Question

In a certain town, 80% of all married men are working, and 75% of all married men are over 35 years old. Among working married men, 70% are over 35 years old. What proportion of non-working married men are over 35 years old?
answer: 95%
working is needed​

Answer 1

It helps to set up a two way table as shown below. Such tables compare 2 different variables. In this case, we're comparing the variables "working status" and "age".

Specifically, the working status separates the men into "working vs non-working". The age variable splits the men into groups of "35 or younger" and "over 35". Usually, but not always, each variable will take on two values.

Let's say this town had 1000 married men. 80% of this is 0.80*1000 = 800 to indicate there are 800 married working men. So we write this in the "total" column for the "working" row. This leaves 1000-800 = 200 nonworking married men, which will go right under the 800.

We're told that 75% of the married men are over 35, so 0.75*1000 = 750 married men are over 35. This goes in the "total" row for the "over 35" column. There are 1000-750 = 250 married men who are 35 and under.

As you can see, the stuff in the total column and the total row must add back to the grand total of 1000 married men overall.

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Another bit of info given is that "Among the working married men, 70% are over 35". We'll only focus on the "working" row. We have 800 total and 70% of this is 0.70*800 = 560 which is the number of working married men over 35. This leaves 800-560 = 240 married men who are not over 35.

At this point, we have 2 spots left in the table. Through guess and check, or using algebra, you should find that there are 190 non-working men over 35 and 10 non-working men who aren't over 35. Make sure that each row and column total checks out.

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By now, the table is fully filled out. See below.

Your teacher now asks "what proportion of non-working married men are over 35 years old?" which means we'll only focus on the "non-working" row. There are 200 men total here, and of this total, 190 are over 35.

So, 190/200 = 0.95 = 95% of the non-working married men are over 35.