TL;DR: In typical retail math, take the discount off the pretax subtotal, then add sales tax to what is left. 20% off $80 is $64, then 8% tax on $64 is $5.12, total $69.12. Tax first then discount is a different store policy and a different total. Read the order. Do not add 20 and 8 to get a mythical 28%.
Discount is percent of the tagged price
20% off $80: 0.20 × 80 = $16 off, pay $64 before tax. Remaining factor 0.80. If a second coupon is 10% off, it usually hits $64, not $80: 0.90 × 64 = $57.60. Sequential discounts multiply remainders. A “20% + 10% extra” ad that means 30% off original would say so. Extra-off-the-already-reduced is the default in many registers. Extra-off-original is a marketing sentence you must verify.
Dollar-off coupons ($10 off) are not percents. Apply them where the coupon says (after % off, or on a category). Mixing $10 off with 20% off without an order is a small tragedy at the register.
Tax is percent of taxable remainder
If tax is 8% of $64, tax = $5.12. Total = $69.12. If the jurisdiction taxes the original $80 even after a discount, tax is 8% of $80 = $6.40, total = $64 + $6.40 = $70.40. Homework will tell you. Real life follows the state. Do not copy a YouTube total from another state.
Some groceries are exempt. Then 8% applies only to the taxable lines. The “8% of the whole cart” shortcut fails in a mixed cart. Split taxable vs not, then percent only the taxable pile.
Why 20% off plus 8% tax is not 12% off
People subtract 8 from 20. That treats tax and discount as the same kind of percent of the same base. They are not. Discount reduces the price. Tax is a new percent of a (possibly new) base. $80 × 0.80 × 1.08 = $69.12, which is not $80 × 0.88. The 0.88 would be “12% off and no tax,” a different planet.
Write the product of factors: 0.80 then 1.08. Two factors, two events. The calculator can do each percent-of-a-number step. It will not know the legal order unless you do.
Employee discounts, member prices, and stacking rules
Stores often forbid stacking two percent coupons, or they apply the better of two. “Better” might mean the larger percent of the same base, or the larger dollar save. 25% of $80 = $20 off. $15 off wins if it is $15 vs 10%. Compare dollars, not the beauty of the percent numeral.
Member prices may already be a percent off list. An extra 20% “off list” vs “off member” is the same trap as sequential discounts. The word after “off” is the base. Circle it on the app screenshot before you feel lucky.
Worked pair you can reuse
Jacket $120, 25% off, 6.5% tax on discounted price. Discounted = 90. Tax = 0.065 × 90 = 5.85. Total = 95.85. Check: 120 × 0.75 × 1.065 = 95.85.
Same jacket, tax on original (unusual homework twist): tax = 0.065 × 120 = 7.80, pay 90 + 7.80 = 97.80. Same 25% and 6.5%, different policy, $1.95 apart. Policy is the problem. The percents were obedient.
Receipts as the answer key
A receipt lists subtotal, discounts, taxable amount, tax. If your reconstruction disagrees, you used the wrong taxable amount, not a broken 6.5%. Match the taxable line, then 6.5% of that line. If the printed tax is not 6.5% of any line, you may have a mixed rate, a rounding rule to the nearest cent, or a bottle deposit that is not tax. Do not force 6.5% onto deposits.
When shopping on a phone, compute the discount first as dollars, then tax, then compare to the checkout page. Checkout pages add shipping, which may be taxable. Shipping was not in the jacket example. Add it as its own line before you accuse the site of “wrong tax.”
Online carts: promo codes versus struck prices
A struck $80 with a “now $64” already applied 20%. A promo code of 10% on top may refuse, or may take 10% of 64. The cart’s order of lines is the policy. Screenshot the lines before you assume 30% off $80. Free-shipping thresholds can add a fake item; that item may be taxable. Then your tax percent looks “wrong” because the whole grew. Expand the order summary.
Price-matching plus a percent coupon is a stack the site may forbid. If it allows both, the match usually sets a new original, then the coupon hits that. Wrong-base fights start here: 20% of the matched price vs 20% of the pre-match list. The cheaper dollar win is the one to compare, not the prettier percent.
Holiday “doorbuster” math in one minute
A $200 listed item, 40% doorbuster, then 10% coupon on remaining, 6% tax on taxable remainder: 200 × 0.60 × 0.90 × 1.06. That product is the total if every percent applies to that one item in that order. If the 10% coupon excludes doorbusters, drop 0.90. If tax is on original in that county (rare in homework, possible in life), tax uses 200 not the discounted taxable. Write the product with only the factors you kept. A doorbuster is not a license to add 40+10+6.
Alcohol taxed, food exempt, one dinner ticket
Some states tax the wine and not the entree. A $54 plate and a $16 glass do not share one taxable subtotal. If the plate is exempt and the glass is taxed at 7%, the tax is 0.07 times 16 = $1.12, not 0.07 times 70. A guest who multiplies the whole ticket by the alcohol rate pays tax on the pasta. A guest who subtracts 7% from the wine as if it were a discount pays $14.88 for the glass and still owes the restaurant $16 plus tax. Exemption is a zero rate on a named line, not a softer rate on the sum.
Ask which lines the rate touches before you combine them. Two rates on one check are two percent-of problems, then a sum. They are not an average rate unless you deliberately weight by dollars, and a diner almost never needs that average to pay.
Free shipping threshold is a dollar fence
A cart waves shipping once pretax goods hit $75. Your items are $68 before a 15% off code. The code hits first in this shop, so the qualifying subtotal becomes 0.85 times 68 = $57.80, and shipping returns. People add the 15% to a mythical shipping percent and conclude they are “about twenty percent better.” Shipping was $6.50 flat, not a percent of anything. After the code you pay $57.80 plus $6.50, which is $64.30, still less than the $68 with free shipping you would have paid without the code. Run both totals. The threshold is a cliff in dollars, and a percent off can push you back over the cliff even while the final cash drops.
