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The amounts of time that three executives worked on a special campaign

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Bunuel
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The amounts of time that three executives worked on a special campaign [#permalink] New post   25 Dec 2017, 01:13
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The amounts of time that three executives worked on a special campaign are in the ratio of 1 to 2 to 5. If they worked an average (arithmetic mean) of 44 hours per person on the campaign, how many hours did the executive who worked the longest spend on the campaign?

A. 220
B. 132
C. 82.5
D. 75
E. 27.5
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C
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DavidTutorexamPAL
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Re: The amounts of time that three executives worked on a special campaign [#permalink] New post   25 Dec 2017, 01:58
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Bunuel wrote:
The amounts of time that three executives worked on a special campaign are in the ratio of 1 to 2 to 5. If they worked an average (arithmetic mean) of 44 hours per person on the campaign, how many hours did the executive who worked the longest spend on the campaign?

A. 220
B. 132
C. 82.5
D. 75
E. 27.5


As we have the ratios and the total, we'll just calculate.
This is a Precise approach.

The three executives together worked for a total of 1 + 2 + 5 = 8 'ratio units'.
Snce they worked for an average of 44 hours, they worked for a total of 44*3 = 132 hours.
Then each ratio unit is worth 132/8 = (80+40+12)/8 = 10 +5 + 1.5 = 16.5 hours.
Therefore the employee who worked the longest (for 5 ratio units) worked for 5*16.5 = 82.5 hours.

(C) is our answer.
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CEdward
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Re: The amounts of time that three executives worked on a special campaign [#permalink] New post   24 Jan 2021, 19:20
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e1:e2:e3 = 1:2:5 = 1x:2x:5x

1x + 2x + 5x = 8x <---Total amount of time spent by all three

Avg = 44 = 8x / 3
x = 16.5

5(16.5) = 82.5

Answer is C.
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Re: The amounts of time that three executives worked on a special campaign [#permalink] New post   10 Jun 2023, 10:38
Bunuel wrote:
The amounts of time that three executives worked on a special campaign are in the ratio of 1 to 2 to 5. If they worked an average (arithmetic mean) of 44 hours per person on the campaign, how many hours did the executive who worked the longest spend on the campaign?

A. 220
B. 132
C. 82.5
D. 75
E. 27.5

\(x + 2x + 5x = 44*3\)

Or, \(8x = 132\)

Thus, \(5x = \frac{132}{8}*5 = 82.50\), Answer must be (C)
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Re: The amounts of time that three executives worked on a special campaign [#permalink]
10 Jun 2023, 10:38
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