91Ó°ÊÓ

A variable is a term that is used to represent an unknown value.

From given, let $x$ be the number of cars she sells to make an annual income of at least $\$40,000$.

Now, the average price of a car she sells is $\$30,500$.

Total price of the cars will be $\$30,500×x$.

She has $1.5\%$of commission on her sells.

That is,

That is equal to $\frac{1.5}{100}×\$30,500×x$.

She also has a salary of $\$24,000$

The inequality is:

$\$24,000+\left(\frac{1.5}{100}×\$30,500×x\right)â‰\yen \$40,000$

Simplify the inequality as shown below:

$\begin{array}{c}\$24,000+\left(\frac{1.5}{100}×\$30,500×x\right)â‰\yen \$40,000\\ \$24,000+457.5x−\$24,000â‰\yen \$40,000−\$24,000\\ 457.5xâ‰\yen \$16,000\\ xâ‰\yen 34.9≈35\end{array}$

Therefore, the number of cars needed to be sold is $xâ‰\yen 35$.

As $x>35$. Thus, Mrs. Lucas needs to sell minimum 35 cars so that she can have an annual income of at least $\$40,000$.