Question

Two numbers have a sum of 23 and a difference of 9 what are the two numbers ?

Answer 1

Let x and y the numbers we are looking for, since they have a sum of 23, we can set the following equation:

$x+y=23.$

Also, since its difference is 9, we can set the following equation:

$x-y=9.$

Adding the first equation to the second one we get:

$x-y+x+y=9+23.$

Simplifying the above equation we get:

$2x=32.$

Dividing the above equation by 2 we get:

$\begin{gathered} \frac{2x}{2}=\frac{32}{2}, \\ x=16. \end{gathered}$

Substituting x=16 in the first equation we get:

$16+y=23.$

Subtracting 16 from the above equation we get:

$\begin{gathered} 16+y-16=23-16, \\ y=7. \end{gathered}$

Answer: The numbers we are looking for are 16 and 7.