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Grade 7 · lesson 1 of 4

Apply a Discount before a Tax

A discount removes a percent of the original price.

About 20 minutes, plus any extended practice

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Supplied materials

  • Paper or a browser scratch area; a calculator is optional unless rounding is requested.
  • Supplied teaching case: A fictional item costs $40. Apply a 20% discount, then 5% tax to the discounted price. What is the final total? Candidate answers: (A) 30 USD (B) 33.6 USD (C) 34 USD (D) 42 USD.
  • Independent check inputs: A fictional item costs $60. Apply a 20% discount, then 5% tax to the discounted price. What is the final total? Candidate answers: (A) 45 USD (B) 50.4 USD (C) 51 USD (D) 63 USD.

Learn the idea

A percent is a ratio per hundred, but its base quantity matters. Successive percent operations act on successive amounts; reverse problems recover the original base rather than simply adding back a percentage. A discount removes a percent of the original price. Tax applied after a discount uses the reduced price, so the two operations can be represented as successive multipliers.

Here is the method on the supplied teaching case. Keep 80% after the discount: $40×0.80=$32.00. Then multiply by 1.05 for tax: $33.60. Tax is not applied to the original price.

Use the taxable base stated in the fictional problem; actual tax rules may differ. Do not add or subtract percent rates as if each acted on the same unchanged dollar amount.

  1. Write or sketch the supplied teaching case, labeling its quantities and restrictions.
  2. Apply the method shown in the worked solution, keeping each intermediate equality or justified inference.
  3. Solve the independent check with its changed inputs before revealing feedback.
  4. Complete the three practice cases; explain which mathematical rule rules out one distractor in each case.
Worked example

See the method in action

Teaching case: A fictional item costs $40. Apply a 20% discount, then 5% tax to the discounted price. What is the final total? Candidate answers: (A) 30 USD (B) 33.6 USD (C) 34 USD (D) 42 USD. Solution: Keep 80% after the discount: $40×0.80=$32.00. Then multiply by 1.05 for tax: $33.60. Tax is not applied to the original price. The final answer is 33.6 USD. Use the taxable base stated in the fictional problem; actual tax rules may differ. Do not add or subtract percent rates as if each acted on the same unchanged dollar amount.

Your turn

Check your reasoning

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Helpful tips
  • A discount removes a percent of the original price.
  • Use the taxable base stated in the fictional problem; actual tax rules may differ.
A fictional item costs $60. Apply a 20% discount, then 5% tax to the discounted price. What is the final total?

Feedback appears here after you check. This is practice, not a graded school assessment.

See the answer and explanation

50.4 USD

Keep 80% after the discount: $60×0.80=$48.00. Then multiply by 1.05 for tax: $50.40. Tax is not applied to the original price.

Take it further

Changed-input task: A fictional item costs $180. Apply a 20% discount, then 5% tax to the discounted price. What is the final total? Candidate answers: (A) 135 USD (B) 151.2 USD (C) 153 USD (D) 189 USD. Show the mathematical reason, not only the selected answer. Expected result: 151.2 USD. Keep 80% after the discount: $180×0.80=$144.00. Then multiply by 1.05 for tax: $151.20. Tax is not applied to the original price.

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More practice: try new cases

Choose an answer for each problem. Explain your method on paper, then use the feedback to decide what to revisit.

More practice: try new cases
1. A fictional item costs $80. Apply a 20% discount, then 5% tax to the discounted price. What is the final total?
Need a hint?
  • A discount removes a percent of the original price.
  • Use the taxable base stated in the fictional problem; actual tax rules may differ.
2. A fictional item costs $100. Apply a 20% discount, then 5% tax to the discounted price. What is the final total?
Need a hint?
  • A discount removes a percent of the original price.
  • Use the taxable base stated in the fictional problem; actual tax rules may differ.
3. A fictional item costs $120. Apply a 20% discount, then 5% tax to the discounted price. What is the final total?
Need a hint?
  • A discount removes a percent of the original price.
  • Use the taxable base stated in the fictional problem; actual tax rules may differ.

Your choices are temporary. Feedback appears after you check all the answers.

Nothing here is saved to an account or sent to a teacher. Keep your own notes or download them before leaving. The score describes these questions; it does not certify subject mastery.

Check the subject sources

These LifeStarter passages, scenarios and exercises are authored for this Academy with AI assistance and review. External resources keep their publishers’ terms. A grade label suggests a starting level; it does not establish alignment with your school’s complete requirements.