman invested of his money in land; what per cent. of it did he so invest ? Solution. The whole of any thing is 100 per cent. of it; hence of the thing is of 100 per cent., which is 40 per cent.; therefore, etc. 20. A man saved of his income, and spent the rest; what per cent. of it did he save? What per cent. did he spend? 9> { 21. Three fourths of a number is what percent. of it? >5 22. Seven eighths of a number is what per cent. of it? 23. Five sixths of a number is what per cent. of it? 24. At 5 per cent., what sum can be insured on a ship bound from Boston to San Francisco, for a premium of $60 ? Solution. Since 5 per cent. is 180 or 2 of the sum insured, the premium, $60, is of the sum insured; $60 is of $1200; therefore, etc. 25. At 2 per cent., what sum can be insured on a house for a premium of $50? 26. $24 is 163 per cent. of what sum ? 27. Seven oranges are 25 per cent. of what? 28. In 1863, a farmer raised 63 bushels of corn on an acre. This was an increase of 12 per cent. on the previous year's crop; how many bushels did he raise on the acre in 1862 ? Solution. Since the increase was 12 per cent., or, of the crop, 63 bushels is of the crop; 63 bushels is of 56 bushels; therefore, the crop of 1862 was 56 bushels to the acre. 29. A grocer sold tea at 50 cents per pound, and thereby gained 25 per cent. on the cost; what was the cost per pound? 30. A grocer sold tea at 45 cents per pound, and thereby lost 25 per cent. on the cost; what was the cost per pound? 31. A merchant sends his agent $42, from which he is to take a commission and expend the rest for coffee. The agent's commission being 5 per cent. on the purchase, what sum will he have to expend? |