Said he, I have not 100; but if I had as many more and 8 geese beside, I should have 100. How many had he?

31. Divide the number 50 into three such parts, that the second shall be 6 times as much as the first, and 12 more; and the third as much as the second, and 2 more.

32. A man bought 6 pounds of coffee and 10 pounds of tea for 260 cents. The tea cost 10 cents per pound more than the coffee. How much did each cost?

33. A man bought 6 barrels of flour and 4 firkins of butter for 68 dollars. He gave 2 dollars more for a firkin of butter than he did for a barrel of flour. How much did he give for each?

he

34. A man bought 3 apples, 4 peaches, 5 pears and 6 oranges for 103 cents. He gave one cent more for a peach than gave for an apple; for an orange he gave four times as much as he did for an apple, and 2 cents more; for a pear he gave as much as he did for an orange. What did he give a piece for each?

SECTION IV.

Introductory Lessons.

1. What number is that, to which if 6 be added, the number will be doubled?

Let x represent the number. Then x and 6 must be equal to 2 x; and it is evident that 6 must be equal to x, otherwise x and 6 would not make 2 x. Hence x is equal to 6, and 6 must be the number required.

2. What number is that, to which if 7 be added the number will be doubled? If 8? If 9? If 10? If 11? If 12? If 13? If 14? If 15?

3. What number is that, to which if 12 be added, the sum will be three times the number?

3x.

Let x represent the number; then x and 12 will be equal to If x and 12 make 3 x, 12 must be 2 x, otherwise x and 12 would not make 3x. Hence, 2 x are equal to 12; x is equal to 6.

4. What number is that, to which if 10 be added the sum will be three times the number? If 18 be added? If 20? If 16? If 30? If 40 ?

5. A young man being asked his age, said, that if the age of his father, which was 66 years, were added to twice his age, the sum would be five times his age. What was his age?

6. A pound of coffee costs 5 cents more than a pound of sugar, and 3 pounds of sugar comes to as much as 2 pounds of coffee. How much does each come to?

7. One number is 10 more than another number, and twice one is equal to three times the other. What are the numbers? 8. One number is 12 more than another, and three times one are equal to five times the other. What are the numbers?

9. One number is 6 more than another, and four times one

are equal to seven times the other.

10. If we take x, from x and 8,

What are the numbers? what will be left?

11. If we take x, from 2 x and 12, what will be left?

12. If we take x and 6, from 3 x and 12, what will be left? 13. If we subtract 6, from x and 6, what will be left? If 15 from 2 x and 30, what?

14. If 2x and 30 be equal to 3 x and 15, and we take 2 x from each of these equals, what will the remainders be?

Ans. 30 will be left of the former and x and 15 of the latter.

15. Will these two remainders be equal?

Ans. They will be equal, for we had two things equal, viz. 3x and 15, 2 x and 30; and we took 2x from each. If we take the same number or quantity from two equal numbers or quantities, the remainders will be equal.

Hence, if 3x and 15, equal 2 x and 30,

x and 15, will equal 30,

And x will be equal to 15. Why?

16. If 3x and 60 are equal to 5 x and 20, will the follow. ing be equal?

17. Given 4

and 80, equal to 6x and 20, to be reduced

by subtraction till you find x equal to some number.

18. A barrel of flour costs 4 dollars more than a bushel of wheat; and two barrels of flour cost as much as ten bushels

of wheat.

What did a bushel of wheat cost? and what did a barrel of flour cost?,

19. A man bought three oxen and four cows. An ox cost 5 dollars more than a cow; whilst the cows and oxen both cost the same sum. What did each cost?

20. Two boys had the same number on their slates; one added 2 to the number, and then multiplied the sum by 6, the other added 8 to it and multiplied the sum by 4, when they found that each had obtained the same result. What was the number?

21. If 3 x stands for a man's age, and x for a woman's age, at the time of their marriage, what will represent their ages 15 years afterwards?

22. A man when he was married was three times as old as his wife. After they had lived together 15 years, he was only How old were they when they were

twice as old as she was.

married?

23. A man is now three times as old as his son; 10 years hence, he will be only twice as old. How old is the man? and how old is his son?

24. A had three times as many dollars as B. A gained 4 dollars every day, and B 8. At the end of 4 days, A had only twice as many as B. How many had each at first?

25. A man bought some wheat, corn and flour. A barrel of corn cost 1 dollar more than a bushel of wheat, and a barrel of flour cost 2 dollars more than a barrel of corn. Ten bushels of wheat, and five barrels of corn cost just as much as five barrels of flour. What was the price of each?

26. When a gallon of wine costs 25 cents more than a gallon of brandy, four gallons of brandy cost as much as three gallons of wine. What was the price of each?

27. A man has 5 sons, each of which is 3 years older than his next younger brother, and the eldest's age is equal to five times the age of the youngest. What are their ages?

SECTION V.

Introductory Lessons.

1. Twelve are of what number?

Let x represent the number; then

of x are equal to

12. If of x are equal to 12, then of x will be equal to of 12, or 4; and if of x is 4, then x will be equal to four times 4, or 16.

2. Twenty are of what number?

3. Fifty are 5 of what number? 10 ?

?

10?

10 ?

10 ?

5. If 12 be added to of a number, the sum will be equal

to the number. What is the number?

Let x represent the number; then
What part of x will 12 be?

to x.

of x be?

6. If 16 be added to equal to the number.

7. If 8 be added to equal to the number.

8. If 4 be added to equal to the number.

9. If 4 be added to

of x and 12 are equal What will the whole

of a certain number, the sum will be What is the number?

of a certain number, the sum will be What is the number?

3 of a certain number, the sum will be What is the number?

of a number, the sum will be equal to the number. What is the number?

10. Three-fourths of a certain number, added to 8, gives 38. What is the number? Added to 11, it gives 38; what is the number? Added to 5? to 14?

11. A man sold a cow for 10 dollars, which was more than she cost him. What did she cost him?

12. Upon measuring the grain produced by a certain field, it was found to be 20 bushels, which was more than was sown. How many bushels were sown?

13. A boy said that if of his age were subtracted from his age, the remainder would be 6 years. What was his age?

14. One-half and of a certain number, and 6 more, are equal to 16. What is the number?

One-half is equal to %, and is equal to . Hence and

are equal to ; then of the number and 6 more make 16. Let x represent the number, then of x and 6 are equal to 16; consequently, 10 must be equal to 1⁄2 of x, ¦ of x, 2; and x equal to 12.

15. One-half and of a certain number and 12 more, make 48. What is the number?

16. Two men having found a bag of money, disputed about the amount of it. One said that,, and of the money made 130 dollars. How much did the bag contain?

17. A man being asked how much money he had; said, that if he had as much more, and half as much more, and 21 dollars, he would have 100. How many dollars had he?

18. A man being asked how many sheep he had; said, that he had of them in one pasture, of them in another, and he had 2 sheep beside. How many sheep had he?

19. One-fourth of a pole is in the water, and in the mud; and there are 22 feet out. How long is the pole?

20. One number is twice as much as another; and added to of the other, and 6 more, are equal to 26. is the number?

of one,

What