2005 CEMC Gauss (Grade 7) Problems/Problem 6

Problem

At a class party, each student randomly selects a wrapped prize from a bag. The prizes include books and calculators. There are $27$ prizes in the bag. Meghan is the first to choose a prize. If the probability of Meghan choosing a book for her prize is $2/3$, how many books are in the bag?

$\text{(A)}\ 15 \qquad \text{(B)}\ 9 \qquad \text{(C)}\ 21 \qquad \text{(D)}\ 7 \qquad \text{(E)}\ 18$

Solution

Since Meghan chooses a prize from $27$ in the bag and the probability of her choosing a book is $2/3$, then $2/3$ of the prizes in the bag must be books. Therefore, the number of books in the bag is $(2/3)(27) = 18$. The answer is $E$.