How many nickles and dimes are $5.20 if there are six times more nickles than dimes?

In looking for the number of nickel and dimes we need to establish first equations:
n = $0.05
d = $0.1

0.05n + 0.1d = 5.20
0.05n = 6 (0.1d) ; n = 0.083d

Then we will solve it by substitution:
0.05(0.083d) + 0.1d = 5.20
0.42d + 0.1d = 5.20
0.52d = 5.20
d = 10

n = 0.083(10)
n = 0.83