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You can work a total of no more than 40 hours each week at your two jobs. Housecleaning pays $4 hour and your sales job pays $8 per hour. You need to earn at least $120 each week to pay your bills. Write and graph a system of inequalities that shows the various numbers of hours you can work at each job.​

User Sga
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Let x be the number of hours you work at your housecleaning job and y be the number of hours you work at your sales job.

The first inequality represents the fact that you can work no more than 40 hours in total between the two jobs:
x + y ≤ 40

The second inequality represents the fact that you need to earn at least $120 per week:
4x + 8y ≥ 120

The third inequality represents the fact that you can only work positive hours at each job:
x ≥ 0
y ≥ 0

Graphically, this system of inequalities can be represented by a region on the xy-plane that is bounded by the lines x + y = 40, 4x + 8y = 120, x = 0 and y = 0.
This region is a triangle where x+y<=40, 4x+8y>=120 and x,y>=0

So, one possible solution is to work between 0 and 40 hours at the housecleaning job, and between 0 and 40 hours at the sales job, as long as the total number of hours worked is 40 or less and the total weekly income is $120 or more.
User Luisa
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