Question 1106102
d dimes
q quarters


{{{system(d=6q,d+q=21,10d+25q=255)}}}

You should need only two equations and not all three of them.  Decide which two you want.


{{{10d+25q=255}}}
{{{2d+5q=51}}}



{{{system(d+q=21,2d+5q=51)}}}

{{{system(2d+2q=42,2d+5q=51)}}}

{{{3q=51-42}}}

{{{3q=9}}}

{{{highlight(q=3)}}}-----------quarters

-

{{{d+q=21}}}
{{{d+3=21}}}
{{{highlight(d=18)}}}-----------dimes


Also notice,  "...six times as many dimes as quarters..."
{{{d=6q}}}
{{{18=6*3}}}
this fits.