Actually I think there is a new way to do this; just let == be congruence, and p be the number of pennies. We know that

p == 3(mod 4)

p == 16(mod 25)

Subtracting 12 on 3(mod 4) gives us p == -9(mod 4), and subtracting 25 on 16(mod 25) gives us p == -9(mod 25), so that means that p == -9(mod 100) which is the same as p == 91(mod 100).