Marisol is being paid $792 to provide nutrition counseling, It took her 8 hours more than she expected, so she earned $4 per hour less

Question

Marisol is being paid $792 to provide nutrition counseling, It took her 8 hours more than she expected, so
she earned $4 per hour less than she originally calculated. How long had she anticipated it would take to do
the job?

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King 5 months 2021-08-24T01:32:44+00:00 1 Answers 2 views 0

Answers ( )

    0
    2021-08-24T01:34:34+00:00

    Answer: 44 hours.

    Step-by-step explanation:

    Marisol is being paid $792.

    We know that the job took her 8 hours more than she expected, so if we define T as the time she expected, this job took her:

    T + 8 hours.

    The amount of money per hour that she expected is calculated as:

    $792/T = X

    And for those 8 extra hours, she won $4 less per hour, then we have:

    $792/(T + 8hs) = X – $4

    Then we have a system of equations:

    $792/T = X

    $792/(T + 8hs) = X – $4

    To solve this, we can notice that in the first equation X is isolated, then we could replace that in the second equation to get:

    $792/(T + 8hs) = $792/T – $4

    Now we can solve this for T.

    $792 = ($792/T – $4)*(T + 8hs)  = $792 + $792*(8hs/T) – $4*T + $32*hs

    0 = $792*(8hs/T) – $4*T + $32*hs

    Let´s multiply this both sides by T

    0*T = ($792*(8hs/T) – $4*T + $32*hs)*T

    0 = $792*8hs – $4*T^2 +$32*T*hs

    This is a quadratic equation, where i will write this witout units so it is easier to read and follow:

    0 = -4*T^2 + 32*T + 792*8

    The solutions cab be found by using the Bhaskara´s formula, these are:

    T = \frac{-32 +- \sqrt[2]{(32^2 - 4*(-4)*(792*8)} }{2*-4}  = \frac{-32 +-320}{-8}

    Then the solutions are:

    T = (-32 + 320)/-8 = -36 hours (This is a negative time, and it does not really have a meaning in this problem, so we can discard this option)

    The other solution is:

    T = (-32 – 320)/-8 = 44 hours.

    Then we can conclude that she expected the job would take 44 hours in total.

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