# Age Word Problems

Age problems may involve one person or more than one person. If there is one person involved, then we can represent his age by an unknown variable and solve it.

For more than one person, we represent their ages by different variables and form equations, which can be solved to find the values of variables. Let us see this in detail below with the help of examples.

Age problems involving single person

*Example*: 8 years ago, if Addie’s age was one-third of the age he will be 12 years, what is his present age?

Let us assume that Addie’s present age = *x* years

Now read the question again and express the given information in terms of *x*.

8 years ago means *x* – 8

Addie’s age was one-third implies

In 12 years means after 12 years which means *x* + 12

Next write an equation, using the given information:

Multiply by 3 on both sides, 3(*x* – 8) = *x* + 12

3*x* – 24 = *x* + 12

Subtract *x* and add 24 on both sides, 3*x* – 24 – *x* + 24 = *x* + 12 – *x* + 24

2*x* = 36

Divide by 2 on both sides, we get *x* = 18** **

**Age problems involving more than one person**

*Example*: Amelia is three times as old as his son, Alvin. Alvin is 4 years older than his sister, Betsy. After 7 years, Amelia will be two times as old as Alvin. What is the present age of Alvin?

Let us assume that the present age of Alvin = *x* years

Amelia’s age = 3*x*

Betsy’s age = *x* – 4

After 7 years:

Alvin’s age = *x* + 7

Amelia’s age = 3*x* + 7 = 2(*x* + 7) {as it is given that Amelia will be two times as old as Alvin)

3*x* + 7 = 2(*x* + 7) implies 3*x* + 7 = 2*x* + 14

Subtract 2*x* and 7 from both sides, 3*x* + 7 – 2*x* – 7 = 2*x* + 14 – 2*x* – 7

3*x* – 2*x* = 14 – 7

*x ***=7 years**

**CHECK POINT**

- After 15 years, Melinda will be two times older than her present age. What is her present age?

- In seventeen years, Perry will be 44 years old. How old is he now?

- Carol is 3 times as old as John today. Twenty years ago, Carol was 5 times as old as John. What is John’s present age?

- Richards is three times as old as his son, Gary. In 15 years, Richards will be only twice as old as Gary. What is Gary’s present age?
- Amanda’s age is five times as that of Bella. Ten years later, Amanda’s age will be thrice that of Bella. What is Amanda’s age?

##### Answer key

- 15 years
- 27 years
- 40 years
- 15 years
- 50 years

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