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A group of juniors and seniors took a test. Exactly $\frac{3}{5}$ of the juniors and exactly $\frac{6}{7}$ of the seniors passed the test. If the number of juniors who passed the test was $\frac{2}{3}$ of the number of seniors who passed the test, what fraction of the entire group passed the test? Express your answer as a common fraction.

 Nov 18, 2022
 #1
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The answer is 7/20.

 Nov 18, 2022
 #2
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S==Seniors  J==Juniors
Let the total number of kids ==123


S==63
j ==60


3/5 J ==36 juniors passed the test
 6/7 S ==54 seniors passed the test


36 / (2/3) ==54 


[36 + 54] / [60 + 63] ==90 / 123 ==30 / 41
30/41 of total students passed the test

 Nov 18, 2022

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