At a track meet 2/5 of the first place finishers went to Ohio State. One half of Ohio State's first place finishers were women. If 2/9 of the first place finishers who did NOT attend Ohio State were women, what fractional part of the total number of first place finishers were men?

Question

Paloma Hurley

Mathematics

8 March, 23:25

At a track meet 2/5 of the first place finishers went to Ohio State. One half of Ohio State's first place finishers were women. If 2/9 of the first place finishers who did NOT attend Ohio State were women, what fractional part of the total number of first place finishers were men?

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Answers (1)

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Gerald Dickerson · Answer 1

2/3

Step-by-step explanation:

The first place finishers can be divided into two groups: those who went to Ohio State, and those who did not attend Ohio State.

2/5 of the first place finishers went to Ohio State. 1/2 of these were women, which means 1/2 were men. The fraction of first place finishers who went to Ohio State AND were men is:

1/2 (2/5) = 1/5

3/5 of the first place finishers did not attend Ohio State. 2/9 of these were women, which means 7/9 were men. The fraction of first place finishers who did not attend Ohio State AND were men is:

7/9 (3/5) = 7/15

So the fraction of first place finishers who were men is:

1/5 + 7/15

= 3/15 + 7/15

= 10/15

= 2/3