Question

One number is 11 less than another. If their sum is increased by eight, the result is 71. Find the numbers.

Short answer

The two numbers are 37 and 26.

Step-by-step solution

Step 1. Given Information

One number is 11 less than another. If their sum is increased by eight, the result is 71.

Step 2. Forming equation

Let one number be $x$and another number be $x-11.$Then,

$$\begin{gathered} Sum+8=71 \\ x+\left(x-11\right)+8=71 \end{gathered}$$

Step 3. Finding numbers

$$\begin{gathered} 2x-3=71 \\ 2x=74 \\ x=37 \\ thenx-11=37-11=26 \end{gathered}$$