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40. If you wish to put 72 pounds of butter into 6 boxes, how many pounds will you put into each box?
41. If you put 84 pounds of butter into boxes that will hold 7 pounds apiece, how many boxes will it take?
42. A farmer bought 9 yards of cloth, at $4 a yard, and paid for it with apples, at $3 a barrel; how many barrels did it take?
43. Two boys are 45 rods apart, and both running in the same direction; the hindmost boy gains on the other 5 rods in a minute; in how many minutes will he overtake him?
44. A grocer bought 5 firkins of butter for $50, and sold them so as to gain $10; what did he pay for each firkin? What did he gain on each? What did he receive for each?
45. How many yards of cloth, at $5 a yard, may be bought for 10 reams of paper, at $2 a ream?
1. WHAT number added to twice itself gives 15? Solution. Any number plus twice the same number is 3 times that number; therefore, 15 is 3 times the required number, and of 15, viz., 5, is the number.
2. What number added to 3 times itself gives 32? 3. William and George together caught 35 fishes, and William caught 3 as often as George caught 2; how many did each boy catch?
4. Two times a certain number, added to 3 times the same number, make 35; what is the number?
5. A boy gave 35 nuts to two of his companions, giving 4 nuts to one of them as often as he gave 3 to the other; how many did he give to each?
6. What number added to
of itself gives 15?
7. A boy being asked how old he was, replied, I am half as old as my sister, and the sum of our ages is 27 years; how old was he?
8. A father gave 64 cents to his two sons, giving as many to the younger as to the older; how many cepts did he give to each?
9. A boy divided 28 peaches among 3 of his com panions, giving twice as many to the first as to the second, and twice as many to the second as to the third; how many did he give to each?
10. A boy gave 42 peaches to 3 of his companions, giving half as many to the first as to the second, and half as many to the second as to the third; how many did he give to each?
11. A and B together have 45 marbles, and A has as many as B; how many has each?
12. A man being asked how many sheep he had, replied that if he had what he then had, and } and } as many more, he should have 55; how many had he?
13. A boy having 48 apples, kept 4 of them himself and gave the rest to Reuben, David, and Samuel, giving as many to David and as many to Samuel as to Reuben; how many did he give to Reuben?
14. A merchant bought a piece of cloth, at $6 a yard, and another piece of the same length, at $2 a yard, and afterward sold the whole, at $4 a yard; did he either gain or lose by the transactions?
15. A fruiterer employed two boys, Frank and Arthur, to sell apples for him. The dealer intrusted 60 apples to each boy, and told him he might sell them at the rate of 5 apples for 2 cents, and Frank sold his as instructed; but Arthur thought he might sell his more readily if he sorted them according to their quality; so he separated them, putting 30 apples into one part of his basket, and the other 30 into another part. He sold the better lot at the rate of 2 apples .for 1 cent, and the poorer lot at the rate of 3 for 1 cent. Now, did the two boys receive equal sums for their entire stock of apples? If not, which was the more profitable to his employer? How much?
16. A'boy was asked how many chickens he had, when he replied that if he had as many more, and and as many more and 2 chickens, he should have 70; how many had he?
17. A boy being asked his age, said that if and 12242 of his age and 10 years more were added to his age, the sum would be 3 times his age; how old was he?
18. A pole 48 feet long has one third as much in the mud as in the water, and twice as much in the air as in the mud and water together; how many feet were there in the water?
19. Suppose that A lends money at 6 per cent., interest payable in bank bills, and that B buys 6 per cent. government bonds, at 20 per cent. premium, which makes the best investment if the bonds are payable in paper in 20 years and the interest on the bonds payable in gold annually, gold being at 50 per cent. premium? Why?
20. Which is the more profitable, to lend money at per cent., or to buy 5 per cent. government bonds, at 10 per cent. premium, the. other conditions being the same as in example 19?
1. DIVIDE 32 into two such parts that the less part shall have the same relation to the greater that 3 has to 5.
Solution. 3 and 5 are 8; therefore, if 32 is divided into 8 equal parts, 3 of those parts will be the less of the two required numbers, and 5 of them will be the greater. 3 times of 32 are 12, the less part, and 5 times of 32 are 20, the greater part.
NOTE. This is usually called Ratio. The ratio of 3 to 5 is⚫ , and the ratio of 12 to 20 is 1, which can be reduced to 3.
2. Two boys bought a melon for 40 cents, and cut
it into 5 equal parts. and the other took 2;
One boy took 3 or the parts, what ought each to pay?
3. Two men hire a pasture for $60. One man keeps 5 cows in the pasture through the summer, and the other keeps 7; how much ought each to pay?
4. Two boys engage to cut a pile of wood for $33. One boy cuts 6 cords while the other cuts 5; how should the pay be divided?
5. Two men engage in trade. One furnishes $7000 and the other $5000, and in a year they gain $2400; how should the profits be divided?
6. A, B, and C hire a pasture for $100. A pastures 3 cows, B 8, and C 9; how many dollars ought each to pay?
7. David, Samuel, and John buy 80 marbles for 20 cents; David takes 1 marble as often as Samuel takes 4, and John 5; how many does each take? What shall each pay?
8. A and B trade in company, furnishing money in the ratio of $4 to $5. They gain $2700; what is the share of each?
9. Two travelers, 54 miles apart, approach each other, one at the rate of 4 miles an hour, and the other at the rate of 5 miles an hour; how far will each travel before they meet?
10. A gentleman gave 28 pears to some children; to each girl 4, and to each boy 3. There were as many boys as girls; how many pears did he give to all the boys? To all the girls?
11. Sarah had 12 cents, and Nancy had 18 cents; they paid all their money for 10 oranges; how many oranges ought each to receive?
12. A, B, and C traded in company. A put in. $2 as often as B put in $3, and as often as C put in $4. They gained $63; what was the share of each?
13. A man failing in business, has property valued at $900; but he owes to A $300, to B $400, and to C
$500; what part of his debts can he pay? How many dollars to each creditor?
14. Addie and Georgie together solved 60 examples, and Addie solved as many as Georgie; how many did each solve?
15. The sum of the ages of William and James is 36 years, and James is as old as William; what is the age of each?
16. Divide $24 between A and B, giving to A $1 as often asof a dollar to B.
17. Edward had a certain number of cents, and found as many more, when he had 32 cents; how many cents will he have left after spending of what 33 he found?
18. Three men, A, B, and C, traded in company. A put in $2 as often as B put in $3, and C put in such a sum that he received $36 of the $66 gained in the year; what was the share of the gain received by A and B, and how many dollars did C furnish as often as A furnished $2?
1. A AND B traded in company. A put in $10 for 2 months, and B put in $8 for 3 months. They gain $88; what is each one's share of the gain?
Solution. A's $10 for 2 months are the same as $20 for 1 month, and B's 8 for 3 months are the same as $24 for 1 month; therefore, the total capital may be considered $44, and A's share is 24 or 1, and B's share is or; of $88 is $40, A's share of the gain, and fr of $88 is $48, B's share.
2. A and B hire a pasture for $11. A pastures 2 horses for 5 weeks, and B pastures 3 horses for 4 weeks; what is each one's share of the expense?
3. Two men, A and B, hire a pasture for $10, and agree that 2 cows shall be reckoned as 1 horse. A