2002 AMC 12P Problems/Problem 6

Problem

Participation in the local soccer league this year is $10\%$ higher than last year. The number of males increased by $5\%$ and the number of females increased by $20\%$ . What fraction of the soccer league is now female?

$\text{(A) }\frac{1}{3} \qquad \text{(B) }\frac{4}{11} \qquad \text{(C) }\frac{2}{5} \qquad \text{(D) }\frac{4}{9} \qquad \text{(E) }\frac{1}{2}$

Solution 1

Let the amount of soccer players last year be $x$ , the number of male players last year to be $m$ , and the number of females players last year to be $f.$ We want to find $\frac{1.2f}{1.1x},$ since that's the fraction of female players now. From the problem, we are given $x=m+f$ $1.1x=1.05m+1.2f.$ Eliminating $m$ and solving for $\frac{1.2f}{1.1x}$ gives us our answer of $\boxed{\textbf{(B) } \frac {4}{11}}.$

Solution 2

WLOG, let the amount of soccer players last year be $100$ , the number of male players last year to be $50$ , and the number of females players last year to be $50.$ That means that this year, the number of players is $110, the number of male players is

2002 AMC 12P (Problems • Answer Key • Resources)
Preceded by Problem 5	Followed by Problem 7
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All AMC 12 Problems and Solutions

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2002 AMC 12P Problems/Problem 6

Contents

Problem

Solution 1

Solution 2

See also