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A3.1 · Interpret purchase incentives

Learn to interpret purchase incentives through clear examples and targeted practice.

Ontario Grade 11 Mathematics

Earning and Purchasing

Read the offer, work out what it is worth, and check the conditions

A store sign says “Save CAD 40 today,” while another says “Get CAD 40 back after purchase.” Both offers mention CAD 40, but they do not work in the same way. The first lowers the amount paid at checkout. The second may require a form and may arrive later. A purchase incentive is a special offer meant to encourage someone to buy. To interpret one, identify what the buyer receives, calculate its value, and read the conditions. The goal is not to choose the offer with the biggest number on its sign. It is to understand what the buyer will actually pay and do.

What you will learn

Identify the benefit and conditions in a purchase incentive.
Calculate a discount or rebate using clear arithmetic or a calculator.
Compare offers by considering the final cost and when a benefit is received.
Explain why an offer may not be as useful as it first appears.

1. Read the offer before doing arithmetic

Start by finding the regular price and the incentive. A discount reduces the price at the time of purchase. A coupon or sale may give a fixed amount off, such as CAD 25, or a percent off, such as 15%. A rebate is money returned after the buyer pays. The buyer may need to submit a receipt or claim form.

Other incentives can work differently. A loyalty program may give points that can later be used toward a purchase. A financing promotion may let a buyer pay over time under stated terms. For any offer, read the fine print: it may name eligible products, an end date, a minimum purchase, or steps the buyer must complete.

A condition is a rule that must be met to receive the advertised benefit. For example, “Save CAD 30 on purchases over CAD 200” does not give the discount to someone buying an item for CAD 180. Do not assume that an offer applies until you have checked its conditions.

Separate the advertised benefit from the rules for receiving it.
A discount is applied at purchase; a rebate is claimed afterward.
Check dates, eligible items, minimum purchases, and required actions.

2. Calculate the value of a discount or rebate

A percent is a number out of 100. To find a percent discount, first find that part of the price, then subtract it from the price. For example, 10% of CAD 80 is CAD 8, so a 10% discount makes the price CAD 72 before any other charges. A calculator is useful, but the meaning of the calculation matters: the discount amount is not the final price.

For a fixed discount, subtract the stated amount from the eligible price. For a rebate, first work out the amount paid at checkout. Then subtract the rebate to find the eventual cost if the claim is approved. Keep the two amounts separate because the buyer must have enough money to pay the checkout amount first.

A spreadsheet can make comparisons easier. Put each offer in its own row. Use columns for regular price, discount or rebate, checkout price, and eventual cost. Enter the offer's conditions in a note column. This helps prevent a delayed rebate from being mistaken for an immediate discount.

\text{reduced price}=\text{original price}-\text{discount amount}

Find the discount amount before finding the reduced price.
For a rebate, distinguish checkout cost from eventual cost.
Use a calculator or spreadsheet to support, not replace, careful reading.

3. Compare the whole offer, not just its headline

Two incentives can have the same advertised value but different usefulness. An immediate discount is certain once the buyer qualifies. A rebate may have the same dollar value, but the buyer must follow the claim instructions and wait. A points offer may be useful to a regular customer, but points are not the same as cash unless the program explains how they can be used.

When comparing offers, use the same starting price and check that each offer applies to the same item. Work out the checkout amount and any later benefit. Then consider the conditions and timing. Ask: Do I qualify? What do I pay today? What must I do afterward? When can I use or receive the benefit?

A lower eventual cost does not always mean an offer is the easiest choice. A buyer may prefer a smaller immediate discount to a larger rebate that requires a lengthy claim. The suitable choice depends on the buyer's needs and whether the conditions can be met. Avoid treating an incentive as a reason to buy something that is not needed.

Compare offers using the same product and starting price.
Include timing and required actions in your interpretation.
State what is known and what depends on completing a condition.

4. Use a repeatable decision process

For each offer, record the price, the benefit, and the conditions. Calculate the amount paid at checkout. If there is a later rebate or points reward, show it separately rather than subtracting it too soon. Finally, describe which offer is more useful for the stated buyer and explain why.

This process also works when a promotion has more than one step. For example, if a coupon applies only after a minimum purchase, first check whether the purchase meets that minimum. If it does not, the coupon value for that purchase is zero. If it does, calculate the discount according to the stated offer.

Clear explanations use specific amounts and conditions. Instead of saying “Offer B is better,” say “Offer B has a lower eventual cost if the rebate claim is approved, but Offer A reduces the checkout amount immediately.” That statement shows both the arithmetic and the practical difference.

Check eligibility before calculating an incentive.
Show immediate and later benefits separately.
Support a choice with amounts and conditions.

