Question 363542
{{{a+b+c+d=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+Q+D+N=208}}}
2.{{{100X+25Q+10D+5N=7710}}}
From eq. 1,
{{{100X=20800-100Q-100D-100N}}}
Substituting,
{{{20800-100Q-100D-100N+25Q+10D+5N=7710}}}
{{{75Q+90D+95N=13090}}}
{{{15Q+18D+19N=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