1989 AJHSME Problems/Problem 9

Problem

There are $2$ boys for every $3$ girls in Ms. Johnson's math class. If there are $30$ students in her class, what percent of them are boys?

$\text{(A)}\ 12\% \qquad \text{(B)}\ 20\% \qquad \text{(C)}\ 40\% \qquad \text{(D)}\ 60\% \qquad \text{(E)}\ 66\frac{2}{3}\%$

Solution

Besides ensuring the situation is possible, the $30$ students information is irrelevant.

From the first statement, we can deduce that $2$ of every $2+3=5$ students are boys. Thus, $2/5=40\% \rightarrow \boxed{\text{C}}$ of the students are boys.

Solution 2

$\frac{30}{2+3} = \frac{30}{5} = 6,$ and that is the base unit. Since there are 2 boys for every 5 people, $6\cdot2=12.$ Applying this into a fraction gives $\frac{12}{30} = \frac{2}{5} = 40\% = \boxed{\text{C}}.$

1989 AJHSME (Problems • Answer Key • Resources)
Preceded by Problem 8	Followed by Problem 10
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All AJHSME/AMC 8 Problems and Solutions

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1989 AJHSME Problems/Problem 9

Contents

Problem

Solution

Solution 2

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