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=(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.