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A worker is paid n dollars per hour for the first 8 hours she works in

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A worker is paid n dollars per hour for the first 8 hours she works in [#permalink]

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New post 24 Dec 2017, 23:37
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A worker is paid n dollars per hour for the first 8 hours she works in a day and for every hour after the first 8 she is paid c dollars. If she works 12 hours on Monday, 7 on Tuesday, 11 on Wednesday, 6 on Thursday, and 4 on Friday, What is her average hourly wage for that week?

A. 40n/(40 + c)

B. 8(n + c)

C. 8(n + c)/5

D. (33n + 7c)/40

E. n + c
[Reveal] Spoiler: OA

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Re: A worker is paid n dollars per hour for the first 8 hours she works in [#permalink]

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New post 25 Dec 2017, 00:03
Bunuel wrote:
A worker is paid n dollars per hour for the first 8 hours she works in a day and for every hour after the first 8 she is paid c dollars. If she works 12 hours on Monday, 7 on Tuesday, 11 on Wednesday, 6 on Thursday, and 4 on Friday, What is her average hourly wage for that week?

A. 40n/(40 + c)

B. 8(n + c)

C. 8(n + c)/5

D. (33n + 7c)/40

E. n + c


We'll go for a Precise solution because calculating an average is usually very simple.

12 hours Monday - 8 hours at $n per hour and 4 hours at $c per hour = 8n + 4c
7 hours Tuesday - 7n
11 hours Wednesday - 8n + 3c
6 hours Thursday - 6n
4 hours Friday - 4n
Combined: n*(8+7+8+6+4) + c*(4+3) = 33n + 7c

If we like we can already mark (D) as it is the only answer that fits.
To validate, we'll finish the calculation by calculating the total number of hours worked: 12+7+11+6+4 = 40

(D): (33n + 7c)/40 is, indeed, our answer.
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Re: A worker is paid n dollars per hour for the first 8 hours she works in [#permalink]

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New post 25 Dec 2017, 11:29
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Bunuel wrote:
A worker is paid n dollars per hour for the first 8 hours she works in a day and for every hour after the first 8 she is paid c dollars. If she works 12 hours on Monday, 7 on Tuesday, 11 on Wednesday, 6 on Thursday, and 4 on Friday, What is her average hourly wage for that week?

A. 40n/(40 + c)

B. 8(n + c)

C. 8(n + c)/5

D. (33n + 7c)/40

E. n + c


\(average=\frac{sum.wage}{total.hours}\)

Per day she receives \(n\) for the first 8 and \(c\) for hours above 8.

She worked a total of \((12+7+11+6+4)=40=hours\)
The sum of her wages was: \(n(7+6+4+8+8)+c(4+3)=33n+7c\)

So her average is: \(\frac{33n+7c}{40}\)

(D) is the answer.
Re: A worker is paid n dollars per hour for the first 8 hours she works in   [#permalink] 25 Dec 2017, 11:29
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A worker is paid n dollars per hour for the first 8 hours she works in

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