Why stacked discounts don't add up the way you'd expect
When two discounts apply sequentially, the second discount is calculated on the already-reduced price — not the original. So 30% off, then 20% off gives: 100 × 0.70 × 0.80 = 56 — a 44% total saving, not 50%.
Retailers use this to make promotions look more generous. '30% off + extra 20% off' sounds like 50% off but isn't. The actual effective discount depends on the order of application — though for multiplication, the order doesn't matter: 0.70 × 0.80 = 0.80 × 0.70.
- 30% + 30% stacked = 51% off total (not 60%)
- 25% + 20% stacked = 40% off total (not 45%)
- 50% + 50% stacked = 75% off total (not 100% — nothing becomes free by stacking halves)
Working backwards: finding the original price
If you see a sale price but want to know what the full price was, divide the sale price by (1 − discount fraction). Sale of $68 after 15% off: $68 ÷ 0.85 = $80 original. This is useful when retailers hide the original price or show 'was / now' comparisons that seem too good.