Lesson 11Percentage Contexts
Let’s learn about more situations that involve percentages.
- I understand and can solve problems about commission, interest, markups, and discounts.
11.1 Leaving a Tip
Which of these expressions represent a 15% tip on a $20 meal? Which represent the total bill?
11.2 A Car Dealership
A car dealership pays a wholesale price of $12,000 to purchase a vehicle.
The car dealership wants to make a 32% profit.
- By how much will they mark up the price of the vehicle?
- After the markup, what is the retail price of the vehicle?
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?
11.3 Commission at a Gym
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?
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.
Lesson 11 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|
- 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 , and the family gets $194,000, because . From the family's perspective, we can think of this as a 3% decrease on the sale price of the home.
Lesson 11 Practice Problems
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?
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?
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 of the selling price.
- How much commission will the salesperson earn by selling a couch for $495?
- How much money will the store get from the sale of the couch?
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):
- if the bank charges 3.8% interest each year?
- if the bank charges 5.3% interest each year?
Match the situations with the equations.
- Mai slept for hours, and Kiran slept for less than that.
- Kiran practiced the piano for hours, and Mai practiced for less than that.
- Mai drank oz of juice and Kiran drank more than that.
- Kiran spent dollars and Mai spent less than that.
- Mai ate grams of almonds and Kiran ate 1.5 times more than that.
- Kiran collected pounds of recycling and Mai collected less than that.
- Mai walked kilometers and Kiran walked more than that.
- Kiran completed puzzles and Mai completed more than that.