Lesson 10Tax and Tip

Learning Goal

Let’s learn about sales tax and tips.

Learning Targets

I understand and can solve problems about sales tax and tips.

Warm Up: 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.

An image of a cash register, price scanner, and pair of sunglasses. The sunglasses have a price tag labeled ten point zero zero dollars. The display on the register indicates 10 point 4 5 dollars.

What do you notice? What do you wonder?

Activity 1: 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.

City 1

item	price (dollars)	sales tax (dollars)	total cost (dollars)
paper towels	$8.00$	$0.48$	$8.48$
lamp	$25.00$	$1.50$
pack of gum	$1.00$
laundry soap	$12.00$
	$x$

City 2

item	price (dollars)	sales tax (dollars)	total cost (dollars)
paper towels	$8.00$	$0.64$	$8.64$
lamp	$25.00$	$2.00$
pack of gum	$1.00$
laundry soap	$12.00$
	$x$

Activity 2: Shopping in a Third City

Here is the sales tax on the same items in City 3.

item	price (dollars)	sales tax (dollars)
paper towels	$8.00$	$0.58$
lamp	$25.00$	$1.83$
pack of gum	$1.00$	$0.07$
laundry soap	$12.00$

What is the tax rate in this city?
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.

Activity 3: Dining at a Restaurant

Problem 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 receipt from a meal showing a subtotal of 42.00, sales tax of 3.99 and a total of 45.99

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?
After tax, the total is $45.99. What percentage of the subtotal is the total?
They actually pay $52.99. The additional $7 is a tip for the server. What percentage of the subtotal is the tip?

Problem 2

The tax rate at this restaurant is 9.5%.

Another person’s subtotal is $24.95. How much will their sales tax be?
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?

Lesson 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 $$ 11.50$ , then the sales tax is $(0.075) \cdot 11.5 = 0.8625$ , which rounds to $86$ cents. The customer pays $11.50 + 0.86$ , or $$ 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 tipis 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.