Question 1187621
.
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?
~~~~~~~~~~~~~~~~



<pre>
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.
</pre>

Solved.


---------------


On chain discounts, &nbsp;see the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/percentage/lessons/Percentage-problems-on-chains-of-discounts.lesson>Percentage problems on chains of discounts</A> 

in this site.