1 nickle = 5 cents

1 dime = 10 cents

1 quarter = 25 cents

let

n = the number of nickels

d = the number of dimes

q = the number of quarters

A clerk was asked to change a $10 = 1000 cents

5n + 10d + 25q = 1000 divide both sides by 5

n + 2d + 5q = 200

She returned 9 more dimes than nickels

d = 9 + n

and twenty-one more quarters than dimes

q = d + 21

plug d = 9 + n into q = d + 21

q = 9 + n + 21

q = 30 + n

by solving the system of equations

plug d = 9 + n and q = 30 + n into n + 2d + 5q = 200

n + 2(9 + n) + 5(30 + n) = 200

by solving we find

n = 4 nickles

click here to see the step by step solution of the equation

d = 9 + 4

d = 13 dimes

q = 30 + 4

q = 34 quarters

the clerk gave back 4 nickles, 13 dimes and 34 quarters.