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

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:

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.