Basic Discount Then Tax

A jacket costs 80 dollars and is 25% off. Sales tax is 8%. What is the final price?

Calculate the discount amount: $80 \times 0.25 = 20$ dollars discount = 20 dollars off

Find the discounted price: $80 - 20 = 60$ dollars = 60 dollars

Calculate tax on discounted price: $60 \times 0.08 = 4.80$ dollars tax = 4.80 dollars tax

Add tax to get final price: $60 + 4.80 = 64.80$ dollars = 64.80 dollars

Answer: The final price is 64.80 dollars

Using Multipliers (One-Step Method)

A 120 dollar item is 30% off with 6% tax. Calculate the final price using multipliers.

Convert discount to multiplier: $100\% - 30\% = 70\%$, so multiply by $0.70$ = Discount multiplier: 0.70

Convert tax to multiplier: $100\% + 6\% = 106\%$, so multiply by $1.06$ = Tax multiplier: 1.06

Combine multipliers: $0.70 \times 1.06 = 0.742$ = Combined multiplier: 0.742

Apply to original price: $120 \times 0.742 = 89.04$ dollars = 89.04 dollars

Answer: The final price is 89.04 dollars

Comparing Two Stores

Store A: 150 dollar shoes, 20% off, 7% tax. Store B: Same shoes at 130 dollars, no discount, 7% tax. Which is cheaper?

Calculate Store A's price after discount: $150 \times 0.80 = 120$ dollars = Store A: 120 dollars before tax

Add tax to Store A: $120 \times 1.07 = 128.40$ dollars = Store A final: 128.40 dollars

Calculate Store B with tax: $130 \times 1.07 = 139.10$ dollars = Store B final: 139.10 dollars

Compare final prices: $128.40 < 139.10$ = Store A is cheaper by 10.70 dollars

Answer: Store A is cheaper at 128.40 dollars (saving 10.70 dollars compared to Store B)

Mistake: Applying tax first, then the discount

Why: This incorrectly calculates tax on the full price instead of what you actually pay. It also violates how stores legally must calculate tax.

Correct: Always apply the discount first. Tax is calculated on the sale price, not the original price.

Mistake: Adding the discount and tax percentages together

Why: Thinking '25% off and 8% tax = 17% off total' is wrong because you can't combine these operations.

Correct: Discount and tax must be applied separately in sequence: discount first, then tax on the result.

Mistake: Forgetting that tax applies to the discounted price

Why: Some students calculate the discount correctly but then add tax based on the original price.

Correct: The tax base is always the price you're actually paying after any discounts.

Black Friday Shopping

During major sales events, stores offer deep discounts. Knowing how to calculate the final price helps you budget.

A 200 dollar TV is 40% off on Black Friday. With 6% sales tax, the final price is $200 \times 0.60 \times 1.06 = 127.20$ dollars.

Online Shopping

E-commerce sites automatically apply discounts and taxes. Understanding the math helps you verify charges.

A 50 dollar order with a 20% coupon code and 9% tax: $50 \times 0.80 \times 1.09 = 43.60$ dollars.

Q: Why do we apply the discount before the tax?

A: By law, stores must charge sales tax only on the amount you actually pay. Since the discount reduces what you pay, tax is calculated on that lower amount.

Q: Does the order matter mathematically?

A: Interestingly, multiplication is commutative, so the final amount is the same either way. However, the legal and practical standard is discount first, then tax. This also makes it clear that you're being taxed on what you actually spend.

Q: What if I have multiple discounts?

A: Apply all discounts first (usually in the order specified by the store), then calculate tax on the final discounted price.