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| Math Central | Quandaries & Queries |
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Question from Leslie, a parent: Question: Janice has some marbles. When she divides them into groups of 4, she has 2 marbles left over. If she divides them into groups of 5, she will also have 2 left over. What is the least number of marbles she can have? |
Hi Leslie,
If Janice had 6 marbles and she divided them into groups of 4 she would have 2 left over. If she had 4 more marbles, that is 10 marbles and she divided them into groups of 4 she would have 2 left over. The same is true if she had 4 more marbles, 14 marbles.
If Janice had 7 marbles and she divided them into groups of 5 she would have 2 left over. If she had 5 more marbles, that is 12 marbles and she divided them into groups of 2 she would have 2 left over, and so on.
Continue to expand both lists,
6, 10, 14, ...
7, 12, 17, ...
and look for the smallest number that appears in both lists.
Penny
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