Question

The yoga class meets twice a week. On Tuesdays, the ratio of men to women is 1:6. On Thursdays, the ratio of men to women is 2:11.  On which day is the ratio of women higher at the yoga class?

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Answer 1

Tuesdays

Explanation:

Given men : women ratios of 1:6 and 2:11 on Tuesdays and Thursdays, respectively, you want to know which day has the higher proportion of women.

Comparing ratios

Ratios are most easily compared of one of the numbers is the same in both ratios. Here, we can double the first ratio to make the number units representing men be 2:

1 : 6 = 2 : 12 . . . . . ratio on Tuesdays

2 : 11 . . . . . . . . . . . ratio on Thursdays

There are relatively more women on Tuesdays. (12 > 11)

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Additional comment

We can also make the number representing men be 1. Dividing the second ratio by 2 gives ...

2 : 11 = 1 : 5.5

Now, we can see that 5.5 is less than 6, so the proportion of women is higher on Tuesdays. These ratios (6, 5.5) are effectively "unit rates", or women per man.