Question

The sum of two numbers is $30$ and their difference is $12$.

What are the $2$ numbers?

Answer 1

Find two numbers is $30$ and their difference is $12$:

What are the $2$ numbers:

Let two numbers be $a$ and $b$.

The sum of these two numbers be $a+b=30$.

The difference between these two will be $a-b=12$.

These are simultaneous equations, so you can solve them by math:

$\begin{array}{ccccc}a& +& b& =& 30\\ a& -& b& =& 12\\ —& —& —& —& —\\ 2a& -& 0& =& 42\end{array}$

Solve the obtained result:

$\begin{array}{rcl}2a& =& 42\\ & \Rightarrow & a=\frac{42}{2}\\ & \Rightarrow & a=21\end{array}$

Put the value of $a$ in the equation to get the value of $b$:

$\begin{array}{rcl}12+b& =& 30\\ & \Rightarrow & b=30-21\\ & \Rightarrow & b=9\end{array}$

Hence, the values of the two numbers are $21\mathrm{and}9$.