17. I bought 4 pairs of shoes at $3.75 a pair, 2 pairs of boots at $6.50 a pair, and 3 hats at $2.75 each, and gave the merchant a fifty-dollar bill. How much change did I get?

18. A man earns $60 a week, and spends $28 a week. How much does he save in 12 weeks?

19. Bought 13 cows at $26 each, 9 horses at $125 each, and 100 sheep at $3.75 each, and sold all for $1750. How much did I lose?

20. Two ships, 2500 miles apart, are sailing towards each other, one at the rate of 87 miles a day, and the other at the rate of 85 miles a day. How far apart will they be at the end of 13 days?

21. Two steamships start from New York to Liverpool, one at the rate of 156 miles a day, the other at the rate of 217 miles a day. How far apart will they be at the end of 9 days?

22. Mr. L. had $100. He bought a suit of clothes for $22, a hat for $3, a pair of shoes for $4, and 4 shirts at $1.75 each. How many books at $1.60 apiece can he get for the remainder of his money?

23. How many men, at a salary of $600 a year, will earn $585,000 in a year?

24. It requires 7,020,000 bricks to build a large foundry. How many teams will it require to draw the bricks in 60 days, if each team draws 6 loads per day and 1500 bricks at a load?

25. From a cistern containing 12,572 gallons of water, 9236 gallons were drawn out, and afterwards, during a rainstorm, 7250 gallons ran in. How much water was there then

in the cistern?

26. I bought a farm of 163 acres at $95 an acre. down $2500, and gave bank-stock valued at $9000. much remained unpaid?

I paid
How

27. A certain cistern holds 11,200 gallons of water. When empty, how many barrels of water, each containing 31 gallons, will it take to fill it?

28. A dairy-man has fodder enough to keep 28 cows 4 months. If he sells 12 cows, how many months will the fodder last the rest?

29. If the difference between two numbers is 1320, and the smaller number is 1750, what is the larger number?

30. The sum of two numbers is 3680, and one of the numbers is 1976. What is the other number?

31. The larger of two numbers is 2560, and their difference is 1177. What is the smaller number?

32. What is the product of 14,625 and 12,349?

33. If the product of two numbers is 7,715,962, and one* of the numbers is 2566, what is the other number?

Did I

34. I paid $36 an acre for 50 acres of wood-land. I sold the wood for $1576, and the land for $17 an acre. gain or lose, and how much?

35. I bought a stock of goods for $12,650, paying $1650 cash, and the balance in monthly payments of $1100 each. How many monthly payments did I make?

36. Twenty-four ladies and 18 gentlemen went on an excursion, and their expenses, which were $1.50 each, were paid by the gentlemen. How much did each gentleman pay?

37. A young man worked a year at $35 a month. He paid $16 a month for his board, and his other expenses amounted to $96. How much money did he save?

38. A stationer paid $95 for gold pens, at $1.90 apiece. How many pens did he buy?

39. Find the cost of 118 pounds of ham, at $.11 a pound; and 227 pounds of bacon, at $.09 a pound.

40. A farmer's wheat crop yielded him $565, his corn $362, his oats $175, and his clover seed $57. He paid a farm hand $18 a month for 9 months, $225 for fertilizers, and $195.85 for repairs and other expenses. How much did he gain on his farm?

41. Mr. D. invested $3000 in business. The first year he gained $560, and the second year he lost $475. The next three years his average yearly gain was $843. How much was he worth at the end of the five years ?

42. A mechanic receives $1200 a year for his labor, and his expenses are $576. In how many years can he save enough to buy 52 acres of land at $72 an acre?

43. A man paid $450 for a horse and a buggy, the horse being valued at $90 more than the buggy. What did he pay for each?

44. I sold a quantity of wood that cost $920 for $1265, thus gaining $3 a cord. How many cords were there ?

45. B bought 30 cows for $1400; but 5 of them died. How much must he receive for each of the rest to incur no loss?

46. A farmer sells 125 acres of land for $85 an acre, and 75 acres of other land at $115 an acre. He invests all the money in another farm that costs him $175 an acre. How many acres are there in the farm ?

47. Light travels at the rate of about 186,000 miles a second. How many seconds does it take to reach us from the sun, a distance of about 95,000,000 miles?

FACTORS.

98. 1. What is the product when 7 is multiplied by 5? What are the numbers 7 and 5 of their product?

2. What numbers multiplied one by the other will produce 63? What are the numbers 7 and 9 of 63 ?

3. What are the factors of a number?

4. Name the factors of the following numbers: 20, 36, 45, 48, 60, 35, 72, 50, 21, 40, 24, 32, 64, 81, 80, 56, 44.

5. What numbers will exactly divide 48? 40? 80? 81? 6. Since 6 exactly divides 48, what part of 48 may it be called?

7. Give the exact divisors of the following numbers: 40, 81, 56, 42, 64, 32, 24, 50, 72, 35, 36, 45, 48, 60.

8. What numbers between 0 and 20 have no exact divisors except themselves and 1? What name is given to such numbers? Prime Numbers.

9. What are the prime numbers between 20 and 40?

10. What numbers between 0 and 40 have exact divisors besides themselves and 1? What name is given to such numbers? Composite Numbers.

11. Select from the following numbers, first, the prime numbers; secondly, the composite numbers: 13, 15, 21, 18, 27,

23, 17, 40, 41, 37, 25, 19, 42, 47, 43, 20, 14, 28, 36, 35, 33, 48, 49, 50, 51, 53, 72, 86, 66, 54, 80, 44, 71, 55, 63, 65, 67, 77, 84, 81, 83, 61, 73, 88, 87, 99, 93, 92, 97.

99. A number that expresses whole units is called an Integer or Integral Number.

Thus, 18, 25, 30, etc., are integers or integral numbers.

100. The integers which multiplied by one another will produce a number are called the Factors of the number.

Thus, 7 and 5 are the factors of 35.

101. An integer that will divide a number without having a remainder is called an Exact Divisor of the number.

Thus, 2, 3, 4, and 6 are exact divisors of 12.

The factors of a number are exact divisors of it.

102. A number that has no exact divisor except itself and 1 is called a Prime Number.

Thus, 1, 3, 5, 7, 11, 13, etc., are prime numbers.

103. A number that has exact divisors besides itself and 1 is called a Composite Number. Hence, a composite number is always the product of two or more factors.

Thus, 12, 18, 21, 40, etc., are composite numbers.

104. A number that is exactly divisible by 2 is called an Even Number.

Thus, 10, 12, 16, 18, etc., are even numbers.

105. A number that is not exactly divisible by 2 is called an Odd Number.

Thus, 3, 5, 9, 11, 13, etc., are odd numbers.