4.3.2: Percentage Contexts
Lesson
Let's learn about more situations that involve percentages.
Exercise \(\PageIndex{1}\): Leaving a Tip
Which of these expressions represent a 15% tip on a $20 meal? Which represent the total bill?
\(15\cdot 20\)
\(20+0.15\cdot 20\)
\(1.15\cdot 20\)
\(\frac{15}{100}\cdot 20\)
Exercise \(\PageIndex{2}\): 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.
- By how much will they mark up the price of the vehicle?
- 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?
Exercise \(\PageIndex{3}\): 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?
Exercise \(\PageIndex{4}\): 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 \((0.03)\cdot 200,000=6,000\), 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.
Practice
Exercise \(\PageIndex{5}\)
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?
Exercise \(\PageIndex{6}\)
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?
- \($3.04\)
- \($12.16\)
- \($18.24\)
- \($19.00\)
Exercise \(\PageIndex{7}\)
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 \(5\frac{1}{2}\%\) 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?
Exercise \(\PageIndex{8}\)
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?
(From Unit 4.2.4)
Exercise \(\PageIndex{9}\)
Match the situations with the equations.
- Mai slept for \(x\) hours, and Kiran slept for \(\frac{1}{10}\) less than that.
- Kiran practiced the piano for \(x\) hours, and Mai practiced for \(\frac{2}{5}\) less than that.
- Mai drank \(x\) oz of juice and Kiran drank \(\frac{4}{3}\) more than that.
- Kiran spent \(x\) dollars and Mai spent \(\frac{1}{4}\) less than that.
- Mai ate \(x\) grams of almonds and Kiran ate \(1.5\) times more than that.
- Kiran collected \(x\) pounds of recycling and Mai collected \(\frac{3}{10}\) less than that.
- Mai walked \(x\) kilometers and Kiran walked \(\frac{3}{8}\) more than that.
- Kiran completed \(x\) puzzles and Mai completed \(\frac{3}{5}\) more than that.
\(y=2.33x\)
\(y=1.375x\)
\(y=0.6x\)
\(y=0.9x\)
\(y=0.75x\)
\(y=1.6x\)
\(y=0.7x\)
\(y=2.5x\)
(From Unit 4.1.5)