there are $4.20 in nickel and quarters. There are 6 more nickels than quarters there. How many coins

there are $4.20 in nickel and quarters. There are 6 more nickels than quarters there. How many coins of each are there

We're given two equations:

1. n = q + 6
2. 0.05n + 0.25q = 4.2

Substitute equation (1) into equation (2):
0.05(q + 6) + 0.25q = 4.2

Multiply through and simplify:
0.05q + 0.3 + 0.25q
0.3q + 0.3 = 4.2

To solve for q, we type this equation into the search engine and we get:
q = 13

To solve for n, we plug in q = 13 into equation (1):
n = 13 + 6
n = 19