A jacket and a shirt originally sold for $80$ dollars and $40$ dollars, respectively.  During a sale Chris bought the $80$ dollar jacket at a $40\%$ discount and the $40$ dollar shirt at a $55\%$ discount.  The total amount saved was what percent of the total of the original prices?
$\text{(A)}\ 45\% \qquad \text{(B)}\ 47\dfrac{1}{2}\% \qquad \text{(C)}\ 50\% \qquad \text{(D)}\ 79\dfrac{1}{6}\% \qquad \text{(E)}\ 95\%$.
Chris would have spent $40 + 80 = 120$ dollars if there were no sale.
The sale means that he saved $80(0.40) + 40(0.55) = 32 + 22 = 54$ dollars.
He saved $\frac{54}{120}\cdot 100\% = 0.45 \cdot 100\% = 45\%$ off the total of the original prices, and the answer is $\boxed{A}$.