Why 25% off plus 10% off is not 35%

The second discount has a smaller starting point

Sequential discounts apply to the price left after the previous discount. On an $80 item, 25% off removes $20 and leaves $60. Another 10% off removes $6 from that $60. You pay $54 before taxes or other costs, saving $26, or 32.5%, compared with $80.

Adding the two percentages would predict a $52 subtotal. That is $2 too low. The mistake comes from taking the second 10% off the original $80 instead of the already reduced $60. Promotional wording can make the distinction easy to miss.

Use what remains, not what comes off

The compact formula is original price × (1 − first discount) × (1 − second discount), with percentages written as decimals. Here that is 80 × 0.75 × 0.90 = 54. The effective discount is 1 − (0.75 × 0.90), which equals 0.325.

Switching the order of two percentage discounts does not change the exact mathematical result. Retailers may round each step to cents, so the final checkout can differ slightly. A dollar coupon makes the sequence more consequential.

A dollar coupon changes the order question

Suppose an $80 item has 25% off and a $10 coupon. Taking 25% off first leaves $60; subtracting $10 makes it $50. Applying the $10 coupon first leaves $70; taking 25% off then makes it $52.50. The difference is $2.50.

Our calculator places the dollar coupon after both percentage discounts. That is an explicit assumption, not a promise about a retailer’s rules. Before relying on the answer, check coupon exclusions, minimum purchase requirements, whether promotions can combine, and when each reduction applies.

Separate a lower price from a future reward

A checkout coupon reduces the payment now. A future store credit or cashback award may require another purchase, a waiting period, approval, or a minimum redemption amount. Record these separately. A $60 payment with a possible $10 future credit does not require the same cash as a $50 payment.

For your own comparison, give a restricted future credit only the value you realistically expect to use. If using it requires an unplanned trip or purchase, include that cost too. Do not subtract a possible reward from the current checkout amount and call the result the price you paid.

The useful number is the alternative total

A discount is measured against a starting price. The size of the discount says nothing by itself about whether that starting price was competitive. An item advertised at $100 with 40% off still costs $60. The same item sold elsewhere at $55 without a sale sticker is cheaper before other costs.

The FTC recommends checking shopping details such as total costs and return terms. For a practical comparison, match the model, size, condition, seller, included accessories, delivery cost, and return conditions. Then compare full checkout totals. A generous return policy can have value, but make that a conscious tradeoff.

If an offer also requires padding your cart to reach a shipping threshold, run the free shipping calculation before choosing. Discounts and shipping each change the same payment, and neither should be evaluated alone.