Estimate sale prices before tax

Ontario Grade 11 Mathematics

Earning and Purchasing

Use friendly numbers and a clear discount plan to estimate what an item will cost before tax.

A store sign says “30% off,” and you want to know whether a jacket fits your budget. You do not need an exact checkout total to make a useful decision. You can estimate the discount, subtract it from the regular price, and get an approximate sale price before tax. A discount is the amount taken off the regular price. The sale price is what remains after that discount. “Before tax” means the estimate does not include sales tax or other charges. This lesson focuses only on estimating that sale price.

What you will learn

Recognize that a sale price before tax is the original price minus the discount.
Estimate a discount by using a nearby price or a familiar percent such as 10%, 25%, or 50%.
Use a calculator or spreadsheet to support an estimate and check whether the answer makes sense.

1. Connect the discount to the sale price

Start with the regular price: the price before the sale discount. A percentage tells you how many parts out of 100 to use. For example, 10% means 10 out of every 100, so 10% of a price is one tenth of that price.

To estimate a sale price, first estimate how much money the discount takes off. Then subtract that estimated discount from the regular price. This works because the sale price is the part of the original price left after the amount taken off.

An estimate is a close, sensible answer rather than an exact one. You can round a price to make the arithmetic easier, but keep track of whether rounding makes your result a little higher or lower.

\text{Sale price} \approx \text{regular price} - \text{estimated discount}

Estimate the discount first.
Subtract the discount from the regular price.
Do not add tax when the task is to estimate the sale price before tax.

2. Use familiar percents and friendly numbers

A friendly number is a nearby number that is easier to work with. For a regular price of CAD 79.95, CAD 80 is a useful friendly number. The difference is only five cents, so using CAD 80 makes a quick estimate simple.

Some percents are especially useful. To find 10% of a price, move the decimal point one place left. To estimate 20%, find 10% and double it. To estimate 25%, find one quarter by dividing by 4. To estimate 50%, find one half by dividing by 2. These are ways to find the discount amount; the sale price still requires subtraction.

For a percent such as 30%, find 10% and multiply that amount by 3. For 15%, combine 10% and 5%; 5% is half of 10%. Use the method that makes the arithmetic clear. When prices are awkward, round first and describe your result as an estimate.

A nearby price can make mental arithmetic easier.
Break a percent into familiar parts when helpful.
After estimating the discount, subtract it from the regular price.

3. Use a calculator or spreadsheet as a check

A calculator can help with the discount calculation, especially when the price or percent is less familiar. Enter the regular price and calculate the chosen percent of it. Then subtract that amount from the regular price. Keep the word “estimate” in mind if you rounded the price before calculating.

A spreadsheet can organize several items. Put each regular price in one column and the discount percent in another. A third column can hold your estimated discount, and a fourth can show the estimated sale price. For an estimate, you may first round the regular price to a convenient amount; make a note of that rounded price so you can explain your result.

Technology does not decide whether an estimate is sensible. Check the result: a discounted sale price should be below the regular price, and the discount should be a reasonable part of that price. A 50% discount should leave about half the price, while a 10% discount should leave most of it.

Use technology to support the arithmetic, not to skip understanding.
Label rounded values so an estimate is not mistaken for an exact price.
Check that the sale price is lower than the regular price.

4. Make a useful buying decision

An estimate is useful when you need to compare a sale with your budget or compare two offers. Keep the method consistent: estimate each discount, subtract it from the regular price, and compare the resulting sale prices before tax.

Be careful when a displayed price has cents. Rounding CAD 79.95 to CAD 80 changes the starting price only slightly. Rounding a much larger amount to the nearest hundred could change the estimate more. Choose a rounding amount that keeps the calculation manageable without hiding a large difference.

If the estimated sale price is close to your budget limit, treat it as a rough guide rather than a guaranteed checkout total. The price before tax is not the same as the amount paid after tax. This lesson estimates only the sale price before tax.

Compare estimates using the same approach.
Round only as much as needed for manageable arithmetic.
Keep the before-tax sale price separate from a final checkout total.

Useful percent estimates

Discount percent	A quick way to estimate it	Example using CAD 80
10%	Divide by 10	CAD 8
20%	Find 10%, then double	CAD 16
25%	Divide by 4	CAD 20
50%	Divide by 2	CAD 40

Worked example

A jacket marked 30% off

A jacket has a regular price of CAD 79.95 and is marked 30% off. Estimate its sale price before tax.

