Lesson 11

Percentage Contexts

Let’s learn about more situations that involve percentages.

11.1: Leaving a Tip

Which of these expressions represent a 15% tip on a $20 meal? Which represent the total bill?

\(15 \boldcdot 20\)

\(20 + 0.15 \boldcdot 20\)

\(1.15 \boldcdot 20\)

\(\frac{15}{100} \boldcdot 20\)

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.

    1. By how much will they mark up the price of the vehicle?
    2. After the markup, what is the retail price of the vehicle?
    Cropped image of new cars.
  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?


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?

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?

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.

Summary

There are many everyday situations where a percentage of an amount of money is added to or subtracted from that amount, in order to be paid to some other person or organization:

goes to how it works
sales tax the government added to the price of the item
gratuity (tip) the server added to the cost of the meal
interest the lender (or account holder) added to the balance of the loan, credit card, or bank account
markup the seller added to the price of an item so the seller can make a profit
markdown (discount) the customer subtracted from the price of an item to encourage the customer to buy it
commission the salesperson subtracted from the payment that is collected

For example,

  • If a restaurant bill is \$34 and the customer pays \$40, they left \$6 dollars as a tip for the server. That is 18% of $34, so they left an 18% tip. From the customer's perspective, we can think of this as an 18% increase of the restaurant bill.
  • If a realtor helps a family sell their home for \$200,000 and earns a 3% commission, then the realtor makes \$6,000, because \((0.03) \boldcdot 200,\!000 = 6,\!000\), and the family gets \$194,000, because \(200,\!000 - 6,\!000 = 194,\!000\). From the family's perspective, we can think of this as a 3% decrease on the sale price of the home.