Question

one number is 9 more than another number. if the sum of the numbers is 65, find both numbers

Answer 1

Let x and y are the two unknown numbers.

One number is 9 more than another number

$x=y+9\quad eq.1$

The sum of the numbers is 65

$x+y=65\quad eq.2$

Substitute eq.1 into eq.2

$\begin{gathered} x+y=65 \\ (y+9)+y=65 \\ y+9+y=65 \\ 2y+9=65 \\ 2y=65-9 \\ 2y=56 \\ y=\frac{56}{2} \\ y=28 \end{gathered}$

So, the value of y is 28

$\begin{gathered} x=y+9 \\ x=28+9 \\ x=37 \end{gathered}$

Therefore, the two numbers are

$\begin{gathered} x=37 \\ y=28 \end{gathered}$