Consumer Math Basics: Markdown and Markup (Original Price, Retail Math, Clearance Calculation)

Consumer Math – Markdown and Markup (Original Price, Retail Math, Clearance Calculation)

Study Guide: Markdown and Markup (Retail Math for Smart Shoppers)

What This Is

Markdown and markup are the math behind sales, discounts, and pricing. Markup is how stores add profit to the cost of an item (e.g., a $5 shirt marked up to $15). Markdown is how they reduce prices to clear inventory (e.g., that $15 shirt on sale for $10). Understanding these helps you: - Spot real deals vs. fake discounts - Calculate final prices before checkout - Compare prices like a pro (e.g., "Is a 30% off sale better than a $20 coupon?") - Avoid overpaying for "clearance" items that aren’t actually a bargain

Real-life scenario: You see a jacket marked "50% off original price of $200" but the tag says "Now $120." Is this really a 50% discount? (Spoiler: No—it’s only 40% off. Stores often inflate "original prices" to make sales seem better.)

Key Terms & Formulas

• Cost Price (CP): What the store paid for the item. Example: A store buys a pair of shoes for $40.
• Selling Price (SP): The price the store charges customers. Example: The shoes are sold for $80.
• Markup (M): The amount added to the cost price to get the selling price. Formula: M = SP – CP Example: $80 (SP) – $40 (CP) = $40 markup.
• Markup Percentage: How much markup is compared to the cost price. Formula: Markup % = (M / CP) × 100 Example: ($40 / $40) × 100 = 100% markup.
• Original Price (OP): The "regular" price before any discounts. Example: A TV is listed at $500.
• Discount (D): The amount subtracted from the original price. Example: $500 TV on sale for $350-$150 discount.
• Discount Percentage: How much discount is compared to the original price. Formula: Discount % = (D / OP) × 100 Example: ($150 / $500) × 100 = 30% off.
• Sale Price (SP): The final price after discount. Formula: SP = OP – D or SP = OP × (1 – Discount %) Example: $500 × (1 – 0.30) = $350.
• Clearance Price: A deeply discounted price to sell leftover inventory. Example: A $100 coat marked down to $25.
• "Was/Now" Pricing: A trick where stores show an inflated "was" price to make the "now" price seem like a bigger deal. Example: "Was $200, Now $100" (but it was never sold at $200).
• Stacking Discounts: Applying multiple discounts (e.g., 20% off + $10 coupon). Formula: Apply percentages first, then dollar amounts. Example: $50 shirt with 20% off-$40, then $10 coupon-$30 final price.

Step-by-Step / Process Flow

1. Calculate a Discount (Markdown)

Scenario: A $80 pair of jeans is 25% off. What’s the sale price?
1. Find the discount amount: Multiply original price by discount %. $80 × 0.25 = $20 discount.
2. Subtract discount from original price: $80 – $20 = $60 sale price. OR Use the shortcut: $80 × (1 – 0.25) = $80 × 0.75 = $60.

2. Calculate Markup (How Stores Price Items)

Scenario: A store buys a lamp for $30 and marks it up 60%. What’s the selling price?
1. Find the markup amount: Multiply cost price by markup %. $30 × 0.60 = $18 markup.
2. Add markup to cost price: $30 + $18 = $48 selling price. OR Use the shortcut: $30 × (1 + 0.60) = $30 × 1.60 = $48.

3. Compare Discounts to Find the Best Deal

Scenario: You want to buy a $120 blender. Which is better? - Option 1: 30% off - Option 2: $35 coupon
1. Calculate Option 1: $120 × 0.30 = $36 discount-$120 – $36 = $84 final price.
2. Calculate Option 2: $120 – $35 = $85 final price.
3. Compare: 30% off is $1 cheaper.

4. Check if a "Sale" is Really a Deal

Scenario: A store advertises "50% off original price of $200" for a vacuum, but the sale price is $120.
1. Calculate the expected sale price: $200 × 0.50 = $100 discount-$200 – $100 = $100 should be the sale price.
2. Compare to actual sale price: $120-$100-This is not a true 50% off sale.
3. Find the real discount: ($200 – $120) / $200 × 100 = 40% off (not 50%).

