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A car stereo is on sale at a 20% discount. The original amount of the stereo is $8500.
If the purchase will include a 12% tax, it would come out cheaper if the discount is applied
before the tax is added to the price. Is it true or false?
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Let's calculate both values.
(1) First discount, then tax. You should pay 6500*(1-0.2)*1.12 = 6500*(0.8*1.12) = 6500*0.896 = 5824 dollars.
(2) First tax, then discount. You should pay 6500*1.12*(1-0.2) = 6500*(1.12*0.8) = 6500*0.896 = 5824 dollars.
As you see, the final amount to pay is the same.
What is interesting, the reducing multiplicative factor is the same in both cases:
it is 0.8*1.12 = 1.12*0.8 = 0.896 in both cases.
It is the key.
Solved.
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On chain discounts, see the lesson
- Percentage problems on chains of discounts
in this site.