Problem:
All of the marbles in Maria's collection are red, green, or blue. Maria has half as many red marbles as green marbles and twice as many blue marbles as green marbles. Which of the following could be the total number of marbles in Maria's collection?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
We can let be the number of red marbles that Maria has. Since Maria has half as many red marbles as green, then we know that she has green marbles. Moreover, since she has twice as many blue marbles as green, then she will have blue marbles. Adding these together gives us , and so the answer must be a multiple of . Among the answer choices, only is a multiple of .
Thus, is the correct answer.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions