Question

The sum of two numbers is $65$.

Their difference is $25$. Find the

numbers.

Short answer

The numbers are$45\&20$

Step-by-step solution

Step 1. Given

Sum$=65$and difference$=25$

Step 2. Calculation

Let the numbers are $x\&y$

So, $x+y=65$and the difference is $x-y=25$

Now find the value of $x$from second equation and put it into first equation.

$$\begin{gathered} x-y=25 \\ x=25+y \\ x+y=65 \\ 25+y+y=65 \\ 2y=65-25 \\ 2y=40 \\ y=20 \end{gathered}$$

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

$$\begin{gathered} x+y=65 \\ x+20=65 \\ x=65-20 \\ x=45 \end{gathered}$$

Step 3. Verification

Verify the values,

$$\begin{gathered} x+y=65 \\ 45+20=65 \\ 65=65 \end{gathered}$$

LHS is equal to RHS