Question

the larger of two integers is 3 more than 5 times the smaller integer. find the two numbers if the smaller subtracted from the larger is 31.

Answer 1

We have two integers (x and y).

The largest integer (y) is 3 more than 5 times the smallest integer (x).

$y=3+5x$

Also, the smaller (x) substracted from the larger (y) is 31.

$y-x=31$

We can replace the value of y from the second equation in the first equation and solve:

$y-x=31\longrightarrow y=31+x$$\begin{gathered} y=3+5x=31+x \\ 3+5x=31+x \\ 5x-x=31-3 \\ 4x=28 \\ x=\frac{28}{4} \\ x=7 \end{gathered}$

Then, the value of y is:

$\begin{gathered} y=31+x \\ y=31+7=38 \end{gathered}$

The integers are 7 and 38.