1995 AJHSME Problems/Problem 14

Problem

A team won $40$ of its first $50$ games. How many of the remaining $40$ games must this team win so it will have won exactly $70 \%$ of its games for the season?

$\text{(A)}\ 20 \qquad \text{(B)}\ 23 \qquad \text{(C)}\ 28 \qquad \text{(D)}\ 30 \qquad \text{(E)}\ 35$

Solution

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

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1995 AJHSME Problems/Problem 14

Problem

Solution