Choose a friendly price
Round CAD 79.95 to CAD 80. The rounded amount is five cents higher, so the estimate will be very slightly higher than an estimate based on the exact regular price.
$\mathrm{CAD}\ 79.95 \approx \mathrm{CAD}\ 80$
Estimate the discount
Find 10% of CAD 80 by dividing by 10. Since 30% is three groups of 10%, multiply that amount by 3.
$0.10 × 80 = 8, 3 × 8 = 24$
Subtract the discount
The sale price is the regular price with the discount taken off. Subtract CAD 24 from the rounded price of CAD 80.
$80 - 24 = 56$

Answer: The estimated sale price is CAD 56 before tax.

Check: The discount is about CAD 24, which is 30% of CAD 80. CAD 56 is below CAD 80, as a sale price should be.

Worked example

A desk marked 15% off

A desk has a regular price of CAD 248 and is marked 15% off. Estimate its sale price before tax using a nearby friendly price.

Round the regular price
Use CAD 250 as a nearby friendly price. It is CAD 2 higher than the regular price, so the estimated sale price will be slightly higher than the result based on CAD 248.
$248 \approx 250$
Find 10% and 5%
Ten percent of CAD 250 is CAD 25. Five percent is half of 10%, so it is CAD 12.50. Add these parts to estimate the 15% discount.
$25 + 12.50 = 37.50$
Estimate the sale price
Subtract the estimated discount of CAD 37.50 from the rounded price of CAD 250. The result is an estimate before tax.
$250 - 37.50 = 212.50$

Answer: The estimated sale price is about CAD 212.50 before tax, or about CAD 213 to the nearest dollar.

Check: Fifteen percent is a little more than one tenth, so a discount of CAD 37.50 on about CAD 250 is reasonable. The sale estimate is below the regular price.

Common mistakes and how to avoid them

Reporting the discount amount as the sale price.

Correction: The discount is the amount taken off. Subtract it from the regular price to estimate the sale price.

Adding the discount to the regular price.

Correction: A discount lowers the price, so subtract the estimated discount.

Calling a rounded estimate an exact price.

Correction: State that it is an estimate and mention any rounding that affected it.

Including tax in a before-tax estimate.

Correction: Stop after estimating the sale price. Tax is outside this estimate.

Lesson summary

A discount is the amount taken off the regular price.
Estimate the discount using familiar percents and, when useful, a nearby friendly price.
Subtract the estimated discount from the regular price to estimate the sale price before tax.
Use a calculator or spreadsheet to check arithmetic, then judge whether the result makes sense.

Check your understanding

Question 1

A backpack costs CAD 60 and is 20% off. What is its estimated sale price before tax?

CAD 12
CAD 48
CAD 72
correctIndex»: 1,

Show answer and explanation

CAD 48

Twenty percent of CAD 60 is CAD 12. Subtract the discount: CAD 60 minus CAD 12 is CAD 48.

Question 2

A lamp costs CAD 39.90 and is 25% off. Round the regular price to CAD 40 and estimate the sale price before tax.

CAD 10
CAD 30
CAD 50
correctIndex»: 1,

Show answer and explanation

CAD 30

One quarter of CAD 40 is CAD 10. Subtract CAD 10 from CAD 40 to estimate a sale price of CAD 30.

Question 3

Which estimate is most sensible for a CAD 100 item marked 50% off?

About CAD 50 before tax
About CAD 100 before tax
About CAD 150 before tax
correctIndex»: 0,

Show answer and explanation

About CAD 50 before tax

A 50% discount is half of CAD 100, or CAD 50. Subtracting that discount leaves about CAD 50 before tax.

Key terms

Regular price: The price before a sale discount is taken off.
Discount: The amount taken off the regular price.
Sale price: The price left after subtracting the discount from the regular price.
Estimate: A close, sensible answer that may not be exact.
Friendly number: A nearby number chosen because it makes arithmetic easier.

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About this lesson and its review

Published by DoAssignment. This reviewed lesson follows Ontario Grade 11 Mathematics (MEL3E), expectation A3.2. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

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