# The ages of the three children in a family are as follows: The middle child is one year older than the youngest, while the oldest is three times as old as the youngest. If the sum of their ages is 21 years, what are their ages?

Aug 7, 2017

Their ages are $4 , 5 \mathmr{and} 12$

#### Explanation:

It is possible to use one variable to define the ages of all $3$ children, because we are told how their ages relate to each other.

Choose the age of the youngest child to be $x$.
It is easier to add and multiply than subtract and divide.

The youngest age is $\textcolor{b l u e}{x}$ years old

The middle child is $1$ year older. This means the age is $\textcolor{red}{x + 1}$

The oldest child is $3$ times older than the youngest, so, $\textcolor{g r e e n}{3 x}$

The sum of their ages is $21$ years. Add the ages together:

$\textcolor{b l u e}{x} + \textcolor{red}{x + 1} + \textcolor{g r e e n}{3 x} = 21$

$5 x + 1 = 21$

$5 x = 21 - 1$

$5 x = 20$

$x = 4$

$x + 1 = 5 \mathmr{and} 3 x = 12$

Their ages are $4 , 5 , 12$

Check" $4 + 5 + 12 = 21$