Aclerk was asked to change a $10 bill. she returned 9 more dimes than nickels and twenty-one more quarters than dimes. how many coins of each did she return? writer

So.. let's say, the amount of dimes is "d" and nickels is "n" and quarters is "q"

"She returned 9 more dimes than nickels", so.. whatever "n" is, "d" is 9 more than that, or d = n + 9

"twenty-one more quarters than dimes", so, whatever "d" is, "q" is 21 more than that, or q = d + 21

we know, she was just changing the $10, so all nickels and dimes and quarters will add up to 10

thus    

solve for "d", to see how many dimes she gave

what about quarters? well, q = d + 21
and nickels?   well, d - 9 = n