2002 AMC 10A Problem 6

Attempt Problem 6 of the 2002 AMC 10A 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 2002 AMC 10A solutions, or check the answer key.

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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?

$15$

$34$

$43$

$51$

$138$

Answer: A

Concepts:linear equation work backwards

Difficulty rating: 1120

Solution:

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

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

Thus, the correct answer is A.

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