SOLUTION: Cookie has 97 coins in her collection – all either nickels, dimes or quarters. If 77 of her coins are quarters and dimes and the total value of her coins is $13.95, how many quarte

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Question 912756: Cookie has 97 coins in her collection – all either nickels, dimes or quarters. If 77 of her coins are quarters and dimes and the total value of her coins is $13.95, how many quarters does she have?
Please help.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
– all either nickels, dimes or quarters.
Cookie has 97 coins in her collection
n+d+q = 97

If 77 of her coins are quarters and dimes
d+q=77

And also that implies that the other 97-77 or 20 coins are nickels.
So n = 20

the total value of her coins is $13.95
5n + 10d + 25q = 1395

So we have this system:

system%28n%2Bd%2Bq+=+97%2Cd%2Bq=77%2Cn=20%2C5n+%2B+10d+%2B+25q+=+1395%29

Substitute n=20

system%2820%2Bd%2Bq+=+97%2Cd%2Bq=77%2C20=20%2C5%2820%29+%2B+10d+%2B+25q+=+1395%29

Simplify

system%28d%2Bq+=+77%2Cd%2Bq=77%2C100+%2B+10d+%2B+25q+=+1395%29

Simplify and delete duplicate equation:

system%28d%2Bq+=+77%2C10d+%2B+25q+=+1295%29 

Solve that system and get d=42,q=35

Solution: 20 nickels, 42 dimes, 35 quarters.

Edwin