I’m cramming for a test and my brain keeps doing cartwheels over percentages. Example: a jacket is $80, there’s a 25% off sale, and then an extra 10% off at the register. My instinct says, “Cool, 35% off,” but my teacher hinted that’s not right because of “the base changing,” which made my thoughts deflate like a sad balloon. How should I actually calculate the final price here? Is there a simple rule for stacking percentage discounts (or increases and decreases) without getting tangled? I tried turning the percentages into decimals and doing something with them, but I’m not sure if that’s even the relevant move or why it works. What’s the best way to set this up so I don’t trip on the ‘percent of what’ part during the test?
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One Response
It’s not 35% because that second 10% isn’t taken off the original price-it’s 10% off the already-discounted price. Start at $80. Take 25% off: multiply by 0.75 to get $60. Then take 10% off that: multiply by 0.90 to get $54. In one shot, that’s 80 × 0.75 × 0.90 = 80 × 0.675 = $54, so you’re paying 67.5% of the original-aka 32.5% off, not 35%. If it were really 35% off, you’d pay $52, which you don’t.
Simple rule so you don’t trip: turn every percent change into a multiplier and multiply them. Discount d% → (1 − d/100); markup m% → (1 + m/100). Mental shortcut for stacked discounts: a% then b% gives a + b − (a·b)/100 off. Here, 25 + 10 − 2.5 = 32.5%. For mixes of ups and downs, use signed rates: net change c satisfies (1 + a)(1 + b) = 1 + c, so c = a + b + ab. Example: up 20% then down 10% gives c = 0.20 − 0.10 − 0.02 = +0.08, so $100 becomes $108.