Question

The sum of two numbers is $17$ and their difference is $3$. What are the two numbers?

Answer 1

Find the two numbers.

Let, the first number be $x$ and the second number be $y$.

Assume that, the first number is greater than the second number. Thus, $x>y$.

Step 1: Write the equations in two variables.

The sum of the two numbers is $17$.

$x+y=17$

The difference between the two numbers is $3$.

$x-y=3$

The pair of linear equations in two variables is:

$$\begin{gathered} x+y=17 \\ x-y=3 \end{gathered}$$

And,

$\begin{array}{rcl}x+y& =& 17\\ & \Rightarrow & y=17-x\end{array}$

Step 2: Solve the equations.

Substitute the above value in the second equation:

$\begin{array}{rcl}x-y& =& 3\\ & \Rightarrow & x-\left(17-x\right)=3\\ & \Rightarrow & x-17+x=3\\ & \Rightarrow & x+x-17=3\\ & \Rightarrow & 2x-17=3\\ & \Rightarrow & 2x=3+17\\ & \Rightarrow & 2x=20\\ & \Rightarrow & x=10\end{array}$

Step 3: Find the second number.

Substitute the value of $x$ in $y=17-x$.

$\begin{array}{rcl}y& =& 17-10\\ & \Rightarrow & y=7\end{array}$

Hence, the two required numbers are $\mathbf{10}$ and $\mathbf{7}$.