A piggy bank contains $24$ coins, all of which are nickels, dimes, or quarters. If the total value of the coins is two dollars, what combination of coins are possible?
So far I have: $n$=# of nickels, $d$=# of dimes, $q$=# of quarters
thus: $5n+10d+25(24-n-d)=200$ $-20n-15d=-400$
Next I would find the gcd using long division but I was wondering how I go about this since all the numbers are negative.
Does this affect the problem or not?