Question

An automobile salesman receives a monthly bonus check if his commission income is at least $7,700.00 in a given month. There are 48 automobiles on the lot for sale and he receives a commission of $700.00 per sale. Which inequality shows the number of automobiles,x , the salesman must sell in order for him to receive a bonus check at the end of the month?

Answer 1

The inequality that represents the number of cars he needs to sell is:
`x \geq 11`

Explanation:

The commission received by the salesman, can be modeled by the following expression:

`\text{commission}(x) = 700*x`

Where "x" is the number of sold cars. Since he needs to achieve a commission value of at least 7700, then the inequality that represents the number of cars he needs to sell is:

`700*x \geq 7700`

We can solve for "x" in order to find the number of cars he needs to sell:

`x \geq (7700)/(700)\\\\x \geq 11`

He needs to sell at least 11 cars.