Question 1209201
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Answer: <font color=red>20%</font>



Explanation
1-0.25 = 0.75 is the first discount multiplier
1-x is the second discount multiplier where 0 < x < 1
(1-0.25)*(1-x) = 0.75(1-x) = proportion of the final price that the customer ends up paying
1-thatProportion = 1-0.75*(1-x) = combined discount multiplier = 0.40
1-0.75*(1-x) = 0.40 solves to x = 1/5 = 0.20 = <font color=red>20%</font>
The second discount must be <font color=red>20%</font>
I'll let the student handle the scratch work when it comes to solving that equation.


Check:
Let's say there's an item worth $100 before any discounts are used.
100*(1-0.25)*(1-0.20) = 60 is the final price after both discounts of 25% and 20% are applied in either order.
The customer ultimately saves 100-60 = 40 dollars, which leads to the 40/100 = 0.40 = 40% discount. This example helps confirm the answer.
Notice that 100*(1-0.40) = 60.


As the hint strongly implies, many students might easily mistake the answer to be 15% since 25+15 = 40. But unfortunately the percentage discounts don't add like that. The percentages do not add because the 1st discount applies to the sticker price while the 2nd discount applies to an amount smaller than the sticker price.


Another way to see why we cant add the percentages: 
Let's say the store owner offered the discounts 30% and 80%. 
If an item starts off at $100 then its final price would be
100*(1-0.30)*(1-0.80) = 14 dollars.
But if we follow the practice of naively adding the percentages then we'd get a 30% + 80% = 110% off discount. Which is completely silly because we can't go over 100%.
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