Question 716172: A collection of coins is worth $6.35. There are 10 more nickels than dimes, and the rest of the coins are quarters. How many quarters are in the collection? I can't find anything like this in the book, please help!!!
Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website! Let  = number of nickels
Let  = number of dimes
Let  = number of quarters
given:
(1)  ( in cents )
(2) 
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You have 3 unknowns, but only 2 equations
so, you need a different approach.
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What is the most quarters you can have?
I know that
 , but that leaves 10 cents,
and I know there are at least 11 nickels
( if there was just 1 dime )
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That leave 35 cents, still no enough for 11
nickels
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Leaving 60 cents, That leaves 11 nickels = 55 cents
but not enough left for 1 dime
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leaving 85 cents.
85 - 55 = 30 or 3 dimes- there are 8 more nickels than dimes
If there were 13 nickels = 65 cents
85 - 65 = 20 cents -that's 2 dimes, I need 3 dimes
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That's 14 nickels and 4 dimes
perfect
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The answer seems to be 21 quarters, 14 nickels, and 4 dimes
There are 21 quarters
check:
OK
There might be a more logical approach to this,
but this will get you there.
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