2017 AMC 8 Problems/Problem 9
Contents
Problem
All of Marcy'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?
Solution 1
3
Solution 2
Since of the marbles are blue and
are red, it is clear that the total number of marbles must be divisible by
. If there are
marbles, then
are blue,
are red, and
are green, meaning that there are
yellow marbles. This is impossible. Trying the next multiple of
,
, we find that
are green,
are red, and
are green, meaning that the minimum number of yellow marbles is
.
Video Solution (CREATIVE THINKING!!!)
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Video Solution
https://youtu.be/rQUwNC0gqdg?t=770
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See Also
2017 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 8 |
Followed by Problem 10 | |
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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