MathIsimple
Back to Unit 2

Lesson 2-1: Percentage Applications

Scenario: Shopping & Business - Learn to calculate taxes, discounts, and commissions in real-world situations!

Duration: 55-70 minutesScenario: Shopping & Business

Learning Objectives

  • Calculate discounts and sale prices
  • Apply tax rates to find total costs
  • Calculate commissions and earnings
  • Compare different percentage scenarios

Shopping Scenario

The Problem

A shirt originally costs $80. It's on sale for 15% off, and there's a 7% sales tax. What is the final price you'll pay?

Step-by-Step Solution:

Original price: $80
Discount: 15% off
Sales tax: 7%

Calculation Process

Step 1: Calculate the discount amount

Discount = $80 × 0.15 = $12

Step 2: Find the sale price

Sale price = $80 - $12 = $68

Step 3: Calculate the tax

Tax = $68 × 0.07 = $4.76

Step 4: Find the final price

Final price = $68 + $4.76 = $72.76

Commission Calculations

Real Estate Commission

A real estate agent sells a house for $450,000 and earns a 3% commission. How much commission does the agent earn?

Calculation: $450,000 × 0.03 = $13,500

The agent earns $13,500 in commission.

Commission Formula

Commission Formula:

Commission = Sale Price × Commission Rate

Remember: Convert percentage to decimal (3% = 0.03)

Percentage Comparison

Interesting Comparison

Compare these two scenarios with a $100 item:

  • Scenario A: Price increases 20%, then decreases 20%
  • Scenario B: Price decreases 20%, then increases 20%

Scenario A

Original: $100
+20%: $100 × 1.20 = $120
-20%: $120 × 0.80 = $96
Final: $96

Scenario B

Original: $100
-20%: $100 × 0.80 = $80
+20%: $80 × 1.20 = $96
Final: $96

Key Insight: Both scenarios result in the same final price! This happens because the percentage changes are applied to different base amounts.

Practice Problems

Problem 1: Sale Price

A laptop costs $1,200. It's on sale for 25% off. What is the sale price?

Your solution:

Discount amount: $1,200 × 0.25 =
Sale price: $1,200 - $300 =

Problem 2: Tax Calculation

A meal costs $45.50. With an 8.5% tax, what is the total cost?

Your solution:

Tax amount: $45.50 × 0.085 =
Total cost: $45.50 + $3.87 =

Problem 3: Commission

A salesperson earns 5% commission on all sales. If they sell $8,500 worth of products, how much commission do they earn?

Your solution:

Commission: $8,500 × 0.05 =

Problem 4: Complex Scenario

A store offers 30% off all items, plus an additional 10% off for students. A student buys a $200 jacket. What is the final price?

Your calculation: