2012 AMC 10B Problems/Problem 4
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[hide]Problem 4
When Ringo places his marbles into bags with 6 marbles per bag, he has 4 marbles left over. When Paul does the same with his marbles, he has 3 marbles left over. Ringo and Paul pool their marbles and place them into as many bags as possible, with 6 marbles per bag. How many marbles will be leftover?
Solution 1
In total, there were marbles left from both Ringo and Paul.We know that . This means that there would be marble leftover, or .
Solution 2 (modulo)
Let be the number of marbles Ringo has and let be the number of marbles Paul has. we have the following equations: Adding these equations we get: We know that so therefore: Thus when Ringo and Paul pool their marbles, they will have marble left over.
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See Also
2012 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
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All AMC 10 Problems and Solutions |
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