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 numbers are$26$and$37$

Step-by-step solution

Step 1. Given information

We have been given that one number is 11 less than another. If their sum is increased by eight, the result is 71.

We have to find the numbers.

Step 2. Form the equations

From the statement One number is 11 less than another we get :

$x-y=11$______ (1)

From, If their sum is increased by eight, the result is 71. We get :

$x+y+8=71$_________ (2)

Step 3. Solve for the equations

From equation (1),

We get $x=11+y$

Put this value in equation (2)

$$\begin{gathered} x+y+8=71 \\ 11+y+y+8=71 \\ 2y+19=71 \\ 2y=52 \\ y=26 \end{gathered}$$

Put this value in equaltion (1)

$$\begin{gathered} x=11+26 \\ x=37 \end{gathered}$$