34. 228169-392 43. 2159450÷2465

35. 503652÷564 36. 467606÷614 45. 5047923÷5631

PROMISCUOUS PROBLEMS.

77. 1. A man gave his older daughter $875, his younger daughter $185 less, and his son $765 more than he gave to both daughters.

did he give to all?

How many dollars

2. A farmer raised 365 bushels of wheat one year, twice as many bushels the next year, and the third year three times as many bushels as in both the two preceding years. How many bushels did he raise in three

years?

3. A wholesale merchant sold a stock of goods to a country dealer for $8,435 and lost $1,956 by the transaction. How many dollars would he have gained if he had sold it for $12,317?

4. A farmer sold 16 loads of potatoes, each load containing 48 bushels. If he has 257 bushels left, how many bushels did he raise?

5. Multiply the sum of 276 and 347 by three times their difference?

6. A speculator bought 276 acres of wild land at $7 an acre, paid $157 in taxes and then sold it at $9 an acre. How many dollars did he make by the transac(How many dollars on each acre would he have gained had there been no expense?)

tion?

7. Two men are 967 miles apart. If they travel toward each other, one at the rate of 48 miles a day and the other at the rate of 57 miles a day, how many miles apart will they be at the end of 6 days?

8. A man sold a mill for $17,360 and lost $1,675. How many dollars would he have received for it if he had gained $1,675?

9. If the dividend is $5,200, and the quotient $89 and the remainder $38, what is the divisor?

10. The difference between two numbers is 7,569,483, and the subtrahend is 379,468. Find the minuend.

11. The smaller of two numbers is contained 18 times in 1,566, and the larger number is 69 times the smaller. Find the larger number.

12. A speculator sold 76 head of cattle for $2,888, and lost $267. At what price per head should he have sold them to gain $265?

13. If 45 acres produce 2,520 bushels of corn, how many bushels does 28 acres produce at the same rate?

14. At a certain election the whole number of votes cast for two opposing candidates was 12,672. The successful candidate received 216 majority. How many votes did each receive?

15. A merchant buys 168 barrels of flour for $672. How many barrels more can he buy for $984 at the same price?

16. A man bought 13 horses at $92 a head, and 15 at $84 a head. He sold them all at $90 a head. How many dollars did he gain?

17. A man sold land at $46 an acre, receiving $4,508 for it. How much would he have received for it if he had sold it at $58 an acre?

18. The divisor is 88, the quotient $248, and the remainder $66. What is the dividend?

19. The telegraph poles along a railroad are set 264 feet apart. How many poles will be required for a line from Chicago to Bloomington, a distance of 126 miles, there being 5,280 feet in a mile?

20. A park is 48 rods long and 32 rods wide. How many times must a boy go around it on his bicycle to travel 45 miles, there being 320 rods in a mile? How many times must he go around the park to travel 1 mile?

21. A garrison of 10,000 men have provisions to last 6 weeks. If 2,500 men are killed in a battle, how many weeks will the provisions last the remainder?

22. The product of two numbers is 40,796. One of the numbers is 124. What is the other?

23. Mr. Wilson sold a quantity of wood for $2,492, that cost $1,424, thus gaining $3 a cord. How many cords were there, and what was the cost per cord?

24. The circumference of each fore wheel of a carriage is 8 feet, and of each hind wheel 12 feet. How many more revolutions will the fore wheels make than the hind wheels in going 38 miles? (See problem 19.)

25. The year 1896 being leap year, contained 366 days. How many hours did it contain? If I had read 2 hours each day, at the rate of 16 pages an hour, how many books of 248 pages each could I have read during the year, and how many pages over?

FACTORS AND FACTORING.

78. Prime and Composite Numbers.

1. What two factors make 22, 25, 36, 49, 56?

2. What number do the factors 2 and 2 and 2 make? 2 and 2 and 3? 2 and 3 and 3? 2 and 2 and 5? 2 and 2 and 2 and 3? 3 and 3 and 3? 2 and 3 and 5? 2 and 2 and 3 and 3?

3. What two factors make 3, 5, 7, 11, 13?

A Prime number is one that can not be made by the multiplication of any other integral number than 1, as 5, 7, 13, 19, 23, etc.

A Composite number is one that can be made by multiplying some other integral number than 1, as 6, 9, 10, 14, 15, etc.

Numbers which have no common integral factor except 1 are prime to each other, as 8 and 9.

An even number is a number that contains 2 as a factor, as 4, 6, 8, etc.

An odd number is one that does not contain 2 as a factor, as 3, 5, 7, etc.

79. Principles.

I.

A factor of any number is also a factor of any multiple of that number.