Question

The larger of two numbers is eight more than three times the smaller number. The sum of the two numbers is fifty-two. Find the two numbers.

Answer 1

Let
`x` be the larger number and
`y` the smaller number.

The first sentence translates to
`x=8+3y`. The second translates to
`x+y=52`.

Since
`x=8+3y`, you can substitute this into the second equation to get


`(8+3y)+y=4y+8=52\implies 4y=44\implies y=11`

Then substituting this into the original second equation gives


`x+11=52\implies x=41`