Problem:
In a jar of red, green, and blue marbles, all but are red marbles, all but are green, and all but are blue. How many marbles are in the jar?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
There are non-blue marbles. That is, there are altogether red and green marbles. There are also non-red marbles and non-green marbles, so there are two more red marbles than green marbles. Therefore there are red marbles and green marble. Because of the non-green marbles are red, the other $54 must be blue. The total number of marbles is .
Let , and be the number of green, blue, and red marbles respectively. Then
Adding all three equations together, , so .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions