No. The successive discounts do not make 80%.

Complete Solution:
Several ways to do the problem:

Solution 1.
If an item originally costs \$100, the tables below show the different final costs. They are not the same.

 Original Price 30% Off Cost on Sale 50% Off Sale Price Final Cost \$100 30% × \$100 = \$30 \$100 - \$30 = \$70 50% × \$70 = \$35 \$70 - \$35 = \$35

 Original Price 80% Off Final Cost \$100 80% × \$100 = \$80 \$100 - \$80 = \$20

Solution 2.
For the item on sale at 30% off, you would need to pay 70% of the price. So an additional discount of 50% off the sale price would bring the price to 35% (that is, 50% of 70%) of the original price.

Thus, a \$100 item would cost \$35 after both discounts. An 80% off sale means that you pay 100% - 80%, or 20% of the original cost of the item. Thus, an item that originally cost \$100 on sale at 80% off costs 20% of \$100 or \$20. The costs are not the same.

Solution 3.
You can generalize the problem.
If P is the original price of an item, with the two discounts, one of 30% followed by another of 50%, you would pay 0.50 (0.70 P ) or 0.35P, which is not the same as 0.20P.

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