Question

The sum of two numbers is $37$.

Their difference is $9$. Find the

numbers.

Short answer

The numbers are$23\&14$.

Step-by-step solution

Step 1. Given 

Sum$=37$and the difference between the numbers is$9$

Step 2. Calculation

Let the numbers are $x\&y$

Therefore, $x+y=37$

and the difference is $x-y=9$

Add the two equations,

$$\begin{gathered} x+y=37\&x-y=9 \\ x+y+x-y=37+9 \\ 2x=46 \\ x=23 \end{gathered}$$

Now put value of $x$in any equation and find the value of $y$.

$$\begin{gathered} x+y=37 \\ 23+y=37 \\ y=37-23 \\ y=14 \end{gathered}$$

Therefore the numbers are$14\&23$

Step 3. Verification

Verify the equation,

$$\begin{gathered} x+y=37 \\ 23+14=37 \\ 37=37 \end{gathered}$$

LHS is equal to RHS