One-eighth of a bookstore’s magazines are sold on a Friday. If \(\frac{\mathrm{1} }{\mathrm{4}}\) of the remaining magazines are sold the next day, what fractional part of the magazines remains at the end of the second day?

One-eighth of a bookstore’s magazines are sold on a Friday. If \(\frac{\mathrm{1} }{\mathrm{4}}\) of the remaining magazines are sold the next day, what fractional part of the magazines remains at the end of the second day?

Detailed Explanation

At the end of the first day, there are 1 - \(\frac{\mathrm{1} }{\mathrm{8}}\) = \(\frac{\mathrm{7} }{\mathrm{8}}\) of the magazines remaining.

\(\frac{\mathrm{7} }{\mathrm{8}}\) * \(\frac{\mathrm{1} }{\mathrm{4}}\) = \(\frac{\mathrm{7} }{\mathrm{32}}\) sold the next day.

So at the end of the second day, there are \(\frac{\mathrm{7} }{\mathrm{8}}\) - \(\frac{\mathrm{7} }{\mathrm{32}}\) =\(\frac{\mathrm{28} }{\mathrm{32}}\) - \(\frac{\mathrm{7} }{\mathrm{32}}\) = \(\frac{\mathrm{21} }{\mathrm{32}}\) of the magazines remaining.

\(\frac{\mathrm{7} }{\mathrm{8}}\) * \(\frac{\mathrm{1} }{\mathrm{4}}\) = \(\frac{\mathrm{7} }{\mathrm{32}}\) sold the next day.

So at the end of the second day, there are \(\frac{\mathrm{7} }{\mathrm{8}}\) - \(\frac{\mathrm{7} }{\mathrm{32}}\) =\(\frac{\mathrm{28} }{\mathrm{32}}\) - \(\frac{\mathrm{7} }{\mathrm{32}}\) = \(\frac{\mathrm{21} }{\mathrm{32}}\) of the magazines remaining.