1 nickle = 5 cents

1 dime = 10 cents

1 quarter = 25 cents

$4.05 = 405 cents

Let

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

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

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

n + d + q = 40

n = d + 7

5n + 10d + 25q = 405

........

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

........

n = 2 nickles

d = 13 dimes

q = 7 quarters

Warren has 7 quarters.