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?

Question

anonymous · Answer

first let's take the value of each. nickels are worth 5 cents, dimes are worth 10 and quarters are worth 25. 
nickels = n
dimes = d
quarters = q

anonymous · Answer

5n + 10d + 25q = 1,000 because we are dealing with cents. 1,000 cents is 10 dollars

anonymous · Answer

it says that 9 more dimes than nickels were returned so d=n+9

anonymous · Answer

5n + 10(n+9) + 25q = 1000

anonymous · Answer

then it says 21 more quarters than dimes so q=21+d and we know that d=n+9, therefore q=n+9+21

anonymous · Answer

5n + 10(n+9) + 25(n+9+21) = 1,000

anonymous · Answer

solve for n

anonymous · Answer

remember that n = nickels, after you solve for n plug in and solve for the rest