1 nickle = 5 cents

1 quarter = 25 cents

let

n = the number of nickles, n>=0

q = the number of quarter, q>=0

A parking meter contains nickles and quarters worth $8.50 = 850 cents

5n + 25q = 850

There are 58 coins in all:

n + q = 58

by solving the system of equations:

5n + 25q = 850

n + q = 58

we find:

n = 30 nickles

q = 28 quarters

click here to see the step by step solution of the system of equations:

there are 30 nickles and 28 quarters in the parking meter.