Question

The sum of two integers is 463, and the larger number is 31 more than 5 times the smaller number. Findthe two integers.

Answer 1

Let the smaller number be x

Let the larger number be y

Since the larger number is 31 more than 5 times the smaller number, it folllows:

`y=5x+31`

The sum of the two integers is 463, it follows

`x+y=463`

Substitute y=5x+31 into the equation

`x+5x+31=463`

Solve for x

`\begin{gathered} 6x=463-31 \\ 6x=432 \\ x=(432)/(6) \\ x=72 \end{gathered}`

Substitute x=72 into y=5x+31

`\begin{gathered} y=5\left(72\right)+31 \\ y=360+31 \\ y=391 \end{gathered}`

Therefore the two integers are 72 and 391