SOLUTION: a piggy bank contains 24 coins,all of which are nickels,dimes and quarters.If the total value of the coins is two dollars,what combinations of coins are possible?

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Question 274250: a piggy bank contains 24 coins,all of which are nickels,dimes and quarters.If the total value of the coins is two dollars,what combinations of coins are possible?
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:
n+%2B+d+%2B+q+=+24
5n+%2B+10d+%2B+25q+=+200
----------------------
8%2A25+=+200
n+%2B+d+%2B+q+=+8
---------------
7%2A25+=+175
5n+=+25
n+%2B+d+%2B+q+=+12
---------------
6%2A25+=+150
10%2A5+=+50
n+%2B+d+%2B+q+=+16
----------------
5%2A25+=+125
15%2A5+=+75
n+%2B+d+%2B+q+=+20
---------------
4%2A25+=+100
20%2A5+=+100
n+%2B+d+%2B+q+=+24
4 quarters and 20 nickels
---------------
2%2A25+=+50
n+%2B+d+%2B+2+=+24
d+=+22+-+n
5n+%2B+10d+%2B+50+=+200
5n+%2B+10%2A%2822-n%29+%2B+50+=+200
5n+%2B+220+-+10n+%2B+50+=+200
5n+=+270+-+200
5n+=+70
n+=+14
and
d+=+22-n
d+=+22+-+14
d+=+8
2 quarters, 14 nickels, and 8 dimes