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

Answer 1

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".