Why 50% Off Beats 30% + 20%
Stacking percentage discounts multiplies the remaining fractions, so 30% off followed by 20% off leaves you paying 56% of the original price, while a single 50% off leaves you paying 50%.
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Why does a single 50% discount save more money than stacking 30% off and then 20% off?
Two signs hang in the same store window: one advertises 50% off, the other promises 30% + 20% off. Both look like the same bargain.
Your gut says 30 + 20 = 50, so the deals must be identical. But the manager swears one is genuinely better than the other.
A side-by-side price calculation on a $100 item (and a $200 item) showing final prices, plus a brief visual showing the difference between sequential percentage reductions and a single one.
Sequential percentage discounts multiply, so 0.7 × 0.8 = 0.56, leaving you paying 44% of the price instead of 50% — only the single 50% off actually halves the price.
- compound interest
- tax calculations
- loyalty point math
- inflation
- 01Two Signs, One StorefrontslideSlot 1Hook
Show two store window signs side by side: '50% OFF' on one and '30% + 20% OFF' on the other, both in bold red lettering above the same $100 jacket.
- Both signs advertise what looks like a 50% discount
- A common intuition is that 30% + 20% must equal 50%
- Only one of these is actually the better deal
PhenomenonTwo sale signs offering what appears to be the same 50% discount on a $100 jacket.
QuestionWhich sign really saves you more money, and why?
- 02Predict the Final PriceinteractiveSlot 2Tension
Set the original price with a slider, then reveal what each discount path actually leaves you paying.
- Drag to pick an original price (e.g., $100, $200, $350)
- Predict the final price under the 50% off path
- Predict the final price under the 30% + 20% path
- Compare your two predictions before revealing the truth
PredictionMost learners predict both paths leave the same final price because 30 + 20 = 50.
Tempting intuitionPercentages add like regular numbers, so stacking discounts feels equivalent to one big discount of the same total.
- 03The Multiplication That Changes EverythingslideSlot 3Reveal
Walk through the math on a $100 item: 50% off leaves $50, but 30% off first leaves $70, then 20% off that $70 leaves $56. Show that 0.5 versus 0.7 × 0.8 = 0.56 is the whole story.
- Single 50% off: $100 × 0.50 = $50 final price
- 30% off first: $100 × 0.70 = $70 remaining
- 20% off that: $70 × 0.80 = $56 final price
- 0.7 × 0.8 = 0.56, which is 44% off, not 50% off
- The second discount is taken on a smaller number, so its dollar value shrinks
EvidenceOn a $100 item, single 50% off costs $50, while 30% + 20% off costs $56 — a $6 difference in the customer's favor for the single discount.
ConclusionStacking percentages never equals their sum; it equals the product of what remains, so 30% + 20% off is only a 44% total discount, not 50%.
Mechanism- 1Each percentage discount multiplies the current price by its retention factor (1 − discount)
- 2Stacking two discounts multiplies those retention factors together: 0.70 × 0.80 = 0.56, so the customer still keeps 56% of the original price
- 04Read Sale Signs the Smart WayslideSlot 4Takeaway
Connect the math back to shopping behavior: always convert stacked percentages into one combined percentage, and recognize the pattern in store cards, coupons, and employee discounts.
- Stacked discounts multiply, they do not add
- To find the true discount, compute 1 − (retention × retention × ...)
- A 10% + 20% coupon is really 28% off, not 30% off
- Apply the same rule whenever percentages layer on top of each other
TransferImagine a coupon stack offering 10% off then 20% off a $80 grocery bill — what does the shopper actually pay?
Expected inferenceThe shopper should compute $80 × 0.90 × 0.80 = $57.60, realizing the combined discount is only 28% off, not 30% off, and adjust their spending decision accordingly.
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