How a percent off is calculated
A discount of D percent multiplies the price by (1 - D/100). Twenty-five percent off means you pay 75 percent, so a $89.99 item becomes 89.99 x 0.75 = $67.49. The saving is the other 25 percent, $22.50. To work backwards from a sale price, divide rather than multiply: an item marked $67.49 after 25 percent off started at 67.49 / 0.75 = $89.99. The same division tells you the original price when a tag shows only the final number.
Worked example with the defaults: $89.99 at 25 percent off is $67.49. Stack an extra 10 percent coupon and you pay 67.4925 x 0.90 = $60.74. Add 7 percent sales tax on that amount, $4.25, and the register total is $64.99. Total savings against the original price are $29.25.
Why stacked percentages do not add
This is the part that costs shoppers money. Twenty-five percent off plus another 10 percent is not 35 percent off. The second percentage applies to the already-reduced price, so the combined multiplier is 0.75 x 0.90 = 0.675, an effective discount of 32.5 percent. The gap widens with bigger numbers: 50 percent plus 30 percent is 0.5 x 0.7 = 0.35, a 65 percent discount, not 80 percent. An honest way to think about it is that each discount takes a slice of what is left, never of the original.
Order does not matter for stacked percentages, because multiplication commutes: 0.75 x 0.90 and 0.90 x 0.75 both give 0.675. Order matters enormously for a dollar-off coupon. On the same $89.99 item with 25 percent off and a $10 coupon, applying the percent first gives 67.49 - 10 = $57.49, while applying the coupon first gives (89.99 - 10) x 0.75 = $59.99. The dollar coupon is worth more when it comes off the higher price, so take the dollars first if the store allows it.
Sales tax and the fine print
Sales tax is charged on what you actually pay, after store discounts and store coupons, so a discount reduces your tax as well as your price. Manufacturer coupons are treated differently in many states: because the store is reimbursed by the manufacturer, states including Texas, Illinois and New York require tax on the pre-coupon amount. Combined state and local rates range from zero in Delaware, Montana, New Hampshire and Oregon to over 10 percent in parts of Louisiana, Tennessee and Alabama.
A few habits keep the math honest. Compare the final price, not the size of the discount, because 40 percent off a padded list price can still beat 60 percent off elsewhere. Check whether the coupon excludes clearance, sale items or specific brands, which is where most stacking attempts fail. And for grocery and household goods, compare unit prices rather than percentages, since a discount on a smaller package can still cost more per ounce.