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A3.4 · Calculate discounts, sale prices, and after-tax costs

Learn to calculate discounts, sale prices, and after-tax costs through clear examples and targeted practice.

Ontario Grade 11 Mathematics

Earning and Purchasing

Grade 11 MEL3E | Study topic A3.4

A jacket is marked at CAD 84 and is on sale for 25% off. The price tag tells you the original price, but you still need to find the discount, the sale price, and the amount you will pay after tax. These are three separate calculations. A calculator or spreadsheet can help, but it is important to know what each number represents. A percent means “out of 100.” For example, 25% means 25 out of 100. In this lesson, you will use that idea to work through everyday shopping situations.

What you will learn

  • Calculate the amount saved from a discount and the sale price.
  • Calculate tax on a sale price and the final after-tax cost.
  • Use a calculator or spreadsheet to check each step and make a sensible money decision.

1. Find the discount and sale price

A discount is the amount taken off an original price. The original price is the price before the discount. The sale price is the price after the discount but before tax.
To find a discount amount, change the percent to a decimal by dividing by 100, then multiply by the original price. For example, 20% becomes 0.20. This works because 20% is 20 hundredths of the price.
Once you know the discount amount, subtract it from the original price. Check that the sale price is lower than the original price. The amount saved should also match the difference between those prices.
On a calculator, enter the original price multiplied by the discount rate. On a spreadsheet, if cell A2 has the original price and B2 has the discount rate entered as 20%, use `=A2*B2` for the discount amount. Subtract that result from the original price to get the sale price.
discount amount=original price×discount rate\text{discount amount}=\text{original price}×\text{discount rate}
  • Discount amount = original price multiplied by the discount rate.
  • Sale price = original price minus discount amount.
  • Use the sale price, not the original price, when you continue to calculate tax.

2. Calculate the after-tax cost

Tax is an amount added to a purchase. The after-tax cost is the sale price plus the tax. For this lesson’s examples, the stated tax rate is 13%. Always use the tax rate given for the situation; this lesson does not cover different product tax rules.
First calculate the tax on the sale price. Change 13% to 0.13, then multiply the sale price by 0.13. Add the tax to the sale price. This order matters: when an item is discounted, tax is calculated on the discounted price in these examples.
A useful check is to confirm that the after-tax cost is greater than the sale price. Also estimate the tax: at 13%, it should be a little more than one tenth of the sale price. Round money to the nearest cent at the end of the calculation unless the task asks otherwise.
A spreadsheet can keep the steps clear. If C2 contains the sale price and D2 contains the tax rate, use `=C2*D2` to find tax, then add the result to C2. Label each cell so you can tell original price, discount, sale price, tax, and total apart.
after-tax cost=sale price+tax amount\text{after-tax cost}=\text{sale price}+\text{tax amount}
  • Tax amount = sale price multiplied by the tax rate.
  • After-tax cost = sale price plus tax amount.
  • Keep the discount and tax calculations separate so the tax is based on the sale price.

3. Use the result to make a purchase decision

A price sign may show only a discount, while your budget must cover the after-tax cost. Calculate the full cost before deciding whether an item fits your budget. If two offers are being compared, use the same steps for each offer and compare their after-tax costs.
Read the details carefully. Check the original price, discount rate, and tax rate. A discount written as a dollar amount is already the amount saved, so subtract it directly. A discount written as a percent must first be applied to the original price.
Calculators reduce arithmetic errors, and spreadsheets are helpful when comparing several items. They do not decide which price to use. You must identify whether a number is an original price, discount amount, sale price, or tax amount before entering it.
For a final check, ask: Is the discount less than the original price? Is the sale price lower than the original price? Is tax added to the sale price? Does the total fit the amount available to spend?
  • Read the price information and identify what each number means.
  • Calculate each offer in the same order before comparing.
  • Use the after-tax cost to check a purchase against a budget.

Price calculation sequence

StageWhat it meansJacket example
Original pricePrice before the discountCAD 84.00
Discount amountAmount taken offCAD 21.00
Sale priceOriginal price less discountCAD 63.00
Tax amountTax calculated on sale priceCAD 8.19
After-tax costSale price plus taxCAD 71.19

Worked example

Example 1: Jacket on sale

A jacket has an original price of CAD 84. The store offers 25% off, and the tax rate for this example is 13%. Find the discount amount, sale price, and after-tax cost.
  1. Find the discount rate
    Convert 25% to a decimal by dividing 25 by 100. This gives the part of the original price that will be taken off.
    25÷100=0.2525\div100=0.25
  2. Calculate the discount amount
    Multiply the original price by 0.25. The result is the amount saved.
    84×0.25=2184\times0.25=21
  3. Find the sale price
    Subtract the CAD 21 discount from CAD 84. The sale price is the amount to use for the tax calculation.
    84−21=6384-21=63
  4. Calculate tax and total
    Find 13% of the CAD 63 sale price, then add that tax to the sale price. Round the tax and total to the nearest cent.
    63×0.13=8.19;63+8.19=71.1963\times0.13=8.19; 63+8.19=71.19
Answer: The discount is CAD 21. The sale price is CAD 63. The after-tax cost is CAD 71.19.
Check: The sale price is below CAD 84, and the total is CAD 8.19 above the sale price. Both checks fit the situation.

