Posted by **Eleana M** on Tuesday, February 1, 2011 at 6:20pm.

Maxie counted her dimes,when she put them in a groups of 4 she had 2 left over, groups of 5 1 left over. What is the smallest number of dimes she could have over if she has more than 10

- Math -
**MathMate**, Tuesday, February 1, 2011 at 8:00pm
You are looking for the smallest number N that satisfies

N mod 4 = 2, ....(1)

N mod 5 = 1 .....(2)

Since N mod 4 = 2 can only be satisfied by an even number, N can only be a number that ends in the digit 6 if (2) is to be satisfied.

Since it is over 10, and 16 does not satisfy (1), we choose 26 as the smallest number over 10 that satisfies the two given conditions.

For a formal treatment of this class of problems, look up the "Chinese remainder theorem".

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