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calculate her gross earnings in a week

Fionas regular hourly rate of pay is $21.50. She is paid at 1.5 times the regular rate of pay for time exceeding 37.5 hours in a week. calculate her gross earning for a week in which she worked 5,0,7,7,5, 8.5,8, and 7 hours on Saturday to Friday respectively 

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Ryan W. | Math & Science TutorMath & Science Tutor
Hello Amie, 
You should start by setting up equations using what you know. 
Here is an equation for how much Fionas is paid per hour when she does not exceed 37.5 hours y= 21.50x. Let y= the amount she is paid and x= the number of hours she work that are equal to or less than 37.5.
When she works over 37.5 hours, "she is paid 1.5 times the regular rate of $21.50". That is she is paid (21.50 x 1.5= 32.25 each hour over 37.5). So y= 21.50x +32.25z. Let z= the number of hours over 37.5. 
The problem says that she worked 5, 0, 7, 7, 5, 8.5, 8 and 7 hours. That is a total of 47.5. This is over 37.5 hours, but by how many hours? To figure this out, do 47.5-37.5= 10. So, let z=10 and x=37.5. Plug this into the equation we formulated.
y=21.50x +32.25z
y=21.50 (37.5) + 32.35 (10) 
y= 806.25 + 323.50
y= 1129.75
Fionas gross earning for the week was $1,129.75.
I hope this helps. If you need any clarifications,let me know. 
Donald K. | Student awaiting medical schoolStudent awaiting medical school
5.0 5.0 (1 lesson ratings) (1)
It appears that this gives Fiona 8 days of the week to work lol.  Its possible that one of the numbers doesn't belong?
So the first thing to do is to calculate how many hours Fiona worked (5+0+7+7+5+8.5+8+7).  If this exceeds 37.5, then you need to know how many hours she went over because the first 37.5 hours gets $21.50, and the remainder receives (1.5 x $21.50).  The set-up should look something like this:
(37.5 x 21.50) +((5+0+7+7+5+8.5+8+7) x (1.5 x $21.50))
Does that make sense?


lol oh my! im sorry it was 5, 0, 7, 7.5, 8.5, 8     i put a comma where there should of been a point! maybe you could explain again? that would be a great help, thanks. Math is very confusing for me no matter how hard i seem too work at it.
Ok so using the numbers above you would first add them together.
5+0+7+7.5+8.5+8+7    (I included the final 7 because it was in your original post.)
Which = 43 hours 
Well then you take 37.5 away from 43 hours (which will provide you with the hours of overtime that she worked.
43 - 37.5 = 5.5 hours
Next you take 37.5 hours and multiply it by $21.50.
37.5 X 21.5 = $806.25
Then you have to calculate your overage hour pay, so you multiply 5.5 (the amount of hours over 37.5) by (21.5 X 1.5) (which is her overage pay per hour).
So 21.5 X 1.5 = $32.25 per overage hour
Then 5.5 hours X 32.25 $/hr = $177.375 (in overage pay)
Finally you combine the two for her total pay.
$806.25 + $177.375 = $983.625
(*If rounding to the nearest cent it would be $983. 63)
Hope this helps!