Q48. - Algebra 2

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.

Step-by-Step Solution

Answer

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

Step 1 - Define the variable.

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

Step 2 - 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 $\$24,000$

Step 3 - 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 $\$24,000+\left(\frac{1.5}{100}\times \$30,500\times x\right)\ge \$40,000$.