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Teacher Guide: Discounts and Tax Together

Learn how to calculate the final price when both a discount and sales tax apply to a purchase.

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10 questions on Taxes & Tips. Students join with a name, you see everyone's score.

For Teachers

Learning Objectives
  • Determine the correct order for applying discounts and sales tax
  • Calculate final prices using step-by-step or multiplier methods
  • Explain why tax is applied after discounts
  • Compare prices across different discount and tax scenarios
Prerequisites
  • • Understanding of percentages and converting to decimals
  • • Ability to calculate percent of a number
  • • Familiarity with sales tax calculations
  • • Basic understanding of discounts and percent off
Discussion Starters
  • 1. Have you ever been surprised by a total at checkout? What might have caused the difference from what you expected?
  • 2. Why do you think the government requires tax to be calculated on the discounted price?
  • 3. If two stores have the same item but different discounts and prices, how would you decide where to buy?
  • 4. A store advertises '50% off plus no tax!' Is this always a better deal than a smaller discount with tax?
Common Misconceptions

Discount and tax percentages can be combined (e.g., 20% off + 10% tax = 10% increase)

Remediation: Show with numbers: 100 dollars at 20% off then 10% tax gives 88 dollars, not 110 dollars. The percentages apply to different base amounts.

The order doesn't matter since it's all multiplication

Remediation: While mathematically equivalent, explain the legal and practical reasons. Also, when stores itemize receipts, they must show tax on the discounted amount.

Differentiation Ideas

For Struggling Students:

  • • Use simpler percentages (10%, 20%, 50%) that are easy to calculate mentally
  • • Break every problem into four steps: original price, discount amount, sale price, tax amount, final price
  • • Provide a visual flowchart showing the order of operations

For On-Level Students:

  • • Practice with realistic percentages (15%, 25%, 7.5% tax)
  • • Compare deals between two stores
  • • Work backwards: Given a final price, find the original

For Advanced Students:

  • • Multiple discounts (e.g., 20% off then additional 10% loyalty discount)
  • • Calculate the 'effective' single discount rate when combining discount and tax
  • • Analyze how different tax rates affect the savings from a discount
Standards Alignment
  • 7.RP.A.3 (CCSS.MATH.CONTENT.7.RP.A.3)

    Use proportional relationships to solve multistep ratio and percent problems

  • 7.EE.B.3 (CCSS.MATH.CONTENT.7.EE.B.3)

    Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers

Lesson Resources
  • visualPrice Breakdown Chart

    Shows how price changes at each step: original, after discount, after tax

  • activityStore Comparison Challenge

    Compare final prices at different stores with varying discounts and tax rates

  • worksheetShopping Scenarios

    Real-world problems involving sales, coupons, and taxes

Lesson Content

Everything students see: definition, examples, common mistakes, applications. Tap to open.

Definition

When shopping, you often encounter both discounts (which reduce the price) and sales tax (which increases the price). The key question is: in what order do we apply them?
The Rule: Always apply the discount first, then calculate tax on the discounted price.
Final Price=Original Price×(1−Discount Rate)×(1+Tax Rate)\text{Final Price} = \text{Original Price} \times (1 - \text{Discount Rate}) \times (1 + \text{Tax Rate})
Why this order? Stores are required by law to charge tax only on the amount you actually pay, not on the original sticker price.

Worked Examples

A jacket costs 80 dollars and is 25% off. Sales tax is 8%. What is the final price?
1

Calculate the discount amount

80×0.25=2080 \times 0.25 = 20 dollars discount → 20 dollars off
2

Find the discounted price

80−20=6080 - 20 = 60 dollars
3

Calculate tax on discounted price

60×0.08=4.8060 \times 0.08 = 4.80 dollars tax
4

Add tax to get final price

60+4.80=64.8060 + 4.80 = 64.80 dollars

Common Mistakes

Applying tax first, then the discount

Why it's wrong: 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.

Adding the discount and tax percentages together

Why it's wrong: 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.

Forgetting that tax applies to the discounted price

Why it's wrong: 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.

Why It Matters

Understanding how discounts and taxes work together is essential for:
  • Smart Shopping: Know exactly how much you'll pay at checkout before you get there
  • Budget Planning: Calculate whether a sale item fits your budget after tax
  • Comparing Deals: Determine which store offers a better final price
  • Avoiding Surprises: No more shock when the total is higher than expected
Every time you see a "25% OFF" sign, you need this skill to know your true cost!

Real World Applications

Black Friday Shopping

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

Example:

A 200 dollar TV is 40% off on Black Friday. With 6% sales tax, the final price is 200×0.60×1.06=127.20200 \times 0.60 \times 1.06 = 127.20 dollars.

1Try It Yourself

You have 100 dollars to spend. A jacket originally costs 120 dollars and is 30% off. Sales tax is 5%.

Can you afford the jacket?

Step 1: Write the mathematical expression

Calculate: 120×0.70×1.05120 \times 0.70 \times 1.05

Online Shopping

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

Example:

A 50 dollar order with a 20% coupon code and 9% tax: 50×0.80×1.09=43.6050 \times 0.80 \times 1.09 = 43.60 dollars.

2Try It Yourself

An online store shows a 90 dollar item with a 15% promo code. Your state has 8% sales tax.

What will you pay at checkout?

Step 1: Write the mathematical expression

Calculate: 90×0.85×1.0890 \times 0.85 \times 1.08

Key Takeaways

  • 1When both discount and tax apply, always calculate discount first, then tax
  • 2Tax is calculated on the discounted price, not the original price
  • 3Use multipliers for faster calculation: (1−discount)×(1+tax)(1 - \text{discount}) \times (1 + \text{tax})
  • 4This order is required by law and reflects what you actually pay

Frequently Asked Questions

Why do we apply the discount before the tax?

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.

Does the order matter mathematically?

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.

What if I have multiple discounts?

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

Glossary

Discount
A reduction in the original price, usually expressed as a percentage (e.g., 25% off)
Sales tax
A government-imposed tax on purchases, calculated as a percentage of the sale price
Multiplier
A decimal used to calculate percent changes in one step (e.g., 0.75 for 25% off)
Sticker price
The original price shown on a product before any discounts

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Understanding Tax Brackets

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Common Tip Percentages

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