Q. 72 - Intermediate Algebra

Question

The sum of two number is $15$. One number is $3$less than the other. Find the numbers.

Step-by-Step Solution

Answer

The required numbers are $6$ and $9$.

Step 1. Given and explanation

There are two numbers whose sum is $15$ and one number is $3$ less than the other number.

Assume the numbers to be $x,y$.

Their sum, i.e., $15$ can be written as $x+y=15$.

And one number is $3$ less than the other can be written as $x=y-3$.

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

We have two equations, i.e. ,

$$\begin{gathered} x+y=15 \\ x=y-3 \end{gathered}$$

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

$$\begin{gathered} (y-3)+y=15 \\ 2y=15+3 \\ 2y=18 \\ y=9 \end{gathered}$$

Step 3. Finding the value of other variable

Putting $y=9$ in
$x+y=15$ gives us,

$$\begin{gathered} x+9=15 \\ x=6 \end{gathered}$$

This shows that the two numbers are $6\&9$.

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
   $$\begin{gathered} x+y=15 \\ 6+9=15 \\ 15=15 \end{gathered}$$
   Hence satisfied.
2. Second equation is 
   $$\begin{gathered} x=y-3 \\ 6=9-3 \\ 6=6 \end{gathered}$$
   Hence satisfied.

Thus our answers are right.