In 1950, the populations of Akron and Bloomington were equal. Since then, Akron’s population has increased by 45%, whereas Bloomington’s population has decreased by 15,000. If the combined population of the two cities has increased by 10% since 1950, what is the current population of Akron?

Answer Choices

Correct answer marked below

A. 60,000

B. 87,000

Correct

C. 96,000

D. 105,000

E. 132,000

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Comments

ChristianJun 10

The combined population increased by 10% is the key. Let each original be x, so original total = 2x. Akron now = 1.45x, Bloomington now = x - 15000. Combined now = 1.45x + x - 15000 = 2.45x - 15000. This equals 1.10(2x) = 2.2x. So 2.45x - 15000 = 2.2x → 0.25x = 15000 → x = 60000. Then Akron now = 1.45 * 60000 = 87000.

MystiqueJun 16

Nice, I got 87000 too. The part that tripped me up was that the 10% increase applies to the combined total, not each city.

SebastianJun 13

How did you get 1.10(2x)? I get that combined increased by 10%, but original combined is 2x, so 10% more is 2.2x. Yes.

LeoJul 29

I set up the equation and got x = 60,000, but then I mistakenly chose 60,000 as the answer. Classic trap. The question asks for current population of Akron, not the original.

VigneshAug 10

Happens to the best of us. The choices include both 60k and 87k, so they know people will do that.

DhruvSep 29

This one is tricky because Bloomington's decrease is a fixed number, not a percentage. I had to read it twice to make sure I wasn't misinterpreting.

AdyantMay 26

Is there a faster way to backsolve? I tried plugging in choices for Akron's current population, but got tangled up. The algebra seems cleaner.

PrabhaankMay 27

Backsolving might be messy because you also need to find Bloomington's original. Algebra is probably faster here.

What this question tests

What it tests

Your ability to compute percentage change, percentage of a whole, and to work backwards from a final value.

Common trap

Treating successive percentage changes as additive — a 10% rise then a 10% fall is not back to the start.