The original price of a shirt is reduced by $50 \%$ to obtain a second price. The store advertises an additional sale, and so this second price is reduced by $40 \%$ to obtain a third price. What is the discount of the third price off the original price?
(A) $80 \%$
(B) $10 \%$
(C) $70 \%$
(D) $65 \%$
(E) $45 \%$
The percentage discount of the third price off the original price does not depend on the original price of the shirt.

That is, we may choose an original price for the shirt and calculate the combined percentage discount.

Since the discounts are given as percentages, letting the original price of the shirt be $\$ 100$ might make the calculations simpler.

If the original price of the shirt is $\$ 100$ and this price is reduced by $50 \%$, the discounted price is half of $\$ 100$ or $\$ 50$.

A further $40 \%$ reduction on $\$ 50$ is equal to a $\frac{40}{100} \times \$ 50=0.40 \times \$ 50=\$ 20$ discount.

After both price reductions, the $\$ 100$ shirt is priced at $\$ 50-\$ 20=\$ 30$ and thus the total discount is $\$ 100-\$ 30=\$ 70$.

The original price of the shirt was $\$ 100$, the final discounted price is $\$ 70$ less, and so the discount of the third price off the original price is $\frac{\$ 70}{\$ 100} \times 100 \%=70 \%$.