Maths Olympiad Prep

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Algebra Difficulty 2.2 Junior Find the answer

A team won 4040 of its first 5050 games. How many of the remaining 4040 games must this team win so it will have won exactly 70%70 \% of its games for the season?

Pick one

Solution

Noting that 70% is the same as 70100=710\frac{70}{100}=\frac{7}{10}, and that, when x is the amount of wins in the last 40 games, the fraction of games won is 40+x50+40=40+x90\frac{40+x}{50+40}=\frac{40+x}{90}, all we have to do is set them equal: 40+x90=710\frac{40+x}{90}=\frac{7}{10} 40+x=6340+x=63 x=(B) 23x=\boxed{\text{(B)}\ 23}

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.