A clerk 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?

I don't know why but this is stumping me. Help plz.!

1 answer

number of nickels ---- x
number of dimes ---- x+9
number of quarters --- (x+9) + 21 = x + 30

so ...

5x + 10(x+9) + 25(x+30) = 1000
5x + 10x + 90 + 25x + 750 = 1000
40x = 160
x = 4

So 4 nickels, 13 dimes and 34 quarters

check:
4 nickesl === $0.20
13 dimes === $1.30
34 quarter == $8.50 for a total of $10.00