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A group of juniors and seniors took a test. Exactly of the juniors and exactly of the seniors passed the test. If the number of juniors who passed the test was 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.

 Apr 21, 2023
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Let j be the number of juniors and s be the number of seniors. We know that 3/5j=2/3(6/7s), so 3/5j=4/7s. Multiplying both sides by 35/12, we get 21j=20s, so j=20s/21. Thus, the fraction of the group that passed the test is 3/5j+6/7s = 3/5(20s/21)+6/7s = 44/35​.

 Apr 21, 2023

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