SOLUTION: A bag contains 208 coins made up of dollars, quarters, dimes & nickels. The total equals $77.10. How many of each type of coin are in the bag? So far I have: a=1.0, b=0.25, c=0

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Question 363542: A bag contains 208 coins made up of dollars, quarters, dimes & nickels. The total equals $77.10. How many of each type of coin are in the bag?
So far I have:
a=1.0, b=0.25, c=0.1, d=0.05
a+b+c+d=7
a+.25b+.1c+.05d=77.10
I have the answer through trial & error of 57 dollars, 56 quarters, 27 dimes & 68 nickels but can't figure out the complete system of equations to get me there.

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
a%2Bb%2Bc%2Bd=7
Where'd the 7 come from??
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Let X be the number of dollars, Q quarters, D dimes, and N nickels.
1.X%2BQ%2BD%2BN=208
2.100X%2B25Q%2B10D%2B5N=7710
From eq. 1,
100X=20800-100Q-100D-100N
Substituting,
20800-100Q-100D-100N%2B25Q%2B10D%2B5N=7710
75Q%2B90D%2B95N=13090
15Q%2B18D%2B19N=2618
Since you do not have any other equations, you have a Diophantine equation in three variables.
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The procedure to solve it is not much different than trial and error so I'm not sure I'm adding much.
Here's a link to show you how to solve these type of equations if you're interested.
http://mathforum.org/library/drmath/view/61325.html