Sale price from a percent off, or the real percent off from a sale price. Both directions, one screen.
Two discounts do not add. 20% off then another 20% off is 36% off total, not 40%. Multiply the remainders: 0.8 x 0.8 = 0.64, so you pay 64%.
A discount tag tells you the percentage. It does not tell you the price. And when a store stacks two discounts, the combined figure is almost never what people assume.
No, and this is the trap. Two successive discounts multiply: 0.7 × 0.8 = 0.56, so you pay 56% of the original, which is a 44% total discount. The gap between 44% and the 50% people expect is exactly why stores stack discounts instead of combining them into one number.
In every US state and in the EU, a percentage discount reduces the taxable amount, so tax is charged on the discounted price. If a store charges tax on the pre-discount total, that is an error worth querying.
Divide by (1 − discount). A $68 sale price at 15% off means 68 / 0.85 = $80 original. Going the other way — adding 15% to $68 — gives $78.20, which is the same base error described above.
That at least one item in the store is 70% off, and most are considerably less. It is a legal advertising phrase in most jurisdictions precisely because of that gap. Treat the number as the ceiling, not the average.
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