Question 1176182
q,d,n,p
Quarters, Dimes, Nickels, Pennies


{{{system(q=2n-1,p-n=4,d=2p)}}}


{{{system(q=2n-1,n=p-4,d=2p)}}}


{{{system(q=2(p-4)-1,n=p-4,d=2p)}}}


{{{system(q=2p-8-1,n=p-4,d=2p)}}}


{{{system(q=2p-9,n=p-4,d=2p)}}}---------These coin equations are all written in terms of p.



The money equation as cents:
{{{25q+10d+5n+p=287}}}


Substitute for each coin other than p:
{{{25(2p-9)+10*2p+5(p-4)+p=287}}}---------One equation in terms of just variable p.

Simplify
.
.
.
{{{highlight(p=7)}}}
-
{{{highlight(q=5)}}}
{{{highlight(n=3)}}}
{{{highlight(d=14)}}}



(!)