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Ten theater students are to begin work on a set for a musica

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Ten theater students are to begin work on a set for a musica

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Ten theater students are to begin work on a set for a musical. Working at a constant rate, they will finish the set in 60 days, but the director of the musical decides they need to finish in 50 days. How many more theater students, working at the same constant rate, must work to finish the set on time?

A. 2
B. 3
C. 5
D. 10
E. 12

OA A

Source: Veritas Prep

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BTGmoderatorDC wrote:
Ten theater students are to begin work on a set for a musical. Working at a constant rate, they will finish the set in 60 days, but the director of the musical decides they need to finish in 50 days. How many more theater students, working at the same constant rate, must work to finish the set on time?

A. 2
B. 3
C. 5
D. 10
E. 12

OA A

Source: Veritas Prep
We are given that 10 theater students will finish a set in 60 days. Since rate = work/time, the rate of those students is 1/60 = 1/60. However, since the set needs to be completed in 50 days, we can create the following proportion to determine how many more students are needed, to complete the job in 50 days:

10 students is to a rate of 1/60 as x students is to a rate of 1/50.

10/(1/60) = x/(1/50)

600 = 50x

12 = x

Thus, 2 more students will be needed to complete the set in 50 days.

Answer: A

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BTGmoderatorDC wrote:
Ten theater students are to begin work on a set for a musical. Working at a constant rate, they will finish the set in 60 days, but the director of the musical decides they need to finish in 50 days. How many more theater students, working at the same constant rate, must work to finish the set on time?

A. 2
B. 3
C. 5
D. 10
E. 12
(50 days)/(60 days) = 5/6.
To finish the job in 5/6 of the normal time, the crew requires 6/5 of the normal number of students -- an increase of 1/5:
(1/5)(10) = 2 more students.

The correct answer is A.

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