let

x = number of nickles

y = the number of dimes

z = number of quarters

1 nickle = $0.05

1 dime = $0.1

1 quarter = $0.25

Warren has 40 coins

x + y + z = 40

the coins total is 4.05

0.05x + 0.1y + 0.25z = 4.05

he has 7 more nickels than dimes

x = 7 + y

by solving the system of equations

x + y + z = 40

x = 7 + y

0.05x + 0.1y + 0.25z = 4.05

we find

z = 7 quarters

Warren has 7 quarters.