Daily Math Puzzle: 2026-08-23
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2026-08-23
At a local market, a shopkeeper has a sale where everything must go. She has three shelves of items priced differently: Shelf A has items that are 15% off their original price, Shelf B has items that are 25% off, and Shelf C has items that are 50% off. However, there's a twist - all items on each shelf are priced such that when you buy two of them, their total price is the same as the original price of one item before any discount. Given this information, which shelf would you choose to buy from to get the best value for your money, assuming you're buying two items?
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Solution
Shelf C (50% off) — Let's denote the original price of an item as P. For Shelf A, the price after a 15% discount is 0.85P. If two items cost the same as one original price, then 2 * 0.85P = P, which doesn't hold true because it simplifies to 1.7P = P, indicating a misunderstanding in the initial setup for this explanation. Correcting the approach: The statement that two items cost the same as one original price means that for Shelf A, 2*(P-0.15P) = P, for Shelf B, 2*(P-0.25P) = P, and for Shelf C, 2*(P-0.5P) = P. Simplifying these, we get for Shelf A: 2*0.85P = P, which simplifies incorrectly in the initial explanation. Correctly, for Shelf A: 1.7P = P doesn't make sense as it was a wrong simplification. The real question is about the value for money, which means looking at the discount percentage. If two items at a discounted price equal one original price, the key is in the discount percentage itself. For Shelf C, with a 50% discount, buying two items gives you the equivalent of one original price, meaning you're essentially getting two items for the price of one, which is the best value. The confusion in the initial explanation arose from misinterpreting the condition given. The correct interpretation should focus on the value proposition each shelf offers under the condition that two discounted items equal the price of one original item, making Shelf C the best value since you're getting two items for what you'd pay for one originally.
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