1 nickel = 5 cents

1 dime = 10 cents

let

n = the number of nickels, n>=0, n is integer

d = the number of dimes, d>=0, d is integer

A piggy bank contains 100 coins consisting of nickels and dimes:

n + d = 100

The total value of the coins is $8.50 = 850 cents:

5n + 10d = 850 divide both sides by 5

n + 2d = 170

by solving the system of equations:

n + d = 100

n + 2d = 170

we find:

n = 30 nickels

d = 70 dimes

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

the bank contains 30 nickels and 70 dimes.