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F1.5 · Compare sale and loyalty offers for best value

Learn to compare sale and loyalty offers for best value through clear examples and targeted practice.

Ontario Grade 8 Mathematics

Financial Literacy

Grade 8 Mathematics — F1.5

A store might offer a sale price, loyalty rewards, or both. A sale lowers the amount paid now. A loyalty reward may lower a later purchase, but only if the shopper can use it. To compare offers fairly, use the same item and starting price, work out each offer carefully, and check any conditions. The examples in this lesson use hypothetical store offers. CAD means Canadian dollars.

What you will learn

  • Work out the price after a sale discount.
  • Find the value of loyalty rewards that can be used on a purchase.
  • Compare offers using the same item and the same starting price.
  • Choose the offer that gives the lower cost or greater value for the shopper.

Start with the amount paid

A discount is an amount taken off a price. A sale that takes off a percentage uses a part of the original price. For example, a 20% discount means taking off 20 out of every 100 equal parts of the price.
To find a sale price, first find the discount amount. Then subtract it from the original price. The original price is the price before the offer. The sale price is the amount paid after the discount.
A useful check is to ask whether the sale price is lower than the original price. If the discount is positive, the sale price should be lower.
sale price=original price−discount amount\text{sale price} = \text{original price} - \text{discount amount}
  • Find the discount amount before finding the sale price.
  • A percentage discount is based on the original price unless the offer says otherwise.

Understand loyalty rewards

A loyalty offer gives a reward to shoppers who meet the store's rules. The reward might be points or a credit to use on a later purchase. A reward is not always the same as money taken off today's bill.
Before counting a reward as savings, check what it is worth and when it can be used. For example, a store may require a minimum points balance or may allow the reward only on a later visit. If the offer does not say that the reward can be used on this purchase, do not subtract it from today's price.
For a fair comparison, look at the value the shopper can actually use. If an offer gives a CAD 5 reward that can be used later, it may be useful, but the shopper still pays the full purchase price today.
  • Check the reward's stated value and the rules for using it.
  • Keep today's cost separate from a reward for a later purchase.

Compare offers fairly

Best value depends on what the shopper wants to compare. If the goal is to spend less today, compare the amount paid today. If a usable reward is also part of the decision, compare both today's cost and the reward's value.
Keep the item, starting price, and purchase conditions the same when comparing. Otherwise, a lower total may come from buying a different item or quantity rather than from the offer.
A simple comparison chart can help. Write each offer in a separate row. Record the price paid now and any reward that can truly be used. Then explain which offer suits the shopper's goal.
amount paid today=original price−discount used today\text{amount paid today} = \text{original price} - \text{discount used today}
  • Use the same starting price for each offer.
  • Do not count a future reward as an immediate discount.
  • State whether your choice is based on lower cost today or total usable value.

A careful decision

A larger-looking percentage does not always mean the best offer. Compare the final amounts in the same units, such as CAD. If one offer gives a reward instead of an immediate price reduction, describe that difference clearly.
Read the offer conditions before deciding. A reward with an expiry date or a minimum purchase requirement may be less useful to someone who cannot meet those conditions. The best offer can depend on the shopper's plans.
When explaining a choice, include the calculation and the reason the comparison is fair. A clear answer tells both which offer is better for the stated goal and what assumption was used.
  • Compare calculated results, not just the wording or size of an offer.
  • Offer conditions affect whether a reward is useful.
  • Explain the goal behind your choice.

Record the offer details

OfferPaid todayReward for laterWhat to compare
Sale discountPrice after discountOnly if also offeredLower cost today
Loyalty rewardPrice charged nowReward value and rulesToday's cost and usable later value

Worked example

Find the sale price

A backpack has a hypothetical original price of CAD 60. A store offers 25% off. What is the sale price?
Backpack price comparison
Backpack price comparisonHypothetical prices in CAD. The sale price is CAD 15 below the original price.60 CADOriginal price45 CADSale price

Hypothetical prices in CAD. The sale price is CAD 15 below the original price.

  1. Find the discount
    The discount is 25% of CAD 60. Since 25% is one quarter, divide CAD 60 into four equal parts. Each part is CAD 15, so the discount is CAD 15.
    60÷4=1560 \div 4 = 15
  2. Subtract the discount
    The sale price is the original price minus the discount. Subtracting CAD 15 from CAD 60 gives CAD 45.
    60−15=4560 - 15 = 45
Answer: The sale price is CAD 45.
Check: CAD 45 is less than the original CAD 60, as it should be after a discount.

