2002 AMC 12A Problem 2

Below is the professionally curated solution for Problem 2 of the 2002 AMC 12A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2002 AMC 12A solutions, or check the answer key.

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Concepts:work backwards linear equation

Difficulty rating: 1020

Cindy was asked by her teacher to subtract $3$ from a certain number and then divide the result by $9.$ Instead, she subtracted $9$ and then divided the result by $3,$ giving an answer of $43.$ What would her answer have been had she worked the problem correctly?

$15$

$34$

$43$

$51$

$138$

Solution:

Let $x$ be the number. Cindy computed $\dfrac{x-9}{3} = 43,$ so $x - 9 = 129$ and $x = 138.$

The correct computation gives $\dfrac{138-3}{9} = \dfrac{135}{9} = 15.$

Thus, the correct answer is A.

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