How to write a system of inequalities for this story problem.?

Mark can work for at most 20 hours a week. He needs to earn at least $75 to cover his weekly expenses. His dog-walking job pays $5 dollars per hour and his car wash job pays $4 dollars and hour. Write a system of inequalities to model the situation.


1 Answer

  • 8 years ago

    I've assigned letter variables to each thing for simplicity's sake...

    Work per week (W) <= 20 hrs

    Total earnings (E) >= $75

    Earnings for dog-walking (ED) = $5/hr

    Earnings for car-washing (EC) = $4/hr

    Hours worked dog-walking (HD)

    Hours worked for car-washing (HC)

    And most importantly, the synthesis:

    HD + HC <= 20


    HD(ED) + HC(EC) >= 75

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