2017 AMC 8 Problems/Problem 9
Contents
Problem 9
All of Macy's marbles are blue, red, green, or yellow. One third of her marbles are blue, one fourth of them are red, and six of them are green. What is the smallest number of yellow marbles that Macy could have?
Video Solution
https://youtu.be/rQUwNC0gqdg?t=770
Solution
The green marbles and yellow marbles form
of the total marbles. Now suppose the total number of marbles is
. We know the number of yellow marbles is
and a positive integer. Therefore,
must divide
. Trying the smallest multiples of
for
, we see that when
, we get there are
yellow marbles, which is impossible. However when
, there are
yellow marbles, which must be the smallest possible.
See Also
2017 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 8 |
Followed by Problem 10 | |
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