Question 957694
q, d, p counts of the coins.
{{{system(q+d+p=20,0.25q+0.10d+0.01p=3.27)}}}


{{{system(q+d+p=20,25q+10d+p=327)}}}


Expect more than one solution for how many of each coin.  Two equations, THREE unknown variables.  Use elementary row operations, but pick a variable to treat as a constant; best choice seems to be p.


Assuming p is a constant although not yet known value,
{{{system(q+d=20-p,25q+10d=327-p)}}}-----simpler system

-
{{{system(25q+25d=25*20-25*p,25q+10d=327-p)}}}
-

E1-E2,
{{{15d=25*20-327-25p+p}}}
{{{15d=173-24p}}}
{{{d=(173-24p)/15}}}


Return again to simple system, 
{{{system(10q+10d=10(20-p),25q+10d=327-p)}}}
-
{{{system(10q+10d=200-10p,25q+10d=327-p)}}}


E2-E1,
{{{15q=(327-p)-(200-10p)}}}
{{{15q=127+9p}}}
{{{q=(127+9p)/15}}}



You want to find what whole number p will make q and d to be whole numbers, and also be sure that q+d+p=20  :
{{{system(d=(173-24p)/15,q=(127+9p)/15)}}}