Question

The sum of two number is $30$. One number is $4$less than the other. Find the numbers.

Short answer

The required numbers are$13$and$17$.

Step-by-step solution

Step 1. Given and explanation 

There are two numbers whose sum is$30$and one number is $4$less than the other number.

Assume the numbers to be $x,y$.

Their sum, i.e., $30$can be written as $x+y=30$.

One number is $4$less than the other can be written as $x=y-4$.

Step 2. Finding the value of first variable by substitution. 

We have two equations, i.e.,

$$\begin{gathered} x+y=30 \\ x=y-4 \end{gathered}$$

Substituting the value of $x$in first equation gives us,

localid="1644337362055" $$\begin{gathered} (y-4)+y=30 \\ 2y=30+4 \\ 2y=34 \\ y=17 \end{gathered}$$

Step 3. Finding the value of other variable.

Putting $y=17$in

$x+y=30$gives us,

$$\begin{gathered} x+17=30 \\ x=13 \end{gathered}$$

This shows that the two numbers are$13\&17$.

Step 4. Check the solution.

We will check the answer by putting in both the equations. If the equations satisfy, our answers are right.

1. First equation is
   $$\begin{gathered} x+y=30 \\ 13+17=30 \\ 30=30 \end{gathered}$$
   Hence satisfied.
2. Second equation is
   $$\begin{gathered} x=y-4 \\ 13=17-4 \\ 13=13 \end{gathered}$$
   Hence satisfied.

Thus our answers are right.