5. Stack Discounts Correctly

Scenario: A $150 jacket is 20% off, then you have a $20 coupon. What’s the final price?
1. Apply percentage discount first: $150 × 0.20 = $30-$150 – $30 = $120.
2. Apply dollar discount next: $120 – $20 = $100 final price. Mistake: Applying the $20 coupon first ($150 – $20 = $130, then 20% off = $104) gives the wrong answer!

Common Mistakes

• Mistake: Thinking "50% off + 20% off" = 70% off. Correction: Discounts don’t add up! Apply them sequentially. Example: $100 item-50% off = $50-20% off = $40 (total 60% off, not 70%).

• Mistake: Ignoring the order of discounts (applying dollar discounts before percentages). Correction: Always apply percentage discounts first, then dollar amounts. Why? Stores design discounts to maximize their profit—don’t let them trick you!

• Mistake: Assuming the "original price" is accurate. Correction: Check prices at other stores or online. Stores often inflate "original prices" to make sales seem better. Example: A "Was $300, Now $150" deal might be a lie if the item was never sold at $300.

• Mistake: Forgetting to compare unit prices (price per ounce, per item, etc.). Correction: Bigger packages aren’t always cheaper. Divide the price by the quantity. Example: A 12-pack of soda for $6 ($0.50 per can) vs. a 24-pack for $15 ($0.625 per can)—the 12-pack is actually cheaper per can!

• Mistake: Not checking for hidden fees (e.g., shipping, taxes). Correction: Always calculate the total cost, not just the sale price. Example: A $50 item with "free shipping" might be cheaper than a $40 item with $15 shipping.

Real-World Insights

1. "Clearance" doesn’t always mean "cheap."
2. Stores often mark up items before putting them on "clearance" to make the discount seem bigger.

3. Tip: Compare clearance prices to similar items at other stores.

4. Stores use "psychological pricing" to trick you.

5. Prices ending in .99 ($19.99) make items seem cheaper than they are.

6. "Buy 1, Get 1 50% Off" is the same as 25% off each item—but sounds like a better deal.

7. Loyalty programs and coupons can be misleading.

8. A "free $10 coupon" might require you to spend $50 first.

9. Tip: Calculate the real discount: $10 off $50 = 20% off (not "free money").

10. Black Friday and holiday sales aren’t always the best deals.

11. Some items (like TVs) are marked up before Black Friday, then "discounted" to their normal price.
12. Tip: Track prices for a few weeks before buying—use tools like CamelCamelCamel for Amazon price history.

Quick Check Questions

1. A store buys a toaster for $25 and marks it up 80%. What’s the selling price? a) $35 b) $45 c) $50 d) $60 Answer: b) $45. ($25 × 1.80 = $45)

2. A $60 shirt is on sale for 30% off. What’s the sale price? a) $18 b) $42 c) $48 d) $54 Answer: b) $42. ($60 × 0.70 = $42)

3. A store advertises "Buy 2, Get 1 Free" on $10 socks. What’s the real discount per sock? a) 20% b) 25% c) 33% d) 50% Answer: c) 33%. (You pay $20 for 3 socks-$6.67 per sock-$10 – $6.67 = $3.33 discount per sock-$3.33 / $10 = 33% off.)

Last-Minute Cram Sheet

1. Markup = Selling Price – Cost Price (How stores add profit).
2. Markup % = (Markup / Cost Price) × 100 (Always based on cost, not selling price).
3. Sale Price = Original Price × (1 – Discount %) (Shortcut for discounts).
4. Discount % = (Discount / Original Price) × 100 (Check if a sale is real).
5. Always apply percentage discounts first, then dollar discounts (Order matters!).
6. "Was/Now" pricing is often fake—compare to other stores.
7. Bigger packages aren’t always cheaper—calculate price per unit.
8. "50% off + 20% off"-70% off (Apply sequentially).
9. "Buy 1, Get 1 50% Off" = 25% off each item (Not 50% off).
10. Clearance items may have been marked up first—compare prices elsewhere.