Quick Answer:
No.
The successive discounts do not make 80%. |
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| 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. |
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| 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 |
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| Original
Price |
80%
Off |
Final
Cost |
| $100 |
80%
×
$100 = $80 |
$100
- $80 = $20 |
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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. |
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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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