Let N= number of nickels and D=number of dimes. So N+D=132, D=132-N.
Value: 0.05N+0.1D=10.10. So 0.05N+0.1(132-N)=10.10.
0.05N+13.2-0.1N=10.10, 3.1=0.05N, N=3.1/0.05=310/5=62. D=132-62=70.
There are 62 nickels and 70 dimes, worth 62×0.05+70×0.10=3.10+7=$10.10.