Question

In the following exercises, translate to a system of equations and solve.

Robert is 15 year years older than his sister, Helen. The sum of their ages is sixty-three. Find their ages.

Short answer

The age of Robert is 39 and age of her sister, Helen is 24.

Step-by-step solution

Step 1. Given Information 

The given data is that Robert is 15 year years older than his sister, Helen. The sum of their ages is sixty-three.

Step 2. Explanation 

Let the age of Helen be x and age of Robert be y.

The sum of their ages is 63 that is $x+y=63--\left(1\right)$

Robert is 15 year years older than his sister, Helen that is$y=x+15--\left(2\right)$

Step 3. Calculation  

Substitute the equation (2) in equation (1) and simplify to get one of the numbers.

$$\begin{gathered} x+x+15=63 \\ 2x=48 \\ x=24 \end{gathered}$$

Substitute the value of x in equation (2) to get the value of y.

$$\begin{gathered} y=24+15 \\ y=39 \end{gathered}$$