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