System of inequality

Question

Jason works for a landscaping company during his summer vacation. He is paid $15 per hour for mowing lawns and $18 per hour for planting gardens. He can work a maximum of 40 hours per week, and would like to earn at least $340 this week. If x represents the number of hours mowing lawns and y represents the number of hours planting gardens; write a system of inequalities that can be used to represent the given conditions.

Determine and state one combination of hours that will allow jason to earn at least $340 this week while working a maximum of 40 hours.

Answer 1

I hope this helps!

That ordered pair (-10,30) is a possible solution to the system. However in this scenario, I overlooked that we are talking about hours worked. There are many possible solutions. For example, 20 hours each, 30 hours mowing and 10 hours planting gardens, etc. Use the Desmos calculator to your advantage and pick a positive x,y coordinate in the overlapping region. :)

Answer 2

40≥x≥0

40≥y≥0

x+y≤40

15x+18y≥340

If you plot these constraints using Desmos, there are several numbers that will work.

If Jason plants only gardens, he will make $720.

If he works 20 hours on each, he will make $660.

If he only mows lawns, he will make $600.