53. In 100 years the population of the United States increased from 3,929,250 to 62,622,250.

average yearly increase?

54. A train runs 350 miles in 11 hours.

What was the

Twenty stops

of 3 minutes each are made. Find the train's average rate an hour while running.

55. Find the cost of 250 tierces of lard, each weighing 340 pounds, at 7 a pound.

56. A produce buyer paid $135 for 3 car loads of melons. At that rate, how much do 10 car loads cost?

57. A farmer bought 160 acres of land at $40 an acre. After spending $600 for improvements, he sold it at a gain of $520. At what price an acre did he sell?

58. If a train runs 36 miles an hour, in how many hours can it run to a place 144 miles distant and return, allowing 1 hour for time lost at the terminus?

59. A farmer owing $790, gave in part payment 250 bushels of wheat at $1 a bushel, and paid the remainder with flour at $6 a barrel.

were required?

How many barrels of flour

60. I have an income of $1800, and my expenses during the year are as follows: rent $300, food $400, service $150, fuel $75, light $20, repairing and replenishing $40, clothing $200, insurance $100, emergency $35, church and charity $50, literature and travel $130. What is my yearly saving?

61. The contractor's bid for building a dwelling house was as follows: excavation $40, foundation and masonry $115.20, brick work and plastering $400, cement floor $35, lumber $800, mill work $175.50, hardware $60, painting $110, plumbing and tinning $260, doors and sash $160, heating $150, labor $680. What was the total bid?

65. The picture gives a good idea of the ordinary farm as laid out into fields for various purposes. The problems which follow show the immense value of our farms as sources of national wealth.

1. In a recent year the yield in bushels of certain leading agricultural products was as follows: corn, 2,030,000,000; oats, 811,000,000; wheat, 632,000,000; potatoes, 273,000,000; apples, 176,000,000; barley, 85,000,000; rye, 27,000,000; buckwheat, 12,000,000. What was the total number of bushels produced? What was the value of the wheat at 75¢ a bushel? If the yield of wheat averaged 16 bu. an acre, how many acres were in wheat?

2. The value of the corn crop in the five greatest corn-producing states in 1900 was as follows: Illinois, $115,000,000; Iowa, $97,000,000; Missouri, $61,000,000; Kansas, $58,000,000; Indiana, $52,000,000. What was the total value for the five states? If 4 bu. of corn sold for $1, how many bushels did each state produce?

3. The value of the tobacco crop in five of the greatest tobacco-producing states in the same year was as folLows: Kentucky, $19,000,000; North Carolina, $8,000,000; Virginia, $7,200,000: Ohio,

Kentucky

North

-$19,000,000

Carolina

$8,000,000

Virginia-$7,200,000

Ohio

$4,900,000
$3,600,000

Connecticut

LEADING TOBACCO STATES

4. The value of the cotton produced in five leading cotton states in a recent year was as follows: Texas, $154,989,000; Mississippi, $85,957,000; Georgia, $76,024,000; Alabama, $57,000,000; South Carolina, $47,219,000. Find the total value of the cotton crop in the five states. If the cotton is valued at $45 a bale, of 500 pounds each, how many bales did Texas produce?

5. In a certain year the value of the vegetable crop in the United States was as follows: Irish potatoes, $98,000,000; sweet potatoes, $20,000,000; onions, $6,600,000; sugar beets, $3,300,000; miscellaneous vegetables, $114,000,000. Find how much the total value of the vegetable crop is exceeded by the value of the cotton crop in the five states named in Example 4.

6. In a recent year the apple crop in five leading states was as follows: New York, 24,110,000 bu.; Pennsylvania, 24,060,000 bu.; Ohio, 20,620,000 bu.; Virginia, 9,840,000 bu.; Illinois, 9,180,000 bu. What was the total value at 35 a bushel? What was the value of Virginia's crop?

7. In the year 1850 the number of farm animals in the United States was as follows: swine, 30,000,000; sheep, 22,000,000; cattle, 18,000,000; horses, 4,300,000; mules,

600,000. In 1900 the number was as follows: cattle, 51,000,000; sheep, 48,000,000; swine, 44,000,000; horses, 14,800,000; mules, 2,400,000.

Find the average yearly

increase of each kind in the 50 years.

8. In a certain year this country had 69,336,000 head of cattle. What was their total value, if the average value was $24 a head?

9. In a recent year this country produced 287,400,000 lb. of wool. If 3 lb. could be bought for $1, what was the total value of the wool produced?

10. In a recent year the value of the horses in five leading states was as follows: Iowa, $77,000,000; Illinois, $69,000,000; Ohio, $50,000,000; New York, $48,000,000; Kansas, $44,000,000. If the total value of the horses in the United States was $1,050,000,000, what was the value of the horses in all the other states? If the average value of horses was $50 a head, how many horses had Iowa that year?

FACTORS AND MULTIPLES

6?

66. 1. What two numbers multiplied together make Then what are the factors (makers) of 6?

2. Is each factor of 6 an exact divisor of 6? 3. Name two factors of 21. Of 35.

Of 35.

Of 33.

67. The integers which multiplied together produce a number are called Factors of that number.

Thus, 5 and 6, or 2, 3, and 5, are the factors of 30.

1. What are the exact divisors (factors) of 10? Of 14? Of 16?

2. Name a factor that is common to both 10 and 24. To both 25 and 35.

3. Name the greatest common factor of 12 and 18.

We have need for factors in changing fractions to smaller denominators.

68. A factor that is common to two or more numbers is called a common factor, or Common Divisor.

Thus, 3 is a common divisor of 9 and 21.

69. The greatest factor common to two or more numbers is called their Greatest Common Divisor.

Thus, 8 is the greatest common divisor of 16, 24, and 32. Why? Is 4 also a common divisor?