swerve wrote:in a certain performance of a 3-act play, the first act was 18 minutes shorter than the third act and half as long as the second act. If the average (arithmetic mean) length of the 3-act was 46 minutes, how many minutes long was the third act?
A. 30
B. 39
C. 46
D. 48
E. 66
Total number of minutes = (number of acts)(average number of minutes per act) = 3*46 = 138.
We can PLUG IN THE ANSWERS, which represent the time for the third act.
When the correct answer is plugged in, the total number of minutes = 138.
B: 39 minutes
Since the first act is 18 minutes shorter than the 39-minute third act, the first act = 39-18 = 21 minutes.
Since the 21-minute first act is 1/2 as long as the second act, the second act = 42 minutes.
Total time = 39+21+42 = 102 minutes.
The total number of minutes is TOO SMALL.
Eliminate A and B.
B: 48 minutes
Since the first act is 18 minutes shorter than the 48-minute third act, the first act = 48-18 = 30 minutes.
Since the 30-minute first act is 1/2 as long as the second act, the second act = 60 minutes.
Total time = 48+30+60 = 138 minutes.
Success!
The correct answer is
D.
Algebra:
Let t = the third act.
Since the first act is 18 minutes shorter than the third act, the first act = t-18.
Since the first act is 1/2 as long as the second act, the second act is twice as long as the first act:
2(t-18).
Since the total number of minutes for all 3 acts = 138, we get:
t + (t-18) + 2(t-18) = 138
4t - 54 = 138
4t = 192
t = 48.
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