Question

The sum of two numbers is $12$

Their difference is $4$.

How do you find the numbers?

Answer 1

Step 1. Find the value of two numbers:

Consider $x$ and $y$ as the two numbers.
Given, the sum of two numbers is $12$.

$x+y=12...\left(1\right)$

The difference between two numbers is $4$.

$x-y=4...\left(2\right)$

Step 2. Simplify the above two equations:

Consider, the second equation:

$\begin{array}{rcl}x-y& =& 4\\ & \Rightarrow & x=4+y\end{array}$

Substitute the value of $x$in equation$\left(1\right)$:

$\begin{array}{rcl}4+y+y& =& 12\\ & \Rightarrow & 4+2y=12\\ & \Rightarrow & 2y=12-4\\ & \Rightarrow & 2y=8\\ & \Rightarrow & y=\frac{8}{2}\\ & \Rightarrow & y=4\end{array}$

Substitute $y=4$ in the equation$\left(1\right)$:

$\begin{array}{rcl}x+4& =& 12\\ & \Rightarrow & x=12-4\\ & \Rightarrow & x=8\end{array}$

Hence, the two numbers are $8$ and $4$.