Q. 74 - Intermediate Algebra

Question

The sum of two number is $-16$. One number is $20$ less than the other. Find the numbers.

Step-by-Step Solution

Answer

The required numbers are $-18$ and $2$.

Step 1. Given and explanation

There are two numbers whose sum is $-16$ and one number is $20$ less than the other.

Assume the numbers to be $x,y$.

Their sum, i.e., $-16$ can be written as $x+y=-16$.

One number is $20$ less than the other can be written as $x=y-20$.

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

We have two equations, i.e. ,

$$\begin{gathered} x+y=-16 \\ x=y-20 \end{gathered}$$

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

$$\begin{gathered} (y-20)+y=-16 \\ 2y=-16+20 \\ 2y=4 \\ y=2 \end{gathered}$$

Step 3. Finding the value of other variable.

Putting $y=2$ in

$x+y=-16$ gives us,

$$\begin{gathered} x+2=-16 \\ x=-18 \end{gathered}$$

This shows that the two numbers are $-18\&2$.

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
   $$\begin{gathered} x+y=-16 \\ -18+2=-16 \\ -16=-16 \end{gathered}$$
   Hence satisfied.
2. Second equation is
   $$\begin{gathered} x=y-20 \\ -18=2-20 \\ -18=-18 \end{gathered}$$
   Hence satisfied.

Thus our answers are right.