Question 1117809
A:
nickles dimes only
{{{system(n+d=30,5n+10d=190)}}}


B:
nickles, dimes, quarters
{{{system(n+d+q=30,5n+10d+25q=190)}}}
(might need to consider more than one solution)


Continuing B:

Let k=q.

{{{system(n+d=30-k,n+2d=38-5k)}}}


E2-E1------->

{{{d=38-5k-30+k}}}
{{{highlight_green(d=8-4k)}}}

Note that only Natural Number values are acceptable if combination must contain nickles, dimes, and quarters.  
Also note {{{k=0}}} not relevant, and {{{k>=2}}} not acceptable, leading to wrong kind of number.

Only k possible is {{{k=1}}}.


{{{d=8-4*1}}}
{{{d=8-4}}}
{{{d=4}}}



Combination should be  {{{system(q=k=1,d=4,n=25)}}}.
Quarters:  1
Dimes:  4
Nickles:  25
Cents total ------- 190