Question 122032
The amount of money in cents for each nickel is 5n, for each dime 10d, and for each quarter 25q.


Your equations for the relationship between the numbers of dimes and nickels and between the numbers of quarters and nickels are backwards.


"3 times as many nickels as dimes" means for every dime there are 3 nickels, or {{{n=3d}}}.  Likewise, twice as many quarters as nickels would be {{{q = 2n}}}.


The basic expression for total amount, t, in the jar would be:
{{{t=5n+10d+25q}}}.  But given the other information, you can express the total amount in terms of the number of any one of the coins:


In terms of nickels:

{{{n=3d}}}, so {{{d=n/3}}}
{{{q=2n}}}

Substituting:
{{{t=5n+10(n/3)+25(2n)=5n+10n/3+50n=15n/3+10n/3+150n/3=175n/3}}}.


In terms of dimes:
{{{n=3d}}}
{{{q=2n=2(3d)=6d}}}


Substituting:
{{{t=5(3d)+10d+25(6d)=15d+10d+150d=175d}}}


In terms of quarters:
{{{q=2n}}} so {{{n=q/2}}}
{{{d=n/3}}} so {{{d=(q/2)/3=q/6}}}


Substituting:
{{{t=5(q/2)+10(q/6)+25q=5q/2+10q/6+25q=15q/6+10q/6+150q/6=175q/6}}}