We have two equations to solve this problem.
Let's call the number of dimes "d" and the number of quarters "q"
\(d+q=100\)
\(0.1d+0.25q=21.4\)
\(0.1(100-q)+0.25q=21.4\)
\(10-0.1q+0.25q=21.4\)
\(0.15q+10=21.4\)
\(0.15q=11.4\)
\(q=76\)
\(d=24\)
There are 76 quarters and 24 dimes.
