Inequalities
Let x = number of hours worked by Quentin.
y = number of cars sold by Quentin.
The total earnings are calculated as:
E = 8x + 280y
He wants to earn at least $1040 per week, thus:
8x + 280y ≥ 1040
Dividing by 8:
x + 35y ≥ 130
Solving for x:
x ≥ 130 - 35y
Supposse he sells not a single car (y = 0). Thus:
x ≥ 130
He needs to work a minimum of 130 hours per week.
One week has 7*24 = 168 hours.
It's possible to work that many hours a week, but it's not reasonable. He would only have 38 hours to sleep, rest, eat, etc.
One solution is y = 0, x = 130 but it's not reasonable in the context of the problem.
There are many other possible solutions. For example, if he sells y = 10 cars in the week (quite possible), then:
x ≥ 130 - 350
x ≥ -220
One solution could be x = -100, y = 10. but it's not possible to work for -10 hours.
