Question

CAR SALES: For Exercise 48 and 49, use the following information.

Mrs. Lucas earns a salary of $\backslash (24,000$per year plus $1.5\%$ commission on her sales. If the average price of a car she sells is $\backslash )30,500$, about how many cars must she sell to make an annual income of at least $\$40,000$.

48. Write an inequality to describe this situation.

Short answer

The inequality is:$\$24,000+\left(\frac{1.5}{100}\times \$30,500\times \text{x}\right)\ge \$40,000$

Step-by-step solution

- Define the variable.

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

- Show the calculation.

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 $\$30,500\times x$.

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

That is,

$1.5\%$of $\$30,500\times x$

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

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

- State the inequality.

From the given, the inequality will be:

$\$24,000+\left(\frac{1.5}{100}\times \$30,500\times x\right)\ge \$40,000$

Therefore, the inequality is $\$24,000+\left(\frac{1.5}{100}\times \$30,500\times x\right)\ge \$40,000$.