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

Vince has 5 times as many dimes as nickels:

d = 5n

In all he has $2.20 = 220 cents:

5n + 10d = 220

by solving the system of equations:

d = 5n

5n + 10d = 220

we find:

d = 20 dimes

n = 4 nickles

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

Vince has 20 dimes.