Buying using the regular price, we have: \($48+$48=$96\)

Buying using the discounted price, we have: \(\displaystyle\${48}+{\left(\frac{{1}}{{2}}\right)}{\left(\${48}\right)}=\${72}\). So, the discount is \($96-$72=$24\) which corresponds to a percent discount of: \(\displaystyle\ \frac{{$24}}{\$96}=\frac{{1}}{{4}}={0.25}={25}\%\)