Discounts, Taxes and Tips

Discounts, taxes, and tips are everyday percent problems. A discount takes money OFF a price. A tax or a tip ADDS money to a price. In every case you find a percent of the original amount, then either subtract or add. Once you can find a percent of a number, you can solve any sale, restaurant bill, or shopping receipt.

Discounts — Percent Off

• A discount is a percent taken OFF the original price; you pay less than the listed price.
• Method 1 (two steps): find the discount as a percent of the price, then subtract from the price. 20% off $50: discount = 0.20 x $50 = $10, sale price = $50 - $10 = $40.
• Method 2 (one step, multiplier): if the discount is 20%, you pay 100% - 20% = 80%. Multiply the price by 0.80. Sale price = $50 x 0.80 = $40.
• The multiplier method is faster once you spot the pattern: 25% off → x 0.75; 30% off → x 0.70; 40% off → x 0.60.
• Always estimate first: 20% off is a small reduction, so the answer should be close to the original.

Sales Tax — Percent Added

• Sales tax is a percent ADDED to the price. The store collects it for the government.
• Method 1 (two steps): find the tax as a percent of the price, then add to the price. 8% tax on $60: tax = 0.08 x $60 = $4.80, total = $60 + $4.80 = $64.80.
• Method 2 (one step, multiplier): if the tax is 8%, you pay 100% + 8% = 108%. Multiply the price by 1.08. Total = $60 x 1.08 = $64.80.
• The multiplier for tax is always more than 1; the multiplier for a discount is always less than 1.
• Common tax rates to recognize: 5% → x 1.05; 7% → x 1.07; 10% → x 1.10.

Tips — Percent of the Bill

• A tip is an extra amount you give a server, usually a percent of the bill before tax.
• Method 1 (two steps): find the tip as a percent of the bill, then add. 15% tip on $40: tip = 0.15 x $40 = $6, total = $40 + $6 = $46.
• Method 2 (mental math with 10%): 10% of $40 = $4, then 5% is half of that = $2, so 15% = $4 + $2 = $6.
• Common tip rates: 10% (lower service), 15% (standard), 20% (great service). Use 10% as a benchmark and double or halve.
• Some bills already include a service charge — check before adding a tip.

Putting It All Together

• Read the problem twice. Underline whether each percent is a discount (subtract), a tax (add), or a tip (add).
• Decide what the percent acts on: the original price, the sale price, or the pre-tax bill. Tax and tip are usually applied to the price BEFORE discount or AFTER, depending on the question.
• Example — discount then tax: $80 jacket, 25% off, then 8% tax. Sale = $80 x 0.75 = $60. Tax = $60 x 1.08 = $64.80.
• Example — bill then tip: $50 meal, 18% tip. Tip = 0.18 x $50 = $9. Total = $50 + $9 = $59.
• Always estimate to check: 25% off is about a quarter, 8% tax is small, 18% tip is roughly a fifth.