What to record when comparing incentives

Offer type	At checkout	Later benefit	What to check
Discount	Pay the reduced price	Usually none	Eligible item and offer dates
Rebate	Usually pay the listed price	Money may be returned after a claim	Claim steps, deadline, and approval
Points	Pay according to the offer	Points may be used later under program rules	How points are earned and used

Worked example

Example 1: Percent discount at checkout

A store lists a small appliance for CAD 160. A coupon gives 15% off the listed price. What is the discount amount and the price after the coupon, before any other charges?

Check eligibility
The coupon applies to this appliance, and no minimum purchase or other condition is stated. The listed price is the amount to use.
Find the discount
Since 15% means 15 out of every 100, find 15% of CAD 160. The calculator result is the amount taken off, not the amount still owed.
$160\times 0.15=24$
Find the reduced price
Subtract the discount from the listed price. This gives the checkout price before any other charges.
$160-24=136$

Answer: The coupon saves CAD 24. The price after the coupon is CAD 136 before any other charges.

Check: The discount is less than the original price, and adding CAD 24 back to CAD 136 gives the listed price of CAD 160.

Worked example

Example 2: Immediate discount compared with a rebate

A store offers a device for CAD 240 with CAD 30 off at checkout. Another store lists the same device for CAD 240 and offers a CAD 45 rebate after purchase. Assume both offers apply and the rebate claim is approved. Compare checkout cost and eventual cost, then explain a practical difference.

Calculate the immediate offer
The CAD 30 is removed at checkout, so subtract it from the listed price to find what the buyer pays that day.
$240-30=210$
Calculate the rebate offer
The buyer first pays the full listed price. If the claim is approved, subtract the rebate to find the eventual cost.
$240-45=195$
Compare the two amounts
The rebate offer has the lower eventual cost under the stated assumption. However, the buyer must pay more at checkout and complete the claim process.
$210-195=15$

Answer: The immediate offer costs CAD 210 at checkout. The rebate offer costs CAD 240 at checkout and CAD 195 eventually if approved. The rebate offer's eventual cost is CAD 15 lower, but it requires a claim and more money at the time of purchase.

Check: The rebate offer's checkout amount remains CAD 240; the CAD 45 is not removed until the claim is approved.

Common mistakes and how to avoid them

Subtracting a percent number directly, such as taking 15 away from a price of CAD 160.

Correction: First calculate 15% of the price. Then subtract that dollar amount.

Treating a rebate as an immediate discount.

Correction: Show the full checkout cost first. Subtract the rebate only when describing the eventual cost, and note that the claim must be approved.

Choosing the offer with the largest advertised number without checking its rules.

Correction: Check eligibility, required actions, timing, and the amount the buyer must pay.

Lesson summary

A purchase incentive offers a benefit to encourage a purchase.
Read the conditions before calculating or comparing an offer.
A discount lowers the checkout price; a rebate is received later if its conditions are met.
Compare checkout cost, eventual cost, timing, and required actions.

Check your understanding

Question 1

A CAD 90 item has a coupon for 20% off. What is the price after the coupon, before any other charges?

CAD 18
CAD 70
CAD 72
CAD 110

Show answer and explanation

CAD 72

20% of CAD 90 is CAD 18. Subtract the discount: CAD 90 minus CAD 18 is CAD 72.

Question 2

A CAD 25 rebate is offered on an item listed for CAD 130. What does the buyer pay at checkout before receiving the rebate?

CAD 25
CAD 105
CAD 130
CAD 155

Show answer and explanation

CAD 130

A rebate is received after purchase. The buyer pays the listed CAD 130 at checkout, then may receive CAD 25 if the claim is approved.

Question 3

A sign offers CAD 40 off, but only on purchases over CAD 250. A buyer's eligible purchase is CAD 235. What should the buyer conclude?

The purchase qualifies because it is close to CAD 250.
The discount is CAD 40 because every buyer receives it.
The purchase does not meet the stated minimum.
The discount changes the purchase to CAD 275.

Show answer and explanation

The purchase does not meet the stated minimum.

CAD 235 is not over CAD 250, so the stated condition is not met and the buyer should not count on the discount.

Key terms

Purchase incentive: A special offer intended to encourage someone to buy.
Discount: An amount or percent taken off a price.
Rebate: Money returned after a purchase, often after the buyer completes a claim.
Condition: A rule that must be met to receive an offer.

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About this lesson

Published by DoAssignment. This AI-assisted lesson follows Ontario Grade 11 Mathematics (MEL3E), expectation A3.1. It is a study resource, not an official curriculum publication.

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