Sale prices at the Ajax Outlet Store are $50\%$ below original prices.  On Saturdays an additional discount of $20\%$ off the sale price is given.  What is the Saturday price of a coat whose original price is $\textdollar 180$?
$\text{(A)}$ $\textdollar 54$
$\text{(B)}$ $\textdollar 72$
$\text{(C)}$ $\textdollar 90$
$\text{(D)}$ $\textdollar 108$
$\text{(D)}$ $\textdollar 110$
First we need to do the first discount, which, at Ajax Outlet Store, would be there any day of the week.
\begin{align*} 180 \times 50\% &= 180 \times \frac{1}{2} \\ &= 90 \\ \end{align*}
If we discount $20\%$, then $80 \%$ will be left, so after the second discount, we get
\begin{align*} 90 \times 80\% &= 90 \times \frac{8}{10} \\ &= 9 \times 8 \\ &= 72 \\ \end{align*}
$\boxed{\text{B}}$