Q. 73 - Intermediate Algebra

Question

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

Step-by-Step Solution

Answer

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

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,

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

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.