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.
Responses