1 quarter = 15 cents

1 dime = 10 cents

let

q = the number of quarters, q>=0, q is integer

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

Leo has 4.80 in dimes and quarters

10d + 15q = 480 divide both sides by 5

2d + 3q = 96

He has 6 more dimes than quarters.

d = q + 6

by solving the system of equations:

d = q + 6

2d + 3q = 96

we find:

d = 22.8

q = 16.8

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

since the solutions of the system are not integers follows that the problem has no solution.