SOLUTION: 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?

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Question 657292: 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?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +n+ = number of nickels
Let +d+ = number of dimes
Let +q+ = number of quarters
given:
(1) +d+=+n+%2B+9+
(2) +q+=+d+%2B+21+
(3) +5n+%2B+10d+%2B+25q+=+1000+ ( in cents )
----------------------------
From (1):
(1) +n+=+d+-+9+
Substitute (1) and (2) into (3)
(3) +5%2A%28+d+-+9+%29+%2B+10d+%2B+25%2A%28+d+%2B+21+%29+=+1000+
(3) +5d+-+45+%2B+10d+%2B+25d+%2B+525+=+1000+
(3) +40d+=+1000+-+525+%2B+45+
(3) +40d+=+520+
(3) +d+=+13+
--------------
and
(1) +n+=+d+-+9+
(1) +n+=+13+-+9+
(1) +n+=+4+
and
(2) +q+=+d+%2B+21+
(2) +q+=+13+%2B+21+
(2) +q+=+34+
She returned
4 nickels
13 dimes
34 quarters
----------
check:
(3) +5%2A4+%2B+10%2A13+%2B+25%2A34+=+1000+
(3) +20+%2B+130+%2B+850+=+1000+
(3) +1000+=+1000+
OK