Quick Answer:
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. 


