Question

Mahmoud earns $450 per week plus a 20% commission as a car salesman. He wants his

Answer 1

The complete question implies that we define an inequality that represents the relationship between the number of hours worked in a week and the weekly sales

The inequality that relates the number of hours to the weekly sales is:

$450 + 0.20x \ge 35y$

We make use of the following representation:

$x \to$ weekly sales from cars.

$y \to$ hours worked in a week

His weekly salary is then calculated as:

Salary (S) = Earnings per week + Commission * Sales from car

So, we have:

$S = 450 + 20\% * x$

Express percentage as decimal

$S = 450 + 0.20* x$

$S = 450 + 0.20x$

Assume he works for y hours in a week.

His hourly rate is:

$Hourly = \frac{S}{y}$ --- i.e. weekly salary divided by number of hours

$Hourly = \frac{450 + 0.20x}{y}$

For this rate to be at least $\ 35$, the following condition must be true

$Hourly \ge 35$ --- i.e. is hourly rate must be greater than or equal 35

So, we have:

$\frac{450 + 0.20x}{y} \ge 35$

Multiply both sides by y

$450 + 0.20x \ge 35y$