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Lesson 1, Topic 4
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# Using Algebra for Solving Word Problems

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First, we need to translate word problems into equations with variables. Then, we need to solve the equation(s) to find the solution(s) to the word problem.

### Example 1

1. What number when added to 8 gives 15?
2. Segun thinks of a number, subtracts 7 from it and the result is 11. What is the number?
3. When a number is multiplied by 4, the result is 24. What is the number?

Solution

1. Let the number added to 8 that gives 15 be x

i.e. $$\scriptsize x \: + \: 8 = 15$$

This statement is true if  x =  7

The number added is 7

$$\scriptsize 7 \: + \: 8 = 15 \: is \: true$$

2. Let y be the number you subtract 7 from to get 11.

i.e. $$\scriptsize y \: – \: 7 = 11$$

The statement is true if y = 18

The number is 18

$$\scriptsize 18 \: – \: 7 = 11$$

3. Let z be the number you multiply by 4 to get 24.

i.e. $$\scriptsize z \: \times \: 4 = 24$$

This statement is true if  z = 6

The number is 6.

### Example 2

A woman is twice as old as her daughter. The woman is x years old.

a. How old is the daughter?
b. How old were they 5 years ago?
c. How old will the woman be in 15 years’ time?

Solution

a. If the woman is x years old, then her daughter is $$\frac{x}{2} \: \scriptsize years.$$

b. 5 years ago, the woman was (x  –  5) years and the daughter was $$\left( \frac{x}{2} \scriptsize \: – \: 5 \right ) \: \scriptsize years$$

c. In 15 years’ time the woman will be (x  +  15) years.