Analytic Math( Grade 10)

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A contractor rented a sander for 5h and a polisher for $50. For another job, she rented the sander for 4h and the polisher for 8h. The rental fees for the job totalled $56. Find the hourly rate charged for each tool.

  • Analytic Math( Grade 10) -

    Sander = X Dollars / hr.
    Polisher = Y Dollars/hr

    Eq1: 5X + 5Y = 60.
    Eq2: 4X + 8Y = 56.

    Multiply Eq1 by -4 and Eq2 by 5 and add.
    -20X - 20Y = -200.
    20X + 40Y = 280.

    20Y = 80,
    Y = 80 / 20 = 4.

    Substitute 4 for Y in Eq1:
    5X + 5*4 = 50,
    5X + 20 = 50,
    5X = 50 - 20 = 30,
    X = 30 / 5 = 6.

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