Question

Two numbers have a sum of 23 and a difference of 9 find the 2 numbers

Answer 1

SOLUTION

Define a variable for the unknown numbers.

$\text{ let the numbers be x and y}$

The sum is 23, implies

$x+y=23$

The difference is 9 is written as

$x-y=9$

Then we have the system of equation

$\begin{gathered} x+y=23\ldots\text{equation}1 \\ x-y=9\ldots\text{equation}2 \end{gathered}$

Add equation 1 and 2.

$\begin{gathered} 2x-0=32 \\ 2x=32 \end{gathered}$

Divide both sides by 2

$\begin{gathered} \frac{2x}{2}=\frac{32}{2} \\ \text{Then} \\ x=16 \end{gathered}$

hence x=16

Recall equation 1

$\begin{gathered} x+y=23 \\ \text{ put x=16} \\ 16+y=23 \end{gathered}$

Subtract 16 from both sides, we have

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

Hence, y=7

Answer: The numbers are 16 and 7