Illustrative Mathematics Grade 7, Unit 4, Lesson 11: Percentage Contexts

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Illustrative Math
Grade 7

Lesson 11: Percentage Contexts

Let’s learn about more situations that involve percentages.

Illustrative Math Unit 7.4, Lesson 11 (printable worksheets)

Lesson 11 Summary

The following diagram shows how to solve problems about commission, interest, markups, and discounts.

Lesson 11.1 Leaving a Tip

Which of these expressions represent a 15% tip on a $20 meal? Which represent the total bill?
15 · 20
20 + 0.15 · 20
1.15 · 20
15/100 · 20

• See Video for Whole Lesson

Lesson 11.2 A Car Dealership

A car dealership pays a wholesale price of $12,000 to purchase a vehicle.

1. The car dealership wants to make a 32% profit.
   a. By how much will they mark up the price of the vehicle?
   b. After the markup, what is the retail price of the vehicle?
   
2. During a special sales event, the dealership offers a 10% discount off of the retail price. After the discount, how much will a customer pay for this vehicle?
   

Are you ready for more?

This car dealership pays the salesperson a bonus for selling the car equal to 6.5% of the sale price. How much commission did the salesperson lose when they decided to offer a 10% discount on the price of the car?

• Show Answer

  6.5% of 15840 = 0.65 · 15840 = 1029.60
  6.5% of 14256 = .065 · 14256 = 926.64
  He lost 1029.60 - 926.64 = 102.96
  

Lesson 11.3 Commission at a Gym

1. For each gym membership sold, the gym keeps $42 and the employee who sold it gets $8. What is the commission the employee earned as a percentage of the total cost of the gym membership?
2. If an employee sells a family pass for $135, what is the amount of the commission they get to keep?

Lesson 11.4 Card Sort: Percentage Situations

Your teacher will give you a set of cards. Take turns with your partner matching a situation with a descriptor. For each match, explain your reasoning to your partner. If you disagree, work to reach an agreement.

Lesson 11 Practice Problems

1. A car dealership pays $8,350 for a car. They mark up the price by 17.4% to get the retail price. What is the retail price of the car at this dealership?
   
2. A store has a 20% off sale on pants. With this discount, the price of one pair of pants before tax is $15.20. What was the original price of the pants?
   A. $3.04
   B. $12.16
   C. $18.24
   D. $19.00
   
3. Lin is shopping for a couch with her dad and hears him ask the salesperson, “How much is your commission?” The salesperson says that her commission is 5 1/2% of the selling price.
   a. How much commission will the salesperson earn by selling a couch for $495?
   b. How much money will the store get from the sale of the couch?
   
4. A college student takes out a $7,500 loan from a bank. What will the balance of the loan be after one year (assuming the student has not made any payments yet):
   a. if the bank charges 3.8% interest each year?
   b. if the bank charges 5.3% interest each year?
   
5. Match the situations with the equations.
   

The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.

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