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Understanding Percentages and Commissions in Real-World Problem Solving

This lesson delves into calculating percentages and commissions through real-world problems. It covers various scenarios, such as finding the commission earned by salespeople like realtors and car salesmen based on property and vehicle sales. Additionally, it discusses conducting surveys and interpreting results, exemplifying how to calculate both monetary gains from commission and percentages from survey data. Students will practice applying these concepts in different contexts, ensuring a strong understanding of critical mathematical equations applicable to everyday situations.

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Understanding Percentages and Commissions in Real-World Problem Solving

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  1. PERCENTS & EQUATIONS II Solving “real world” problems

  2. Commission The amount of money a sales person receives based on the amount of sales. A realtor earns 7% of the selling price for each house that they sell. A car salesman earns 8% of the selling price for each car that they sell.

  3. Commission Problems • A realtor makes 7% commission on the sale of a house that sells for $150,000. To the nearest dollar, how much was the commission for this sale. • Commission is 7% of the price • Word-for-word translation: c = 0.07(150,000) • c = $10,500

  4. EXAMPLE 1 • A pharmaceutical sales representative earns 4.5% commission for sales made. How much commission is earned on a sale of $3000? (nearest dollar) • 0.045(3000) = c • c = $135

  5. EXAMPLE 2 • A salesman earns $350 on a sale of $10,000. What was the percent commission that was earned? • 350 = 10,000(c) • 350/10,000 = c • 0.035 = c • As a percent, 3.5%

  6. SURVEY QUESTIONS • 35% of the 500 people surveyed thought that taxing soda to fight obesity was a good idea. How many people was this? • 0.35(500) = P • P = 175

  7. EXAMPLE 1 • 1,067 people answered yes to the question, “Do you feel good about your life overall?” If this is 93% of the total number surveyed, how many people were surveyed? • 0.93(P) = 1067 • P = 1067/ 0.93 • P = 1147.3 or 1147 people

  8. EXAMPLE 2 • During a telephone survey, 414 people, or 46% of those called, said that they were watching station RFGT at the time of the call. How many people were called? • 0.46(x) = 414 • x = 414/ 0.46 • x = 900

  9. COMBINING WITH PROPORTIONS • Write and solve a proportion. What is 72% of 16? (nearest tenth) • How do you know what things go where? • Use the wording to set up the proportion

  10. Write and solve a proportion. What is 72% of 16? (nearest tenth) • Since this says the 72% is multiplied by 16, they must be in opposite locations.

  11. Write and solve a proportion. What is 72% of 16? (nearest tenth) • 16 must be in the denominator to be multiplied by the 16

  12. ASSIGNMENT 6.7B: 17 – 20, 30, 40 – 43 NEXT QUIZ: WEDNESDAY, MARCH 17TH

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