Question 1053338
pennies,nickels, dimes, quarters;
p, n, d, q;


{{{system(0.1d=0.25q/2,0.05n=-0.5+0.1d,0.01p=0.05n/2,n+d+q+p=97,0.01p+0.05n+0.1d+0.25q=6)}}}


Notice the description indicates five equations but only needs four variables to be solved.


First goal is to simplify the system.
This is one possible system found along the way:
{{{system(4d=5q,n=2d-10,2p=5n,p+d+n+q=97,p+5n+10d+25q=600)}}}


A possible next step could be substitute for n in four of the equations and obtain this possible system:
{{{system(4d=5q,p=5d-25,p+11d+q=147,p+60d+25q=850)}}}


...exactly which direction of steps you take anywhere in the process is up to you.  Continued substitution?  Elimination?  Matrix row operations?


Continuing the solution process here, substituting for p,

{{{system(4d=5q,16d+q=172,13d+5q=35)}}}