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

Sue has $2.10 = 210 cents in nickles and dimes:

5n + 10d = 210 divide both sides by 5

n + 2d = 42

she has 9 more dimes than nickles

d = n + 9

by solving the system of equations:

n + 2d = 42

d = n + 9

we find:

n = 8 nickles

d = 17 dimes

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

Sue has 8 nickles and 17 dimes.