Work out the price after a percentage off, or the discount implied by two prices.
A percentage-off discount removes a fixed fraction of the original price. To find the final price: multiply the original by the discount rate to get the dollar savings, then subtract. To find the implied discount from two prices: divide the difference by the original. Stacked discounts (e.g., 20% off, then 10% off) are not simply additive — two stacked discounts of 20% and 10% equal 28% off, not 30%.
Final price
Final price = Original price × (1 − Discount% / 100)
Implied discount
Discount % = (Original price − Sale price) / Original price × 100
Each subsequent discount is applied to the already-reduced price, not the original. A 20% discount on $100 gives $80. A further 10% on $80 gives $72 — a total of 28% off, not 30%. The formula is: combined = 1 − (1 − d1)(1 − d2).
Divide the sale price by (1 − discount/100). If you paid $75 after a 25% discount, the original was 75 / 0.75 = $100.
'25% off $80' means you subtract 25% of $80, leaving $60. '25% of $80' is just $20. The distinction matters when reading sale tags — 'save 25%' and 'pay 25%' mean very different things.