Worked example

Example 2: Compare a discounted work bag with a budget

A work bag has an original price of CAD 126 and is marked 15% off. The tax rate for this example is 13%. A student has CAD 124 available. Find the after-tax cost and decide whether the bag fits the budget.
  1. Convert the discount percent
    Divide 15 by 100 to write the discount as a decimal. This gives the portion of CAD 126 that will be removed.
    15÷100=0.1515\div100=0.15
  2. Find the amount saved
    Multiply CAD 126 by 0.15 to calculate the discount amount.
    126×0.15=18.90126\times0.15=18.90
  3. Find the sale price
    Subtract CAD 18.90 from the original price. Tax will be calculated on this sale price.
    126−18.90=107.10126-18.90=107.10
  4. Find the after-tax cost
    Calculate 13% of CAD 107.10, then add the tax. Keep the money amount to the nearest cent.
    107.10×0.13=13.923≈13.92;107.10+13.92=121.02107.10\times0.13=13.923\approx13.92; 107.10+13.92=121.02
  5. Compare with the budget
    Compare the after-tax cost with CAD 124. Since CAD 121.02 is less than the available amount, the bag fits the budget.
    124−121.02=2.98124-121.02=2.98
Answer: The discount is CAD 18.90, the sale price is CAD 107.10, and the after-tax cost is CAD 121.02. The bag fits the CAD 124 budget, with CAD 2.98 left.
Check: Tax is about 13% of the sale price, and the after-tax cost is greater than the sale price but less than the budget.

Common mistakes and how to avoid them

Subtracting 25 from the original price for a 25% discount.
Correction: A percent is a part of the price, not a dollar amount. Find 25% of the original price first.
Calculating tax on the original price after a discount.
Correction: In these examples, calculate tax on the sale price, after subtracting the discount.
Calling the sale price the final cost.
Correction: The sale price is before tax. Add the tax amount to find the after-tax cost.
Rounding the tax too early or writing only a whole-dollar answer.
Correction: Keep the calculation accurate and report money to the nearest cent.

Lesson summary

  • Change a discount percent to a decimal and multiply by the original price to find the discount amount.
  • Subtract the discount amount from the original price to find the sale price.
  • Multiply the sale price by the tax rate to find tax, then add tax to find the after-tax cost.
  • Check the final cost against the budget and use a calculator or spreadsheet to verify arithmetic.

Check your understanding

Question 1

A pair of shoes costs CAD 90 before tax and has a 20% discount. What is the sale price before tax?
  1. CAD 18.00
  2. CAD 70.00
  3. CAD 72.00
  4. CAD 108.00
Show answer and explanation
CAD 72.00
The discount is CAD 90 multiplied by 0.20, which is CAD 18. Subtract CAD 18 from CAD 90 to get a sale price of CAD 72.

Question 2

A discounted item has a sale price of CAD 50. The tax rate is 13%. What is its after-tax cost?
  1. CAD 50.13
  2. CAD 56.50
  3. CAD 63.00
  4. CAD 43.50
Show answer and explanation
CAD 56.50
Tax is CAD 50 multiplied by 0.13, or CAD 6.50. Add the tax to the sale price: CAD 50 plus CAD 6.50 is CAD 56.50.

Question 3

A tool has an original price of CAD 160 and a discount of 10%. Tax is 13%. Which is the after-tax cost?
  1. CAD 144.00
  2. CAD 160.00
  3. CAD 163.20
  4. CAD 144.00 plus CAD 18.72, which is CAD 162.72
Show answer and explanation
CAD 144.00 plus CAD 18.72, which is CAD 162.72
The discount is CAD 16, so the sale price is CAD 144. Tax on CAD 144 is CAD 18.72. Adding them gives an after-tax cost of CAD 162.72.

Key terms

Original price
The price before a discount is applied.
Discount
An amount or percent taken off a price.
Sale price
The original price after subtracting the discount, before tax.
Tax
An amount added to a purchase at the stated tax rate.
After-tax cost
The sale price plus the tax amount.

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Published by DoAssignment. This reviewed lesson follows Ontario Grade 11 Mathematics (MEL3E), expectation A3.4. It is a study resource, not an official curriculum publication.

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