1985 AJHSME Problems/Problem 16

Problem

The ratio of boys to girls in Mr. Brown's math class is $2:3$ . If there are $30$ students in the class, how many more girls than boys are in the class?

$\text{(A)}\ 1 \qquad \text{(B)}\ 3 \qquad \text{(C)}\ 5 \qquad \text{(D)}\ 6 \qquad \text{(E)}\ 10$

Solution

Let the number of boys be $2x$ , it follows that the number of girls is $3x$ . These two values add up to $30$ students, so $2x+3x=5x=30\Rightarrow x=6$

The difference between the number of girls and the number of boys is $3x-2x=x$ , which is $6$ , so $\boxed{\text{D}}$

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1985 AJHSME Problems/Problem 16

Problem

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