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## 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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Mathematics
5 months
2021-08-24T01:32:44+00:00
2021-08-24T01:32:44+00:00 1 Answers
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## Answers ( )

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:

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.