Illustrative Mathematics Grade 7, Unit 4, Lesson 10: Tax and Tip

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Illustrative Math
Grade 7

Lesson 10: Tax and Tip

Let’s learn about sales tax and tips.

Illustrative Math Unit 7.4, Lesson 10 (printable worksheets)

Lesson 10 Summary

Many places have sales tax. A sales tax is an amount of money that a government agency collects on the sale of certain items. For example, a state might charge a tax on all cars purchased in the state. Often the tax rate is given as a percentage of the cost. For example, a state’s tax rate on car sales might be 2%, which means that for every car sold in that state, the buyer has to pay a tax that is 2% of the sales price of the car.
Fractional percentages often arise when a state or city charges a sales tax on a purchase. For example, the sales tax in Arizona is 7.5%. This means that when someone buys something, they have to add 0.075 times the amount on the price tag to determine the total cost of the item.
For example, if the price tag on a T-shirt in Arizona says $11.50, then the sales tax is (0.075) · 11.5 = 0.8625, which rounds to 86 cents. The customer pays 11/50 + 0.86, or $12.36 for the shirt.
The total cost to the customer is the item price plus the sales tax. We can think of this as a percent increase. For example, in Arizona, the total cost to a customer is 107.5% of the price listed on the tag.
A tip is an amount of money that a person gives someone who provides a service. It is customary in many restaurants to give a tip to the server that is between 10% and 20% of the cost of the meal. If a person plans to leave a 15% tip on a meal, then the total cost will be 115% of the cost of the meal.

Lesson 10.1 Notice and Wonder: The Price of Sunglasses

You are on vacation and want to buy a pair of sunglasses for $10 or less. You find a pair with a price tag of $10. The cashier says the total cost will be $10.45.
What do you notice? What do you wonder?

• See Video for Whole Lesson

Lesson 10.2 Shopping in Two Different Cities

Different cities have different sales tax rates. Here are the sales tax charges on the same items in two different cities. Complete the tables.

Lesson 10.3 Shopping in a Third City

1. Here is the sales tax on the same items in City 3.
   
2. For the sales tax on the laundry soap, Kiran says it should be $0.84. Lin says it should be $0.87. Do you agree with either of them? Explain your reasoning.

Lesson 10.4 Population Growth

1. Jada has a meal in a restaurant. She adds up the prices listed on the menu for everything they ordered and gets a subtotal of $42.00.
   a. When the check comes, it says they also need to pay $3.99 in sales tax. What percentage of the subtotal is the sales tax?
   b. After tax, the total is $45.99. What percentage of the subtotal is the total?
   c. They actually pay $52.99. The additional $7 is a tip for the server. What percentage of the subtotal is the tip?
   
2. The tax rate at this restaurant is 9.5%.
   a. Another person’s subtotal is $24.95. How much will their sales tax be?
   b. Some other person’s sales tax is $1.61. How much was their subtotal?

Are you ready for more?

Elena’s cousins went to a restaurant. The part of the entire cost of the meal that was tax and tip together was 25% of the cost of the food alone. What could the tax rate and tip rate be?

• Show Answer

  Example:
  Tax rate = 15%
  Tip rate = 10%
  Any answer would be acceptable as long as tax rate + tip rate = 25%

Lesson 10 Practice Problems

1. In a city in Ohio, the sales tax rate is 7.25%. Complete the table to show the sales tax and the total price including tax for each item.
   
2. The sales tax rate in New Mexico is 5.125%. Select all the equations that represent the sales tax, t, you would pay in New Mexico for an item of cost c?
   
3. Here are the prices of some items and the amount of sales tax charged on each in Nevada.
   a. What is the sales tax rate in Nevada?
   b. Write an expression for the amount of sales tax charged, in dollars, on an item that costs dollars.
   
4. Find each amount:
   3.8% of 25
   0.2% of 50
   180.5% of 99
   
5. On Monday, the high was 60 degrees Fahrenheit. On Tuesday, the high was 18% more. How much did the high increase from Monday to Tuesday?
   
6. Complete the table. Explain or show your reasoning.

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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