# Harvey is 3 times as old as Jane. The sum of their ages is 48 years. What is the age of each?

Oct 12, 2017

$\text{Jane's' age" = 12years and "Harvey's age} = 36 y e a r s$

#### Explanation:

Let $\text{Jane's' age} = x$

Hence, Harvey is $3 \times$ as old as Jane

$\therefore \text{Harvey's age} = 3 \times x = 3 x$

Sum of their ages..

$\text{Jane's' age" (x) + "Harvey's age} \left(3 x\right) = 48$

$x + 3 x = 48$

$4 x = 48$

Divide both sides by $\textcolor{red}{4}$

$\frac{4 x}{\textcolor{red}{4}} = \frac{48}{\textcolor{red}{4}}$

$\frac{\cancel{4 x}}{\cancel{4}} = \frac{48}{4}$

$x = \frac{48}{4}$

$x = 12$

Substituting each values..

$\text{Jane's' age} = x$

$\text{Jane's' age} = 12 y e a r s$

and..

$\text{Harvey's age} = 3 x$

$\text{Harvey's age} = 3 \left(12\right)$

$\text{Harvey's age} = 36 y e a r s$