An Intellectual Arithmetic, Upon the Inductive Method

pastures 2 horses and 4 cows for 3 weeks, and B pastures 3 horses and 2 cows for 2 weeks; how many dollars shall each pay ?

4. 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 $5. B's money was in twice as long as C's, and A's twice as long as B's. They gained $38; what was each one's share of the gain?

5. A and B trade in company. A puts in $10 for 2 months, and B puts in $9 for 3 months. They lose $94; what is the loss of each?

6. A and B cut a field of grain for $42. A works 12 days, and B works 6 days. What sum should each receive, if B can do as much in 2 days as A can do in 3 days? How much does A earn per day? How much B? 7. Two men, A and B, agree to do à piece of work for $88. A employs 3 men 4 days, and B employs 5 men 2 days; what part of the pay shall each have? How many dollars?

8. A man divided $40. between his 4 sons and 3 daughters, giving each son as much as each daughter; what was the share of each?

9. Divide 15 peaches between B and C, so that B may have 3 peaches more than C.

10. The sum of 2 numbers is 21, and the greater exceeds the less by 5; what are the numbers?

11. A and B together have 40 cents, and A has 10 cents less than B; how many cents has each ?

12. David bought twice as many pears as John, and after David had eaten 6 and John 4, they together had 26; how many pears had each remaining?

13. If 2 melons are worth 12 oranges, and 8 oranges are worth 24 apples, how many apples shall I give for 3 melons?

14. If 2 oxen are worth 3 cows, and 4 cows are worth 24 sheep, what is 1 ox worth, supposing a sheep to be worth $7?

15. A hare is 7 of his own leaps before a hound, and takes 5 leaps while the hound takes 3, but 4 of the hound's leaps are equal to 7 of the hare's; how many leaps must the hound take to gain on the hare the length of one of the hare's leaps? How many leaps must the hound take to catch the hare? Solution. Since 1 of the hound's leaps is of a leap of the hare, 3 of the hound's leaps are equal to 21, or 5 of the hare's leaps; hence, in taking 3 leaps the hound gains of one leap of the hare, and therefore he must take 4 times 3 leaps, or 12 leaps, to gain 1 leap of the hare; and to gain 7 leaps, he must take 7 times 12 leaps, or 84 leaps.

16. Charlie is 10 of his own steps before John, and takes 6 steps while John takes 5, but 3 of John's steps are equal to 4 of Charlie's; how many steps must John take to gain the length of one of Charlie's steps? How many steps can Charlie take before John will

catch him?

17. A lady wishing to buy a certain number of yards of silk for a dress, finds that if she pays a dollar a yard she will have 5 dollars left; but if she pays a dollar and a half per yard, she must get trusted for 2 dollars.; how many yards does she wish to buy?

18. A man and his wife would eat a sack of flour in 15 days, and after living together for 6 days the woman alone would consume the remainder in 24 days; how many days would the whole sack last the woman? How many days the man?

19. A boy being asked how many hens he had, said that if he had half as many more and four hens and a half, he should have 3 dozen; how many hens had he?

20. A farmer, questioned with regard to the number of his sheep, said that if he had as many more, half as many more, and 2 sheep and a half, he should have 100; how many had he?

21. A boy engaged to live with a man 30 days, agree

ing to receive 3 shillings a day for every day he worked, and to pay 2 shillings a day for his board every day he played. At the end of the 30 days he received 60 shillings; how many days did he work?

22. A fish's head weighs 5 pounds, his tail weighs as much as his head added to half the weight of his body, and his body weighs as much as his head and tail together; what is the weight of the fish?

23. A and B start from towns which are 48 miles apart, and travel toward each other until they meet, when it appears that of the distance A has traveled is equal to of the distance B has traveled; how far has each traveled?

24. A purse and its contents are worth 41 shillings, and 3 of the value of the purse are equal to 1⁄2 of the value of the contents; what is the value of the purse?

25. Seven times a certain number is 15 more than 4 times the same number; what is the number;

26. What number is that to which if its half and its fourth be added, the sum will be 35 ?

27. What sum of money can I obtain at a bank for a note of $36, payable in 90 days?

28. If a 5 cent loaf weighs 24 ounces when flour is worth $6 per barrel, what ought it to weigh when flour is worth $9 per barrel?

29. A man failing in business, is able to pay only 80 per cent, of his debts; how much will he pay on a debt of $30?

30. Bought 8 lb. of honey at one time, 36 lb. at another time, 101 lb. at another, and 617 lb. at another; how many pounds did I buy at the four times?

31. A, B, and C can do a certain piece of work in 4 days. A can do of it in 1 day, and B can do 1 of it in 1 day; in how many days can C do the whole work?

32. A gentleman being asked the time of day, replied that of the time past from noon was equal to of the time to come before midnight; what was the time?