Question

One number is eight more than another. If their sum is increased by 17, the result is 95. Find the numbers.

Short answer

The numbers are $35$and $43$.

Step-by-step solution

Step 1. Given information

We have been given that one number is eight more than another. If their sum is increased by 17, the result is 95.

We have to find the numbers.

Step 2. Form the equations

From the statement: One number is eight more than another. If their sum is increased by 17, the result is 95.

We get,

$$\begin{gathered} x=y+8\_\_\_\_\_\_\_\left(1\right) \\ x+y+17=95\_\_\_\_\_\_\left(2\right) \end{gathered}$$

Step 3. Solve for the equations

Put equation (1) in (2)

$$\begin{gathered} x+y+17=95 \\ y+8+y+17=95 \\ 2y+25=95 \\ 2y=70 \\ y=35 \end{gathered}$$

Put the obtained value of y in equation (1)

$$\begin{gathered} x=y+8 \\ x=35+8 \\ x=43 \end{gathered}$$