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25 Jul 2017, 22:40
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C
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Difficulty:
55%
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Question Stats:
63% (02:09) correct
37%
(02:31)
wrong
based on 169
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Scott paid his daughters Ally and Jordan each an allowance of d dollars for their work on the family's landscaping. They worked together for 12 hours, after which Jordan had to leave to meet a study group and Ally worked 3 more hours alone. To be fair to Ally, Scott paid her an additional amount so that each girl would receive the same hourly rate. In total, how many dollars did Scott spend?
A. 27/d
B. 5d/4
C. 9d/4
D. 27d
E. 30d
A. 27/d
B. 5d/4
C. 9d/4
D. 27d
E. 30d
26 Jul 2017, 16:19
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Bunuel
Scott paid his daughters Ally and Jordan each an allowance of d dollars for their work on the family's landscaping. They worked together for 12 hours, after which Jordan had to leave to meet a study group and Ally worked 3 more hours alone. To be fair to Ally, Scott paid her an additional amount so that each girl would receive the same hourly rate. In total, how many dollars did Scott spend?
A. 27/d
B. 5d/4
C. 9d/4
D. 27d
E. 30d
A. 27/d
B. 5d/4
C. 9d/4
D. 27d
E. 30d
Since wage (hourly rate) is payment/hours:
Jordan’s wage is d/12
Ally’s wage is d/15
Since Scott paid Ally an additional amount so that each girl would receive the same hourly rate, we can designate the additional amount as x:
d/12 = (d + x)/15
15d = 12(d + x)
15d = 12d + 12x
3d = 12x
d = 4x
d/4 = x
Thus, Scott paid out d + d + d/4 = 4d/4 + 4d/4 + d/4 = 9d/4.
Answer: C
General Discussion
26 Jul 2017, 00:32
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It has been given that Ally and Jordan each receive d dollars for the work.
In order to compensate, Ally was given an additional amount.
Let that amount be x, which is equal to \(\frac{d}{4}\) because she was paid for an addition \(\frac{3}{12}(\frac{1}{4})\) hours.
Hence, the total amount paid is \(2d + \frac{d}{4} = \frac{9d}{4}\)(Option C)
In order to compensate, Ally was given an additional amount.
Let that amount be x, which is equal to \(\frac{d}{4}\) because she was paid for an addition \(\frac{3}{12}(\frac{1}{4})\) hours.
Hence, the total amount paid is \(2d + \frac{d}{4} = \frac{9d}{4}\)(Option C)
