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2002 AMC 10A Problem 6

Problem 6 of 25EasierAlgebra

Cindy was asked by her teacher to subtract 33 from a certain number and then divide the result by 9.9. Instead, she subtracted 99 and then divided the result by 3,3, giving an answer of 43.43. What would her answer have been had she worked the problem correctly?

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Solution

Let xx be the number. Cindy computed x−93=43,\dfrac{x-9}{3}=43, so x−9=129x-9=129 and x=138.x=138. The correct computation is 138−39=1359=15.\dfrac{138-3}{9}=\dfrac{135}{9}=15. Thus, the correct answer is A.

More practice

Concepts: linear equation · work backwards

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.