SOLUTION: using only 85 coins to make $6.25 and there are 3 times the number of nickel then there are dimes what coins are used

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Question 668799: using only 85 coins to make $6.25 and there are 3 times the number of nickel then there are dimes what coins are used
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!

I'll assume you don't mean to use pennies or half dollars

then let q = the number of quarters
     let d = the number of dimes
    then 3d = the number of nickels.

Then there is a "coin equation" and a "money equation":


The "coin" equation is

 %28matrix%284%2C1%2C%0D%0A%0D%0A+++++The%2Cnumber%2C+of%2C+quarters%29%29 + %28matrix%284%2C1%2C%0D%0A%0D%0A+++++The%2Cnumber%2C+of%2C+dimes%29%29 + %28matrix%284%2C1%2C%0D%0A%0D%0A+++++The%2Cnumber%2C+of%2C+nickels%29%29 = 85


The "money" equation is:

 +  +  = $6.25


system%28q%2Bd%2B3d=85%2C0.25q%2B0.10d%2B0.05%283d%29=6.25%29
Simplify:
system%28q%2B4d=85%2C0.25q%2B0.10d%2B0.15d=6.25%29
Simplify some more:
system%28q%2B4d=85%2C0.25q%2B0.25d=6.25%29
Multiply the second one through by 100 to clear of decimals:
system%28q%2B4d=85%2C25q%2B25d=625%29
Divide the second equation through by 25
system%28q%2B4d=85%2Cq%2Bd=25%29
  
Solve that and get q=5 and d=20

So there are 5 quarters, 20 dimes, and since there are 3d nickels,
there are 3(20) or 60 nickels.

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If you allow pennies there are two more solutions:

12 quarters, 12 dimes, 36 nickels and 25 pennies

19 quarters, 4 dimes, 12 nickels and 50 pennies.

But there are no solutions using half dollars.

Edwin