1 dollar,1 penny,1 nickel,1 dime,1 quarter worth 100 ; 1 ; 5 ; 10 ; 25 in cents respectively.

The remaining coins have : 10 - 3 = 7 (coins)

Their total value is : 100 - 25 x 3 = 25 (cents)

Hence,each remaining coin must worth less than 25 cents.So,there can be 3 kinds of coins : pennies,nickels,dimes.

Let p,n,d be the number of coins of each kind\(\left(p,n,d\in N\right)\)

We have :\(\left\{{}\begin{matrix}p+n+d=7\\p+5n+10d=25\end{matrix}\right.\)\(\Rightarrow4n+9d=18\)

\(\Rightarrow n=\dfrac{18-9d}{4}=9\times\dfrac{2-d}{4}\) but \(n\in N\)

\(\Rightarrow2-d⋮4\Rightarrow d=2\)\(\Rightarrow\left\{{}\begin{matrix}p+n+2=7\\p+5n+20=25\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}p+n=5\\p+5n=5\end{matrix}\right.\)

\(\Rightarrow4n=0\Rightarrow n=0\Rightarrow p=5\)

Hence,the remaining coins include 5 pennies and 2 dimes