marie puts dimes in groups of 4 with 2 dimes left over. When she puts them in groups of 5, she had 1 left over? What is the smallest number of dimes she could have if she has more than 10?
in groups of 4 with 2 left over:
6 10 14 .... 94 98 102 106 110 114
in groups of 5 with 1 left over :
6 11 16 21 .....96 101 106 111 116 ....
looks like 106
or
4a + 2 = 5b + 1
4a = 5b - 1
a = (5b-1)/4
but 5b+1 > 100
5b > 99
b > 99/5 or 20, 21, ...
let b = 21, then a= 26
notice 4(26) + 2 = 106
and 5(21)+1 = 106
so he has 106 dimes
check:
106 dimes > $ 10
106 divided by 4 is 26 with a remainder of 2
106 divided by 5 is 21 with a remainder of 1