Inequalities

Question

You have 2 jobs, one pays 5 dollars per hour and other pays 6 dollars per hour. You can work no more than 20 hours each week but you need atleast 90 dollars per week. Write a system of inequalities to represent and give 2 solutions to ur system

Answer 1

Hi Ramtin,

If x and y are the number of hours for the job paying $5/hr and $6/hr respectively

x ≥ 0, y ≥ 0

x + y ≤ 20

5x + 6y ≥ 90

To look for solutions find the intercepts of the lines and their point of intersections 

x + y =20 has intercepts at (0, 20) and (20, 0).

5x + 6y =90 has intercepts at (0, 15) and (18, 0)

Rewrite and solve for x and y.

y = 20 - x and plug into the second equation

5x + 6(20 - x) = 90

5x + 120 -6x =90

                 -x = -30 

x = 30, y = 20 -30 = -10 intersection point is (30, -10) This is not a solution y<0.

You can determine the solution you want from the above values that obey the inequalities.