~ 4.10 ~
Tax and Tip
Learning Targets
I understand and can solve problems about sales tax and tip.
Notes
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.
Activities
10.2 Shopping in Two Different Cities
Sales tax is a fee paid to the government. The amount of tax is a percentage of the price of the item. In some places, there are different sales tax rates for different types of items (like clothing, food, medicine, cars, etc.).
Different cities have different sales tax rates. Here are sales tax rates for nearby cities.
Riverside: 8.75%
Moreno Valley: 7.75%
San Bernardino: 7.75%
Temecula: 8.75%
Orange: 7.75%
Los Angeles: 9.5%
Here are the sales tax charges on the same items in two different cities. The cities in this question have a single sales tax rate for all items. Complete the tables.
City 1
City 2
Add to Your Notes
Sometimes we want to know just the amount of the tax, 0.06x, and sometimes we want to know the total cost, which is the price plus the cost, x + 0.06x = 1.06x. When there’s a certain tax that gets applied to goods, it is called a tax rate. Tax rates are usually described in terms of percentages.
When multiple pairs of values are known, like these activities today, work to find an exact tax rate. If only 1 pair is known, use the exact tax rate found from that pair of values.For example, if we only knew information about the paper towels, we could use that tax rate for all the items.
10.4 Dining at a Restaurant
In some restaurants, people pay the server a tip in addition to paying for the meal. Tips usually range between 10% and 20% of the cost of the meal.
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.
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?
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?
Add to Your Notes
In this lesson, we saw fractional percentages used for sales tax.
To calculate fractional percentages, like sales tax, you can use double number lines, tables, or equations.
Summary
Assignment
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