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 the answer is $\boxed{\text{D}}$.

See Also

1985 AJHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 15
Followed by
Problem 17
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AJHSME/AMC 8 Problems and Solutions


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