SOLUTION: Mark is a working student, and he can work for at most 20 hours a week. He needs to earn at least Php 3,500 to cover his weekly expenses. His service-crew job pays Php 150 per ho

Question 1162858: Mark is a working student, and he can work for at most 20 hours a week.
He needs to earn at least Php 3,500 to cover his weekly expenses. His
service-crew job pays Php 150 per hour and his job as a car wash attendant
pays Php 75 per hour.
What variables will you use?
What system of inequalities represent the information?
Show your solution.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
as far as i know, systems of ineqalities are solved graphically.
your inequalities are:
x + y <= 20
150x + 75y >= 3500
using the desmos.com calculator, graph the opposite of these inequalities.
you will graph:
x + y >= 20
150x + 75y <= 3500
the area of the graph that is not shaded will be your solution.
the graph looks like this.

you can see from the graph that the region of feasibility occurs when y is less than 0.
since both x and y have to be greater than or equal to 0, you have no solution.
a simple test will confirm this to be true.
20 * 150 = 3000.
that's the most that can be made if the number of hours has o be less than or equal to 20.

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