Considering that: 1 Nickel = $0.05 and 1 Dime =$0.1 you can write two
equations:
0.05N+0.1D=6.9
N+D=96
Where N is the number of Nickels and D the number of Dimes.
Solving the system formed by the two equations (for substitution, for example)
you get your result.