Learning goals
- Calculate a sale price from an original price and a percent-off discount
- Add sales tax to a pre-tax amount and work backward from a tax-inclusive total
- Apply discount and tax in the correct order when both appear in one purchase
Two different percent adjustments
A discount lowers the price you pay for an item. Sales tax raises the total because tax is added on top of the taxable amount.
Both use percents, but they move in opposite directions. A 20% discount means you keep 80% of the original price. An 8% sales tax means you pay 108% of the taxable subtotal.
Stores usually apply the discount first, then charge tax on the discounted price — not on the original sticker price. That order changes the final amount.
Percent-off discount
sale price = original × (1 − discount% ÷ 100)
Alternatively: discount amount = original × (discount% ÷ 100), then sale price = original − discount amount. A 25% off tag means multiply the original by 0.75.
Sales tax on a subtotal
total with tax = pre-tax × (1 + tax rate% ÷ 100)
Tax owed = pre-tax × (tax rate% ÷ 100). If you know the tax-inclusive total and the rate, pre-tax = total ÷ (1 + tax rate% ÷ 100).
Example 1 — Sale price after a discount
Given
A pair of shoes is marked $120.00 with a 30% off sign. What is the sale price before tax?
Steps
- Original price (whole) = $120.00.
- Discount rate = 30%, so you pay 100% − 30% = 70% of the original.
- Sale price = 120 × 0.70 = 84.
Answer
The sale price is $84.00 before tax.
Tip: Quick check: 10% of 120 is 12, so 30% is 36 off → 120 − 36 = 84.
Example 2 — Add sales tax to a subtotal
Given
Your grocery subtotal is $50.00 and the local sales tax rate is 8%. What is the total at checkout?
Steps
- Pre-tax subtotal = $50.00.
- Tax = 50 × 0.08 = 4.
- Total = 50 + 4 = 54 (or 50 × 1.08 = 54).
Answer
You pay $54.00 including tax.
Example 3 — Discount first, then tax
Given
Same shoes: $120.00 original, 30% off, then 8% sales tax on the discounted price.
Steps
- Discounted price = 120 × 0.70 = $84.00.
- Tax on $84.00 = 84 × 0.08 = $6.72.
- Final total = 84 + 6.72 = $90.72.
Answer
You pay $90.72 at the register.
Tip: Taxing the full $120.00 first would give 120 × 1.08 = $129.60 before discount — that is not how most retailers calculate checkout.
Taxing the original price after a discount
Common mistake
Compute 30% off $120.00 → $84.00 then add 8% of $120.00 ($9.60) as tax because “tax is always on the sticker price.”
Better approach
Tax applies to the taxable subtotal — here $84.00 — so tax = 84 × 0.08 = $6.72. Always confirm whether tax is on the discounted amount.
Stacking two discounts by adding percents
Common mistake
“Extra 10% off already 20% off” → 20 + 10 = 30% off the original.
Better approach
Apply sequentially: after 20% off you pay 80%; another 10% off that price means 0.80 × 0.90 = 0.72 of the original (28% off total), not 30%.
Check your understanding
1.A $200.00 jacket is 15% off. What is the sale price?
Answer: 200 × 0.85 = $170.00.
2.Pre-tax total is $80.00 and tax is 6%. What do you pay?
Answer: 80 × 1.06 = $84.80.
3.$90.00 item, 10% off, then 5% tax on the discounted price. Final total?
Answer: Sale = 90 × 0.90 = 81; tax = 81 × 0.05 = 4.05; total = $85.05.
4.You paid $108.00 after 8% tax on a pre-tax bill. What was the pre-tax subtotal?
Answer: 108 ÷ 1.08 = $100.00.
Key takeaways
- Percent off: sale price = original × (1 − discount% ÷ 100).
- Sales tax: total = pre-tax × (1 + tax rate% ÷ 100).
- When both apply, discount usually comes first; tax is charged on the discounted subtotal.
- Stacked discounts multiply the remaining fractions — do not add the percents.