Solving Word Problems with Simple Equations |

For these word problems:

- a) Make a "

- b) Translate the words into an equation in that variable,

- c) Solve the problem and give your answer in words (with units).

1) A number increased by 35 is 51. What is that number? ( *solution* )

2) One number is eight times a smaller one. If the smaller number is subtracted

from the larger one, the remainder is 21. Find the two numbers. ( *solution* )

3) When 32 is subtracted from 7 times a number, we get 24. What is the number? ( *solution* )

4) If 12 times a number be increased by 5, the sum is 25 more

than 7 times the number. What is the number? ( *solution* )

5) The length of a lot is 5 times its width. The perimeter is 300ft.

What are the length and width of this lot? ( *solution* )

6) Frank is 5 years older than Fred. The sum of their ages is 25.

How old is each of them? ( *solution* )

7) Five less than 10 times a number, is the same as

the sum of 19 and 8 times the number. What is the number? ( *solution* )

8) Our hockey team played 152 games this season.

They won 30 games more than they lost. How many games did they win? ( *solution* )

9) The sum of two consecutive integers is 113. What are the integers? ( *solution* )

10) Find three consecutive integers whose sum is 114. ( *solution* )

**SOLUTIONS**

1) a number increased by 35 is 51. What is that number?

- a) Let

- b) the equation is:

- c) we subtract 35 from both sides of the = to get

2) One number is eight times a smaller one. If the smaller number is subtracted

from the larger one, the remainder is 21. Find the two numbers.

- a) Let

- b) the equation is: 8

- c) combine

3) When 32 is subtracted from 7 times a number, we get 24. What is the number?

- a) Let

- b) the equation is: 7

- c) we add 32 to both sides, then divide by 7: 7

4) If 12 times a number be increased by 5, the sum is 25 more

than 7 times the number. What is the number?

- a) Let

- b) the equation is: 12

- c)

5) The length of a lot is 5 times its width. The perimeter is 300ft.

What are the length and width of this lot?

- a) Let

- b) the equation is: 2(5

- c) divide through by 2; collect terms: 6

The Width measures 25 ft. so the length measures 5 × 25 or 125 ft.

6) Frank is 5 years older than Fred. The sum of their ages is 25.

How old is each of them?

- a) Let

- b) the equation is:

- c) remove brackets, collect terms to get 2

Fred and Frank are 10 and 15years old respectively.

7) Five less than 10 times a number is the same as

the sum of 19 and 8 times the number. What is the number?

- a) Let

- b) the equation is: 10

- c) we

8) Our hockey team played 152 games this season.

They won 30 games more than they lost. How many games did they win?

- a) Let

- b) the equation is games won + games lost = total games:

- c) collect the

The team won 91 games.

9) The sum of two consecutive integers is 113. What are the integers?

- a) Let

- b) the equation is:

- c) we get 2

10) Find three consecutive integers whose sum is 114.

- a) Let

- b) the equation is:

- c) simplifying we get: 3

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