his real value, and sold him to B for 25 per cent. more than his value: how much per cent. did A make on his purchase? How much per cent. would B lose were he to sell the horse for the same price that A gave?

20. A lady has 2 silver cups, and but one cover for both; the cover weighs 10 ounces; now, if the cover be put on the first cup, it will make the weight double that of the second, and if the cover be put on the second, it will make the weight triple that of the first: what is the weight of each?

21. There is a bin containing 30 bushels of wheat; if I take from it 10 bushels and add 10 bushels of rye, then take away 10 bushels of the mixture and add 10 bushels more of rye, then take away 10 bushels of this mixture and add 10 more of rye, supposing the wheat and rye to have been thoroughly mixed each time, how many bushels of wheat, and how many of rye would the bin contain?

22. If I should each time add the 10 bushels of rye before taking out the 10 bushels of the mixture, and perform the operation three times, as in the last example, how many bushels of each would remain in the bin?

23. If a merchant purchases goods for cash to the amount of $500, when money is worth 2 per cent. a month, what sum will he gain by selling the goods at the end of 4 months, but on 3 months' credit, at an advance of 20 per cent. upon the cost?

24. A father said to his son, "4 years ago I was 3 times as old as you, but 8 years hence I shall be 2 times as old as you"; what was the age of each ?

25. A gentleman let of his money at 5 per cent., and the remainder at 6 per cent.; the interest amounted to $90; what were the sums let?

26. In 1854 James was 10 times as old as William, but in 1862 he was only twice as old; how old is each of them the present year?

27. A has 50 per cent. more property than B, and B has 50 per cent. more than C; how much per cent. more has A than C? How much per cent. less has C than A?

28. A man, being asked the time of day, answered that of the time past midnight was equal to of the time past noon; what was the hour?

29. If you divide $27.50 between A and B, giving A $2 as often as you give B $63, how much will each receive?

30. A cistern has 3 pipes; the first will fill it in 1 hours, the second will fill it in 2 hours, and the third will empty it in 14 hours; if the pipes are all open at the same time, how long will it take to fill the cistern?

31. If an army march 150 miles in 7 days, by marching 8 hours a day, how far should it march in 5 days, by marching 10 hours a day?

32. The sum of two numbers is 5%, and their difference 1; what are they?

33. After spending of my money, I found if I had spent $13 less, I should have spent just my money; how much did I have?

of

34. A grocer has two kinds of tea, one of which is worth 40 cents a pound, and the other 50 cents a pound; how many pounds of each must be taken to form a chest of 40 pounds, which shall be worth 44 cents a pound?

35. The sum of three numbers is 18, the sum of the first and second is equal to the third, and half the sum of the first and third is equal to the second; what are the numbers?

36. A farmer employed 3 men and 3 boys one

day for $5, and another day, at the same wages, 4 men and 6 boys for $8; what was the daily wages of each?

37. What number is that to which if 3 and 14 be separately added, the first sum will be second?

of the

38. Three men, A, B, and C, each have a sum of money in their pockets; A has $ 3, A and C together have 3 times as much as B, and B and C together have 11 times as much as A; how much have B and C, respectively?

39. Smith, Jones, and Brown each have a sum of money at interest at 5 per cent., and these sums are to each other as,, and, respectively; the annual income of the three sums taken together is $90; what is the principal that each one has at interest?

40. Three men hired a pasture for $76; at first A put in 4 horses and 8 cows, B 6 horses and 12 sheep; afterwards, when the grass was half eaten up, C put in 24 sheep; now, supposing every horse eats, in a given time, as much as 4 sheep, and every cow as much as 3 sheep, what ought each man to pay?

41. Robinson, Savage, and Harrison agree together to do a piece of work; they are to receive for it $200, to be divided in the proportion of 5, 4, and 3, respectively, for the same amount of work; but Robinson, whose labor is worth most, is absent of the time, and Harrison, whose labor is worth least, is absent of the time; how should the money be justly divided among them?

APPENDIX.

EXERCISES INVOLVING LARGE NUMBERS.

LESSON LV.

This and the following Lessons are intended only for advanced classes, and may be omitted at the option of the teacher.

1. What is the sum of 38 and 46?

SOLUTION. 38 is 3 tens and 8; 46 is 4 tens and 6; 38 and 46 are then 3 tens and 4 tens, or 7 tens, and 8 and 6, or 14; 14 is 1 ten and 4; therefore 38 and 46 are 7 tens and 1 ten and 4, which are 8 tens and 4, or 84.

2. What is the sum of 23 and 25?
3. What is the sum of 57 and 34?
4. How many are 37 and 39?
5. How many are 51 and 27?
6. How many are 68 and 54?

NOTE.

62

29 and 33?

76 and 18 ?

and 28 ? 26 and 67 ?

6 tens and 5 tens are 11 tens; 8 and 4 are 12, or 1 ten and 2; 11 tens and 1 ten and 2 are 12 tens and 2 or 122.

7. How many are 66 and 67? 8. How many are 93 and 14? 9. How many are 83 and 36? 10. How many are 95 and 21? 11. How many are 54 and 13? 12. How many are 84 and 74? 13. How many are 13 and 63? 14. How many are 98 and 22? 15. How many are 53 and 63?

58 and 45? 56 and 65? 68 and 12? 70 and 25 ? 28 and 42? 21 and 62? 45 and 15? 36 and 43? 75 and 26?

How many are

47 and 38?

75 and

22?

22.

How many are 23. How many are 95 and 16? 24. How many are 101 and 17? 25. How many are 203 and 37? 26. How many are 180 and 25? 27. How many are 68 and 34?

309 and

27 and 126?

28. How many are 58 and 95? 137 and 101? 29. How many are 154 and 44? 106 and 94? 30. How many are 130 and 67? 219 and 31?

54 and 68?

90?

2.

LESSON LVI.

1. How many are 60, 17, and 2? How many are 25, 72, and 3? 3. How many are 44, 32, and 7? 4. How many are 13, 45, and 61? 5. How many are 57, 6, and 43? 6. How many are 16, 93, and 12? 7. How many are 99, 40, and 5? 8. How many are 70, 56, and 8? 9. How many are 20, 50, and 13? 10. How many are 27, 38, and 30? 11. How many are 50, 41, and 11? 12. How many are 15, 27, and 70 ? 13. What is the sum of 19, 75, and 15? 14. What is the sum of 68, 49, and 1? 15. What is the sum of 60, 35, 6, and 5? 16. How many are 50, 40, 7, and 3? 17. How many are 65, 25, 10, and 7?