Worked example

Compare a sale with a usable reward

A lunch bag costs CAD 40. Store A offers 10% off. Store B charges CAD 40 and gives a CAD 6 reward that can be used on a later purchase. Which offer costs less today, and what is the reward's value?
Today's cost for each offer
Today's cost for each offerHypothetical costs in CAD. The CAD 6 later reward is not included in today's cost.36 CADStore A sale40 CADStore B today

Hypothetical costs in CAD. The CAD 6 later reward is not included in today's cost.

  1. Work out Store A's discount
    Ten percent is one tenth. One tenth of CAD 40 is CAD 4. Subtract that discount from the original price to find what is paid today.
    40÷10=440 \div 10 = 4
  2. Compare today's costs
    Store A costs CAD 36 today. Store B costs CAD 40 today because its reward is for a later purchase, not this bill. Store A costs less today.
    40−4=3640 - 4 = 36
  3. Describe the reward fairly
    Store B also gives a CAD 6 reward. If the shopper can use the reward later under the offer's rules, it has value, but it does not change the CAD 40 paid today. The shopper should choose based on whether lower cost now or a later reward matters more.
Answer: Store A costs less today: CAD 36 rather than CAD 40. Store B gives a separate CAD 6 reward for later, so it may suit a shopper who can use that reward.
Check: The comparison does not subtract Store B's reward from today's bill because the offer says it is for a later purchase.

Worked example

Compare two offers that both apply now

A water bottle has a hypothetical original price of CAD 50. Offer A gives 20% off now. Offer B gives CAD 8 off now. Which offer has the lower price?
Water bottle offer prices
Water bottle offer pricesHypothetical final prices in CAD after discounts applied now.40 CADOffer A42 CADOffer B

Hypothetical final prices in CAD after discounts applied now.

  1. Calculate Offer A
    Find 20% of CAD 50. Ten percent is one tenth, or CAD 5. So 20% is twice that amount, or CAD 10. Subtract CAD 10 from CAD 50.
    2×(50÷10)=102 × (50 \div 10) = 10
  2. Calculate Offer B
    Offer B takes CAD 8 off the same CAD 50 price. Subtract the discount to get its price.
    50−8=4250 - 8 = 42
  3. Compare the results
    Offer A gives a price of CAD 40. Offer B gives a price of CAD 42. Both discounts apply now, so comparing the final prices shows that Offer A is lower by CAD 2.
    50−10=4050 - 10 = 40
Answer: Offer A is the better value for a lower price today. It costs CAD 40, which is CAD 2 less than Offer B.
Check: Offer A's discount of CAD 10 is larger than Offer B's discount of CAD 8, and the final prices confirm the choice.

Common mistakes and how to avoid them

Subtracting a later loyalty reward from the amount paid today.
Correction: Keep the reward separate unless the offer says it can be used on this purchase.
Comparing only the discount percentages.
Correction: Calculate each final price. A fixed amount and a percentage can be compared by converting both to amounts off the same original price.
Choosing the offer with the biggest reward without checking its rules.
Correction: Check when the reward can be used and whether the shopper can meet any conditions.

Lesson summary

  • Find the amount of a sale discount, then subtract it from the original price.
  • Check whether a loyalty reward applies now or later.
  • Compare offers using the same item and starting price.
  • Explain whether the choice is based on lower cost today or on a reward the shopper can use.

Check your understanding

Question 1

A notebook costs CAD 30. A store offers 10% off. What is the sale price?
  1. CAD 27
  2. CAD 29
  3. CAD 20
  4. CAD 33
Show answer and explanation
CAD 27
Ten percent of CAD 30 is CAD 3. Subtract CAD 3 from CAD 30 to get CAD 27.

Question 2

A store charges CAD 25 today and gives a CAD 4 loyalty reward for a later visit. How much does the shopper pay today?
  1. CAD 21
  2. CAD 25
  3. CAD 4
  4. CAD 29
Show answer and explanation
CAD 25
The reward is for later, so it is not subtracted from today's bill. The shopper pays CAD 25 today.

Question 3

A game costs CAD 40. Offer A takes CAD 6 off now. Offer B gives 10% off now. Which has the lower price?
  1. Offer A, at CAD 34
  2. Offer B, at CAD 36
  3. Both, at CAD 34
  4. Offer A, at CAD 36
Show answer and explanation
Offer A, at CAD 34
Offer A gives CAD 40 minus CAD 6, or CAD 34. Ten percent of CAD 40 is CAD 4, so Offer B costs CAD 36. Offer A is lower.

Key terms

Original price
The price before an offer is applied.
Discount
An amount taken off a price.
Sale price
The amount paid after a sale discount.
Loyalty reward
A benefit given to a shopper under a store's loyalty offer, such as points or credit.
Best value
The offer that best meets the shopper's goal after its cost and usable rewards are compared.

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Published by DoAssignment. This reviewed lesson follows Ontario Grade 8 Mathematics, expectation F1.5. It is a study resource, not an official curriculum publication.

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