yard, and paid for the same in wood, at $7 per cord; how much did it take? 12. What cost 96 bushels of potatoes, at 25 cents a bushel? NOTE. 25 cents is of a dollar. 13. If the sum of two numbers is 5, and their difference is 3, what are the numbers? NOTE. The sum of two numbers, added to their difference, gives twice the greater of the numbers. Because, in adding the sum and difference, the greater is added to itself, and the less subtracted from itself. In subtracting the difference from the sum, we subtract from the greater increased by the less, itself decreased by the less. This gives twice the less; once the greater in the sum, and once the less in the difference. Hence, if the sum of two numbers is 5, and their difference 3, the greater is of 5 and 3, or 4; and the less is of 5 less 3, or 1. 14. The sum of two numbers is 17, and their difference 5; what are they? 15. The sum of two numbers is 65, and their difference 19; what are they? 16. Two boys, on counting their money, found that the one had $46 more than the other, and together they had $54; how much had they each? 17. The sum of two numbers is 152, and their difference 68; what are they? 18. If 25 barrels of flour cost $1314, how much will 3 barrels cost? 19. What cost of a hogshead of molasses, at of a dollar a gallon? 20. What number, increased by 1, by, and by of itself, will amount to 39? 21. A and B undertake to travel round a circular island 20 miles in circuit, both starting from the same point, and going round in the same direction; when A has travelled 19 miles, and B 8, how far apart are they? 22. Divide $100 between A, B and C, so that B shall have $20 more than A, and C $15 less than B. 23. A man who has 60 sheep and lambs, finds that the number of the sheep, less the number of lambs, is of the flock; how many are there of each kind? 24. What part of the principal is 7 per cent. interest? 25. At what per cent. interest will $10 become $15, in 5 years? 26. The difference of two numbers is 5, and the less number is of the greater; what are the numbers? 27. When an article is sold at of its cost, what is the loss per cent.? 28. John Smith gave 9 cents a dozen for apples, and had 12 cents left; but, had he paid 12 cents a dozen, he would have spent all his money; how many apples did he buy? NOTE. - The 12 cents left was how many cents a dozen? 29. A man bought a certain number of quires of paper, at 18 cents a quire, and had 84 cents left; had he bought just as many quires at 24 cents a quire, he would have had 6 cents left; how much money had he? 30. Bought rice at 6 cents a pound, and sold it at 8 cents a pound; what per cent. was the gain? 31. A gentleman bought 15 cords of wood, oak and pine, for $55; he paid $5 a cord for the oak, and $3 a cord for the pine; how many cords were there of each, and how much did each kind cost? 32. A laborer agreed to work 30 days for $2 a day, and for every day he was idle to pay of a dollar for his board; he received $38; how many days was he idle? LESSON LXV. 1. How many yards of cambric which is of a yard wide, will be required to line 30 yards of cloth that is 12 yards wide? 2. In a certain school of the pupils study algebra, geometry, and the remainder arithmetic; what per cent. of the whole are in each of the studies named? 3.less, plus, multiplied by 1, is how many times ? 4. A dog one night killed 17 sheep, which was 53 per cent. of a flock; how many of the flock were spared? 5. If 4 bushels of wheat cost $92%, what cost of a bushel ? 6. Joseph earned $1 week for board, and carnings for clothes; at he save in 4 weeks? a day, and spent $3.50 a of the remainder of his that rate, how much can 7. If two men together can mow a field in 10 days, and one of them alone can mow it in 15 days, in what time can the other mow it? 8. The head of a fish is 9 inches long; the tail is as long as the head and half the body, and the body is as long as the head and tail both; how long is the fish? = NOTE. The head and tail the body; the head and tail the head the head + the body; then, twice the head the body-the body the body; and the length of the body = 4 times the length of the head. 9. Bought a watch, chain and key, for $125; the watch cost 5 times as much as the chain, and the key cost 95 per cent. less than the watch; what was the cost of each? 10. In what time will a given principal double itself, at 5 per cent. interest? 11. A man can dig a ditch in 3 days, and his son in 5 days; in what time can they dig it together? 12. Jason has 25 per cent. more money than Edward; what per cent. less has Edward than Jason? 13. In how long a time will $60 gain $6.30, 7 per cent. interest? at 14. How much water must be mixed with 10 gallons of brandy, worth $8 a gallon, that the mixture may be worth only $7 a gallon? 15. A and B set out to travel round a certain island which is 20 miles in circuit; A travels at the rate of 5 miles an hour, and B 7 miles an hour; how long will it take B to overtake A? 16. yard? What cost 69 yards of cloth, at 33 cents a NOTE. 33 is of 99, and 99 is 100 less 1. 17. If $100 have been borrowed at 6 per cent. interest, for 1 year, how long must $250 be loaned at the same rate per cent. to requite the favor? 18. At what per cent. interest will $30 become $60 in 12 years? 19. If you should purchase a lot of sheep, at $2.50 apiece, and should lose of the number, at what price each must you sell the rest so as neither to gain nor lose? 20. A man left of his estate to his wife, of the remainder to his son, and of the remainder to his daughter; the three legacies amounted to $900; how much was the whole estate? 21. A lady having a number of peaches, gave away of them, and of the remainder, and had 27 left; how many had she? 22. Four men rent a field for $16; A puts in 6 cows, B 8 cows, C 4 cows, and D as many cows as his paying of the rent entitles him to; what part of the rent did A, B and C each pay, and how many cows did D put in? 23. Sold a watch for $35, and thereby lost 25 per cent., when there ought to have been gained 30 per cent.; how much was it sold below its proper value? 24. Sold a cart for $30, and thereby lost 20 per cent.; at what price should it have been sold to have gained 20 per cent.? 25. If 4 horses consume 21 bushels of grain in 6 days, how many bushels will 8 horses consume in 12 days? 26. A circular garden is 3 rods in diameter; what is its circumference? NOTE. The circumference of a circle, or the distance round it, is 22, nearly, of its diameter, or the distance across it through the centre. 27. A certain circular pond is 11 miles in circumference; what is its diameter? 28. The sum of two numbers is 19, and twice the first added to 5 times the second is 74; what are the numbers? 29. Williams and Brown enter into business together; Williams puts in 4 times of what Brown does; they both put in $1680, and gain $700; what is each one's share of the gain? 30. A barrel of flour and a cord of wood cost $17, and 2 barrels of flour cost $10 more than a cord of wood; how much does each cost? 31. A hare starts 25 leaps in advance of a hound, and takes 4 leaps to the hound's 3; but 2 of the hound's leaps equal 3 of the hare's; how |