Khan/khan-exercises — Issue #10388: Percentage word problems 2 - discount rounding
Author: KhanBugz
Created: 2012-01-05 09:20:10+00:00
State: open
Labels: firefox, snowleo, wrong-or-unclear

Reporter: zac.thompson@gmail.com

Below is the question and "solution" as provided by you.

However, the method provided for determining the answer gives a slightly incorrect result, since she can actually afford $32.90 (discounted price will be $25.004, which results in a cost to her of $25). Although she only has $25, she can afford any marked price that results in a discounted price of < $25.005 (rounded to the nearest cent), which will produce the correct result if $25.005 is used in place of $25 in the equation below. Although I'm not sure whether students should be expected to come up with this insight on a problem at this level, it seems unfair to claim that $32.90 is incorrect, especially when a test of the "correct" answer lets a smart student see that there is room for another discounted penny with rounding ($32.89 * 0.76 = $24.9964).

Rounding adds a lot of fuzziness to percentage word problems, especially when working with monetary values. I suggest that the numbers for this problem be adjusted to no longer permit this ambiguity. If not, then either $32.89 or $32.90 should be considered "correct".

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Jessica has $25 to spend at a store. The store currently has a sale where the sale price is 24% off the marked price. What is the highest marked price that Jessica can afford? (Round to the nearest cent, or hundredth of a dollar.)

Let x be the highest marked price that Jessica can afford.

x−0.24x=sale price=amount Jessica has to spend

0.76x=$25

x=$32.89

[percentage_word_problems_2.html?seed=58&problem=store-percentages](http://sandcastle.khanacademy.org/media/castles/Khan:master/exercises/percentage_word_problems_2.html?seed=58&problem=store-percentages&debug)

[Answer timeline](http://sandcastle.khanacademy.org/media/castles/Khan:master/exercises/percentage_word_problems_2.html?seed=58&problem=store-percentages&debug&activity=%5B%5B%22incorrect-activity%22%2C%22%5C%2232.90%5C%22%22%2C59%5D%2C%5B%22incorrect-activity%22%2C%22%5C%22%2432.90%5C%22%22%2C3%5D%2C%5B%22correct-activity%22%2C%22%5C%22%2432.89%5C%22%22%2C8%5D%5D)

["32.90","$32.90","$32.89"]

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