Markups, Discounts, and Sales Tax

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Concept Review

Discounts: The Math Behind "50% Off!"

Walk into any store and you'll see signs screaming "30% OFF!" or "SAVE 25%!" But here's the question: when you see a $60 jacket marked "40% off," can you instantly know you'll pay $36? Let's unlock the math behind every sale.

A discount is simply a reduction from the original price. Think of it like this: if the original price is a whole pizza, the discount is the slice someone cuts away before you buy it. You pay for what's left.

The Two-Step Discount Dance

Every discount calculation follows the same pattern:

Step 1: Calculate the discount amount (how much money gets "cut away")
Step 2: Subtract that amount from the original price to find the sale price

Real Example: Gaming Headset Sale

Original Price: $80 | Discount: 25% off

Step 1 Calculate discount amount: $80 × 0.25 = $20

Step 2 Find sale price: $80 - $20 = $60

Result: You save $20 and pay $60!

The Percent-to-Decimal Bridge

Remember: percentages are just fractions in disguise. 25% = 25/100 = 0.25. When you see "30% off," your brain should instantly think "multiply by 0.30" to find the discount amount.

🔑 Key Insight

Here's what stores don't want you to realize: you can skip Step 2 entirely! If something is 25% off, you're paying 75% of the original price. So $80 × 0.75 = $60 directly. One calculation instead of two.

Beyond Basic Discounts

The same logic applies whether you're calculating a simple markdown, figuring out member discounts, or even understanding markups (where stores add to their cost). Sales tax works similarly too—it's just an "upward discount" added to your purchase.

🎯 Key Takeaway

Every "50% OFF!" sign is really asking you to multiply and subtract. Once you master this two-step dance, you'll never be surprised at the register again—and you might even catch when the store makes a mistake in your favor.

Sample questions

1. A $40 shirt is on sale for 25% off. What is the discount amount?

○ $15

○ $20

○ $30

✓ $10

Answer: $10 — Discount = 25% of $40 = 0.25 × 40 = $10.

2. The same $40 shirt with 25% off. What is the sale price?

✓ $30

○ $10

○ $32

○ $50

Answer: $30 — Sale price = $40 - $10 = $30.

3. A bicycle originally costs $240 and is marked 15% off. What is the sale price?

○ $36

✓ $204

○ $216

○ $225

Answer: $204 — Discount = 0.15 × 240 = $36. Sale price = $240 - $36 = $204.

Skills in this topic

Calculate the amount of a discount and the sale price
Calculate the markup and the final retail price
Calculate sales tax and the total cost of an item
Calculate a restaurant tip and the total bill
Solve multi-step problems involving both discounts and sales tax

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