SECTION 62.-1. Three fifths of the persons at a certain meeting were ladies. If there were 96 gentlemen present, how many ladies were at the meeting? 2. If § of $120 is 4 times the cost of my coat, and my vest costs as much as my coat, what is the cost of both coat and vest? 3. If from a certain number increased by 7 you subtract 3, and multiply the remainder by of 20, the product is 80; what is the number? 4. P is worth $3600; and 1⁄2 of this sum is twice the value of Q's property. How much is Q worth? 5. of Oscar's age is 8 years less than of Lucy's, and in 5 years Lucy will be 32; how old is Oscar? 6. of the men in a regiment were killed, wounded, and captured; 300 escaped uninjured. Of how many was the regiment composed? 7. F's property consists of a house, land, and stock. His house is worth of the whole, his stock, and his land is worth $400. What is his whole property worth? What is his house worth? His stock? 8. James is 18 years old, and of his age is of half his brother's age; how old is his brother? 9. A is three score years and ten. If of B's age is of C's, and of C's is of A's, how old is B? 10. If to of the number of sheep in a certain flock you add 70, you will double their number; how many sheep are in the flock? MODEL. 70 sheep equal the difference between of the flock and twice the flock, or 0.10-3=3. If 70 sheep are seven fifths of the flock, one fifth is 4 of 70, or 10; and five fifths, or the whole flock, are 5 times 10, or 50. Ans. 50 sheep. 11. John, having lost all but of his marbles, won 48 more, and by so doing doubled his original number. How many had he at first? 12. A person, having lost of his chickens, bought 76 more, and then found that he had three times as many as at first; how many was that? 13. Grace is now the age of Blanch; were she 5 years older, she would be half Blanch's age. What is the age of each? 14. Hugh spent the rest for cherries. of his money for a melon, and If the melon cost 20c., and the cherries were 6 for a cent, how many cherries did he buy? 15. From a liberty-pole 24 feet high, & of the whole, less 5 feet, was sawed off; how many feet were left standing? SECTION 63.—1. A pole increased by of its own length would be 12 ft. long; what is its length? MODEL. The length of the pole, being of itself, when increased by of itself, must be g of itself, and this we are told equals 12 ft. If six fifths of the length are 12 ft., one fifth is of 12 ft., or 2 ft.; and five fifths, or the whole length, are 5 times 2 ft., or 10 ft. Ans. 10 ft. 2. A horse was sold at a profit of of its cost. It brought $112; what was the cost? 3. A horse was sold for of its cost, and thereby a loss of $16 was incurred; what was it sold for? 4. A horse was sold for 24 times its cost, and a profit of $125 was thereby realized. What did the horse cost? 5. When to a lot of iron are added two other lots, and as heavy as the first, the whole weighs 106 lb. What was the weight of the first lot? 6. Twice A's age, increased by of his age, is 56 years; how old is A? 7. After losing $200 and giving away $450, a person found that he had of his property left. much was his property worth? How 8. One tenth of a farmer's sheep died, and were sold. On buying as many more as then remained, he had 28; what number had he originally? 9. After selling of his coal, and then of the remainder, a coal-dealer found that he had 20 tons left. How many tons had he at first? 10. A library having taken fire, of the books were burned, of what remained stolen, and only 750 saved. How many books were in the library? 11. A farmer sent of his grain to market. ‡ af the grain sent was corn; the rest, 396 bushels, was wheat. How much grain had he left? 12. of the cost of some furniture, increased by $50, equals the selling price. If there was a profit of $10, what did the furniture cost? 13. If from of a certain number you subtract 6, the remainder is 50; what is the number? 14. If to of a certain number you add 41, the sum is 54; what is the number? 15. What number is that, § of which increased by 13 is 273 ? 16. What number is that, of which divided by 6 is 31? SECTION 64.-Fractions having a common denominator are to each other as their numerators. to as 4 is to 5. is Fractions that have not a common denominator may be reduced to other fractions that have, and are to each other as the numerators of the latter. is to as 8 is to 9, since = and 1=1% 1. is to as what two numbers? 2. 3. 4. is to is to 5. is to as what two numbers ? as what two numbers ? 6. If an estate is divided into two shares that are to each other as 4 to 3, what parts of the estate will these shares be? MODEL. To find shares that are to each other as 4 to 3, we divide the whole into 4+3 equal parts (that is, into 7 equal parts, or sevenths), and take four of these (#) for the first, and five (4) for the second. Ans. and . 7. If we divide a number into two parts that are to each other as 3 to 7, what fractions of the number are these parts ? 8. Three partners, A, B, and C, agree that A shall have $3 of their profits to B's $2 and C's $1. What part of the profits must each receive? 9. Suppose that these partners make $600, how many dollars should each receive? 10. To divide a number into parts that are to each other as 6 to 9, what fractions of it must we take? 11. Divide 45 into two parts that are to each other as 6 to 9. 12. To divide a number into three parts that are to each other as 2, 3, and 4, what fractions of the number must we take ? 13. Divide 72 into three parts that are to each other as 2, 3, and 4. 14. To divide a number into parts that are to each other as and, what fractions of it must we take ? 15. Divide 19 into two parts that shall be to each as and §. 16. Two numbers, making up 28, are to each other as 5 and 9; what are the numbers ? 17. Divide 60 into three parts that shall be to each other as 2, 5, and 3. 18. A and B enter into a speculation, A contributing $200 and B $300. The profit is $140; divide it between them in proportion to the sums contributed. 19. Two boats, leaving places 100 miles apart, sail toward each other, one at the rate of 12 miles an hour, and the other 8. By the time they meet, how many miles has each gone? 20. Three partners divide their profits according to the money they put in. The first put in $1000, the second $3000, the third $4000. Their profit for a year being $2800, how much should each have? 21. A man has $500 to divide between three creditors, to whom he owes respectively $1000, $1500, and $2500. They are to be paid in proportion to their claims; how much should each receive? 22. A, B, C, and D, hire a pasture for $18. A turns in 4 cows, B 6, C 3, and D 5; how much should each pay? |