algebra

You can work a total of no more than 34 hours per week at your two jobs. House cleaning pays $8 per hour and your sales job pays $6 per hour. You need to earn at least $245 per week to cover your expenses. Write a system of inequalities that shows the various numbers of hours you can work at each job.

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  1. Your total pay for the 2 jobs must be at least 245 dollars.

    Pay1 + Pay2 >= 245

    The pay for your first job, cleaning, is 8 dollars times the number of hours, h, worked at that job.

    Pay1 = 8h

    So:

    8h + Pay2 >= 245

    The pay for your second job, sales, is 6 dollars times the number of hours worked at that job.

    Pay2 = 6 * SalesHours
    or
    Pay2 = 6x

    So:

    8h + 6x >= 245

    That's one inequality.

    We also know that the total number of hours worked, h + x, cannot exceed 34. So:

    h + x <= 34

    There's a second inequality. Almost done.

    It is impossible to work less than 0 hours at a job, so both h and x, individually, can be a minimum of 0. Therefore:

    h >= 0 <= x

    So the final set of inequalities is as follows:

    8h + 6x >= 245
    h + x <= 34
    h >= 0 <= x

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