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

Jane has four times as many dimes as nickles:

d = 4n

The total value of the coins is $3.60 = 360 cents:

5n + 10d = 360

We have the following system of equations:

d = 4n

5n + 10d = 360

........

click here to see the system of equations solved for d and n

........

d = 32 dimes

n = 8 nickles

Jane has 8 nickles and 32 dimes.