FERMAT 1998 Problem 22

There are four unequal, positive integers a,b,c, and N such that N=5a+3b+5c. It is also true that N=4a+5b+4c and N is between 131 and 150. What is the value of a+b+c?

Answer Choices
A. 13
B. 17
C. 22
D. 33
E. 36