Question

One number is five more than another. If their sum is increased by nine, the result is 60. Find the numbers.

Short answer

The numbers are $23$and $28$.

Step-by-step solution

Step 1. Given information

We have been given that one number is five more than another. If their sum is increased by nine, the result is 60.

We have to find the numbers.

Step 2. Form the equations

From the statement: One number is five more than another. If their sum is increased by nine the result is 60, we get

$x=y+5$_______ (1)

$x+y+9=60$_______ (2)

Step 3. Solve for the equations

Put equation (1) in (2)

$$\begin{gathered} x+y+9=60 \\ y+5+y+9=60 \\ 2y+14=60 \\ 2y=46 \\ y=23 \end{gathered}$$

Put the value of y in (1)

$$\begin{gathered} x=23+5 \\ x=28 \end{gathered}$$