Official Guide Explanation:
Problem Solving #166




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Solution and Metadata

Question: 166
Page: 176
Difficulty: 5 (Moderate)
Category 1: Word Problems > Mixture Problems >
Category 2: Arithmetic > Percents > other

Explanation: If the team won 80% of its first 100 games, that means it won 80 games. If we say that the remaining number of games is x, and it won 50% of those, it won ((x)/2) more games. If the team won 70% of its games overall, we can set up a ratio: (70/100) = ((80 + ((x)/2))/(100 + x)). After simplifying the left side to (7/10), cross - multiply and solve for x:

7(100 + x) = 10(80 + ((x)/2))

700 + 7x = 800 + 5x

2x = 100

x = 50

Since x stood for the remaining games, and there were 100 games before that, the total number of games is 100 + 50 = 150, choice (D).

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