1974 AMC 12 Problem 7

Attempt Problem 7 of the 1974 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1974 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

A town’s population increased by

1{,}200

people, and then this new population decreased by

11\%.

The town now had

32

less people than it did before the

1{,}200

increase. What is the original population?

1{,}200

11{,}200

9{,}968

10{,}000

none of these

Let

P

be the original population and apply the decrease to

P+1200

The final population is both

0.89(P+1200)

and

P-32

Let the original population be

P.

Then

0.89(P+1200)=P-32.

Therefore

0.11P=1100,

giving

P=10{,}000.

Therefore, the correct answer is D.

Problem 7 in other years