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

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