9. Two boys had 50 marbles; the second had three times as many as the first and 10 more. How many had each?

10. There are three numbers which make 36; the first is twice as many as the second and 6 more; and the third three times as many as the second and 12 more. What are the num

bers?

11. A man has four sons, the sum of whose ages is 48 years. Each one is 4 years older than his next youngest brother. What are their ages?

SECTION IV.

Simple Equations.

1. x+4 represents the sum of x and 4, what will repre sent twice as much as x + 4?

Ans. Twice x and twice 4, or 2 x + 8.

2. What will represent four times as much as x + 4? 7

6 times? 9? 8? 5?

represent twice as much as 2x+8? 5 3 times? 8? 4?

6?

4. What will represent 3 times 5x+1? 6 times? 4

times? 8 times? 5 times?

5. Multiply 4x+7 by 5.

By 9.

7? 9? 10?

By 3. By 8. By 4. By 6.

To the second he

6. A father gave his four sons 60 cents. gave 4 more than to the first; to the third twice as many as the second, and to the fourth as many as the third and 4 more. How many did he give to each?

7. A man bought two horses and a carriage for 158 dollars. For the second horse he gave twice as much as the first and 6 more, and for the carriage he gave twice as much as for the second horse and 7 more. What did he give for each horse,

and what for the carriage?

8. A says to B, your age is 10 more than mine; and twice your age is equal to three times mine. What was the age of each?

9. One number is 6 more than another; and twice one is equal to three times the other. What are the numbers?

10. One number is 12 more equal to three times the other.

than another; and twice one is What are the numbers?

11. There are two numbers; one is 20 more than the other, and three times one is equal to five times the other. What are the numbers?

12. There are three numbers; the second is 2 more than the first, and the third 2 more than the second; and three times the first is equal to the second and third. What are the numbers?

13. A man when he was married was three times as old as his wife; after they had lived together 15 years he was only twice as old. How old was each, when they were married?

14. A man bought some sugar and coffee. The coffee was 4 cents a pound more than the sugar; and 7 pounds of the coffee came to three times as much as 3 pounds of sugar. Wha was the price per pound of each?

For one

15. A man bought a number of barrels of flour. half he gave 12 dollars more than for the other half, and three times the price of one half is equal to twice the price of the other half. What did he give for each half?

and

16. A man bought some oxen, some cows, and some sheep. There were 2 more cows than oxen, and 6 more sheep than Cows. The oxen at 29 dollars a-piece, the cows at 20, the sheep at 2. The oxen came to as much as the cows and sheep. How many were there of each kind?

This sign 19

SECTION V.

Simple Equations.

called minus, shows that the number before which it stands, is to be subtracted. X- - 6 represents 6 subtracted from x; or, a number less than x by 6; or, the diffe

C

rence between x and 6.

The number or quantity which has before it, is called a negative number, or quan

1. What would represent the result of 10 subtracted from 2x? 5 from 3 x ? 8 from x? 7 from 5x? 3 from 6x? 2. What will represent a number less than 3 x by 7? 4x by 2? x by 8? 2x by 4? 7 x by 9?

3. What will represent the difference between x and 5? 2x and 3? 8x and 9? 3 x and 7? 5 x and 4?

4. There are two numbers; one wants 6 of being three times the other; and the sum of the two numbers is 18. the numbers ?

What are

Here the first member of the equation is 6 less than 4. Increase the first member by 6, and it becomes 4 x.

Increase the second member by 6 and it becomes 18+ 6, or 24.

6. Two men trade in company and gain 150 dollars, of which, one has four times as much as the other wanting 5. How much has each?

7. A man being asked the age of his two sons; said, that the age of his elder son was three times that of his younger wanting 20 years; and that his own age was equal to the sum of

their ages; and that all their ages together were equal to 144 years. What were their ages ?

8. Two men bought a lot of ground for 186 dollars; the second paid twice as much as the first, wanting $6. How much did each pay?

SECTION VI.

Simple Equations.

1. Add x. 6 and x-4 together. One is 6 less than x, and the other is 4 less than x.

The two added together will make

2. What will represent the sum of x 10 and 2x-11?

Of 5 x 3 and 2x·

6 and 12x. and 3 x 10?

3. What will

·24?

-8? Of 3 x. 9 and 8x

5? Of 4x

x+6 and x-4 added together make? When added we have 2 x with 6 added to one, and 4 subtracted from the other, which is equivalent to adding 2 to the 2 x, The sum of x+6 and x 4 is therefore =2x+2.

4. What is the sum of 2 x +6 and 3x- 10? Of x+8 and 3 x -2? Of 8x- 10 and 6x+8? Of 4x+9 and 6 x

Of 5x-7 and 10x+4? Of 7x+12 and 9x

7. A man bought 3 horses for $243. gave 5 dollars more, and for the third, 8 What did he give for each?

For the second he less, than the first.

8. There is a certain number, such, that if one less by 6, and one greater by 12, be added together, the sum will be 24. What is the number?

9. A man divided his estate among his three sons, giving the second twice as much as the first and 6 more; the third, three times as much as the first wanting 20. His whole es tate was £ 580. What did each receive?

10. A man, when he was married, was 4 years older than his wife. Four years before, the sum of their ages was 44 years. What were their ages when they were married?

6. What are 8 times 3x 12? 9 times? 6? 7? 5? 4? 2? 3? 9?

7. Two candidates received the same number of votes at an election. If one had received 50 more and the other 100 less, then one would have received twice as many votes as the other. How many votes did each receive?

8. Says A to B, you are 4 years more than twice as old as I am; 20 years ago you were three times as old as I was. What are their ages at present?

9. A has twice as much money as B; but if A had 20 dollars less, and B 30 dollars more, they would each have the same sum. How much has each?

10. A man bought 9 apples, 8 pears, and 7 peaches for 344 cents. The apples came to twice as much a-piece as the pears, wanting 2 cents; and the peaches came to three times as much a-piece as the pears, wanting 2 cents. How much were they a-piece?

SECTION VIII.

Simple Equations.

1. Two numbers make 20, and one wants 4 of being three times the other. What are the numbers?