Question 935847
d, q, h for dimes quarters half-dollars;
Coin count: {{{d+q+h=70}}};
Ratio description:{{{q/d=3}}};
Money count: {{{0.1d+0.25q+0.5h=17.75}}}


The money count equation,
{{{d+2.5q+5h=177.5}}}
{{{2d+5q+10h=355}}}


The ratio equation becomes {{{q=3d}}}.


System of Equations:
{{{system(2d+5q+10h=355,q=3d,d+q+h=70)}}}
The easiest thing to do is substitute for q in the money count and coin count equations, and then you have a system of two equations in two unknowns, d and h.



<b>The process of solving</b>


The money count,
{{{2d+5(3d)+10h=355}}}, when substituting according to q=3d.
{{{2d+15d+10h=355}}}
{{{17d+10h=355}}}


The coin count,
{{{d+(3d)+h=70}}}, when substituting q=3d.
{{{4d+h=70}}}


You have now a simpler system in d and h:
{{{system(17d+10h=355,4d+h=70)}}}.
Solve this system using either substitution method or Elimination method.  Guessing that you forgot how to use Elimination, solve one of these equations for either variable and substitute this into the other equation, and solve for the value of the single variable present.  


Solving first for h seems easiest.
{{{4d+h-4h=70-4d}}}
{{{h=70-4d}}}
'
{{{17d+10(70-4d)=355}}}
{{{17d+700-40d=355}}}
{{{17d-40d+700=355}}}
{{{-23d+700=355}}}
{{{-23d=355-700}}}
{{{23d=700-355}}} when multiplied both sides by {{{-1}}}.
{{{23d=345}}}
{{{23d/23=345/23}}}
{{{highlight(d=15)}}}


You should be able to work through finding the values for q and h.