Math CentralQuandaries & Queries


Question from Tomco, a parent:

7/10 of the population believed 175,104,000 to be true - what is the total population.

We keep coming up with about 227,000,000 by just adding 30% to 175. Why doesn't that work?

We have since figured out the answer to be 250...but why?

Hi there.

If 7/10 of a group is men and there are 70 men, how many women are there? Not 30% of 70 (which would be 21), but rather, 30% of the total of 100.

The reason it isn't working for you is because you need to keep in mind that the 7/10 (i.e. the 70%) is the portion of the total population, so 30% of the total population is what you need to find, not 30% of the 70%.

In specific, note that 70% of 250 million is 175 million and 30% of 250 million is the other 75 million. Add them up to get 100% of the total: 175+ 75 = 250.

To find the correct answer from the information you are given you can use a little algebra. Let P be the total population then what you know is that

7/10 × P = 175,104,000

Now multiply both sides by 10/7 to get

P = 175,104,000 × 10/7

Stephen La Rocque and Harley Weston

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