Discount and Sale Price

What is a Discount?

A discount is a reduction in the original price.

Expressed as:

• Percent off: "20% off"
• Dollar amount: "$10 off"

Result: Sale price (lower than original)

Calculating Discount Amount

Discount Amount = Original Price × Discount Rate

Example 1: Find Discount

Shirt costs $40 with 25% off. How much do you save?

Given:

• Original price = $40
• Discount rate = 25% = 0.25

Calculate: Discount = 40 × 0.25 = 10

Answer: Save $10

Example 2: Larger Discount

Laptop costs $800 with 15% off. What's the discount?

Calculate: Discount = 800 × 0.15 = 120

Answer: $120 off

Finding Sale Price

Method 1: Subtract discount from original

Sale Price = Original Price − Discount Amount

Example: Using Subtraction

Original = $40, Discount = 25% off

Step 1: Find discount

• 40 × 0.25 = 10

Step 2: Subtract

• 40 − 10 = 30

Answer: Sale price = $30

Method 2: Direct calculation

If discount is 25% off, you pay 75% (100% − 25%)

Sale Price = Original Price × (100% − Discount %)

Example: Using Direct Method

Original = $40, 25% off

Calculate: 40 × 0.75 = 30

Answer: Sale price = $30

Both methods give the same answer!

Multiple Discounts

Sometimes there are multiple discounts!

Example: Coupon + Sale

Store has 20% off sale. You have a 10% coupon.

Original price: $100

Method: Apply discounts one at a time

Step 1: Apply 20% off

• Sale price = 100 × 0.80 = 80

Step 2: Apply 10% coupon to new price

• Final = 80 × 0.90 = 72

Answer: $72 final price

Note: NOT the same as 30% off ($70)!

Adding Sales Tax

After finding sale price, often need to add tax.

Total Cost = Sale Price + (Sale Price × Tax Rate)

or

Total Cost = Sale Price × (1 + Tax Rate)

Example: With Tax

Sale price = $50, Sales tax = 6%

Method 1:

• Tax amount = 50 × 0.06 = 3
• Total = 50 + 3 = 53

Method 2:

• Total = 50 × 1.06 = 53

Answer: $53 total cost

Complete Purchase Problem

Example: From Original to Final

Original price: $80 Discount: 30% off Tax: 7%

Step 1: Find sale price

• 80 × 0.70 = 56

Step 2: Add tax

• 56 × 1.07 = 59.92

Answer: Final cost = $59.92

Finding Original Price

If you know sale price and discount, find original!

Original Price = Sale Price / (1 − Discount Rate)

Example: Work Backwards

Sale price = $45 after 25% off. What was original?

Given:

• Sale price = $45
• Discount = 25% off
• Paid 75% of original

Solve: Original = 45 / 0.75 = 60

Answer: Original price was $60

Comparing Discounts

Which is better?

Example: Two Offers

Store A: $50 item with 20% off Store B: $50 item with $12 off

Store A: 50 × 0.20 = $10 off → Pay $40 Store B: 50 − 12 = $38

Answer: Store B is better ($38 < $40)

Markup vs. Discount

Markup: Increase from cost to retail

• Store buys for $20, sells for $30 (50% markup)

Discount: Decrease from retail

• Retail $30, sale for $24 (20% off)

Different starting points!

Calculating Percent Saved

Percent Saved = (Discount Amount / Original Price) × 100%

Example: What Percent Off?

Original = $80, Sale price = $60

Step 1: Find discount amount

• 80 − 60 = 20

Step 2: Find percent

• (20 / 80) × 100% = 25%

Answer: 25% off

Real-World Applications

Shopping: Find best deals

• Compare percent off vs. dollar off
• Calculate final cost with tax

Budgeting: Plan purchases

• How much will I actually pay?
• Can I afford it with my budget?

Business: Price products

• Set sale prices that attract customers
• Calculate profit after discount

Holiday sales: Black Friday, Cyber Monday

• Stack coupons and sales
• Find total savings

Tips for Success

Always:

• Read carefully: % off vs. $ off
• Convert percent to decimal
• Apply discounts in order (if multiple)
• Add tax AFTER discount
• Check if answer is reasonable

Common mistakes:

• Adding percents instead of applying sequentially
• Forgetting to convert percent to decimal
• Calculating tax on original instead of sale price

Practice