1987 AMC 8 Problem 18

Below is the professionally curated solution for Problem 18 of the 1987 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1987 AMC 8 solutions, or check the answer key.

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Concepts:fraction work backwards

Difficulty rating: 960

18.

Half the people in a room left. One third of those remaining started to dance. There were then $12$ people who were not dancing. What was the original number of people in the room?

$24$

$30$

$36$

$42$

$72$

Solution:

Of those remaining, $\dfrac13$ danced, so $\dfrac23$ did not. Thus $\dfrac23$ of the remaining people equals $12,$ giving $18$ remaining.

Those $18$ are half the original group, so the room started with $2 \times 18 = 36$ people.

Thus, the correct answer is C .

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