Difference between revisions of "2007 AMC 8 Problems/Problem 20"

Revision as of 22:41, 9 December 2012

Problem

Before district play, the Unicorns had won $45$ of their basketball games. During district play, they won six more games and lost two, to finish the season having won half their games. How many games did the Unicorns play in all?

$\textbf{(A)}\ 48\qquad\textbf{(B)}\ 50\qquad\textbf{(C)}\ 52\qquad\textbf{(D)}\ 54\qquad\textbf{(E)}\ 60$

@@ Line 1: / Line 1: @@
-Regular season wins and losses are related in two ways:
+==Problem==
+Before district play, the Unicorns had won <math>45</math> of their basketball games. During district play, they won six more games and lost two, to finish the season having won half their games. How many games did the Unicorns play in all?
-wins / (wins + losses) = 0.45
+<math> \textbf{(A)}\ 48\qquad\textbf{(B)}\ 50\qquad\textbf{(C)}\ 52\qquad\textbf{(D)}\ 54\qquad\textbf{(E)}\ 60 </math>
-wins + 6 = losses + 2
-So wins + 4 = losses or wins = losses - 4
-so wins / (wins + wins + 4) = 0.45 or 9/20
-so 20 * wins = 18 * wins + 9 * 4
-so wins = 9 * 2 = 18
-so losses = 22
-so regular season games = 40.
-So the total number of games is 40 + 6 + 2 = 48, or (A).
-This is easily checked by finding 45% of 40 = 18 and noticing an 18-22 record + a 6-2 record is a 24-24 record. So another reasonable strategy in this context is to just check each of the answer choices.

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Difference between revisions of "2007 AMC 8 Problems/Problem 20"

Revision as of 22:41, 9 December 2012

Problem