Question 126374
The question should have been "what are the equations for this?"


You have a situation where you can express a relationship between the numbers of things and another relationship between the values of those things.  Meaning that you will have to develop a system of equations and solve them.


Let q be the number of quarters and d be the number of dimes.  The quantity relationship is {{{q = d + 7}}} because there are 7 more quarters than dimes.


Each quarter is worth 25 cents so the total value of q quarters in cents is 25q.  Likewise for the dimes, the total value is 10d.  We know that the total value of all the coins is $3.50 or 350 cents, so we can write:


{{{25q + 10d = 350}}}


Into this equation we can substitute the expression for the number of quarters in terms of dimes:


{{{25(d+7)+10d=350}}}
{{{25d+175+10d=350}}}
{{{35d+175=350}}}
{{{35d=175}}}
{{{d=5}}}


So there are 5 dimes.  Since there are 5 dimes, there must be {{{5+7=12}}} quarters.


Check.

{{{25*12=300}}}
{{{10*5=50}}}

{{{300+50=350}}}