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5.5: Consumer Percent

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Introduction

A Student Council Meal

After the student council meeting, Cameron’s Mom offered to take all of the students out for lunch. They went to their favorite restaurant, “Howie’s Burger Place” for a lunch of burgers and fries. From the restaurant menu, each student ordered the burger special which costs $12.95 each but includes a drink, and a dessert. After eating, Cameron looked at the bill. He saw that 5 students ordered the burger special.

The sales tax is 7%. The food server was particularly attentive so Cameron’s Mom decided to give her an 18% tip. Cameron began to work through the math in his head. How much was the total bill?

That is an excellent question. This lesson is all about different consumer percents. Pay close attention and you will be able to solve this problem at the end of the lesson.

What You Will Learn

By the end of this lesson, you will know how to complete the following tasks.

  • Find retail prices given wholesale prices, markups and sales tax.
  • Find sale prices given regular prices, discounts and sales tax.
  • Find original prices given total receipt amounts.
  • Solve real-world problems involving discounts, markups, sales tax and tips.

Teaching Time

I. Find Retail Prices Given Wholesale Prices, Markups and Sales Tax

We’ve now seen on many occasions how practical percent is in everyday life. In most things you purchase, percent is used in one way or another to calculate a final price, a discount, tax or a tip. Your understanding of this is important in making sure that you get charged the right price and that you tip appropriate amounts as well.

Let’s start by looking at wholesale prices and markups.

Most companies are in business to make a profit. Companies generally offer goods or services or both. Stores that sell you products like hairspray, potato chips, and video games, buy those products from the companies that make them. Because they buy so many of the same products, they get special prices called wholesale prices. They figure out how much each piece or unit costs them and then they charge you a certain amount more for each product. The difference is called the gross profit. After they pay all of their other expenses like wages, utility bills, insurance, etc., they hope to have some money left over. This is their profit.

Knowing just how much to charge for each product is sometimes tricky. If a company charges you too much, you may not purchase products from them. Companies have to study the market and their true costs in order to calculate the best price to charge to remain competitive but still make a profit. After studying the market, they decide on a markup—a percent by which they will increase the wholesale price to get the retail price. So the wholesale price is what the companies pay for the product and the retail price is what the company charges for the same product. The percent increase from the wholesale price to the retail price is the markup.

Example

Let’s suppose a company sells toothpaste. They buy the toothpaste for $1.10 per tube; this is the wholesale price. Remember, they may buy a case of 200 tubes all at once. In order to make a profit, they mark the price up by 65%; this is their markup. So in order to calculate the retail price, they increase the wholesale price by 65%.

Let’s figure out the retail price given the wholesale cost and the percent of the increase.

Amount of change: 1.10 \times .65 = .715

Add increase to the wholesale price: 1.10 + .715 = 1.815

Round off the price to the nearest whole cent: retail price is $1.82.

The retail price of the toothpaste is $1.82.

Example

A florist gets a dozen roses for $15. They charge a markup of 120%. What is the retail price of a dozen roses?

Amount of change: 15 \times 1.20 = 18

Add increase to the wholesale price: 15 + 18 = 33

The florist charges $33 for a dozen roses.

To calculate the retail price:

  1. Find the amount of change by multiplying the wholesale cost with the % of increase. Remember to convert the percent to a decimal to multiply.
  2. Then add the increase to the wholesale price.
  3. This is the new retail price.

Take a few minutes to write these steps in your notebook.

Sometimes, you will also have to deal with sales tax.

On most products that you purchase, stores also charge you a sales tax which is determined by the government. This money is paid to the government so that they can provide services to the people. Tax is usually a percent increase that is added to the retail price.

If you were to buy a dozen roses from the company in the previous example, you would pay $33. Let’s suppose there is a tax of 6%. This would be an increase of 6% so we would use a similar process to find the final price. Because this deals with money, we round the calculations to the nearest cent (or hundredths place).

Amount of tax: 33 \times .06 = 1.98

Add tax to the retail price: 33 + 1.98 = 34.98

The total price with tax is $34.98.

To calculate sales tax:

  1. Multiply the retail by the percent of the sales tax. You will need to convert this percent to a decimal first.
  2. Then add that amount to the retail price.
  3. This is the final cost to the customer.

Write these steps down in your notebook.

II. Find Sale Prices Given Regular Prices, Discounts and Sales Tax

Fortunately for the consumer, price changes aren’t always increases. In order to reduce inventories or motivate buyers, stores often have sales in which they discount prices by a percent. Instead of a percent increase, this is a percent decrease. We can calculate these sale prices.

Example

At the end of the summer, a clothing store puts all swimwear on sale. They offer a discount of 60%. If the regular price is $29.99 on a bikini, what is the sale price?

Amount of discount: 29.99 \times .60 = 17.99

Subtract discount from original price: 29.99 - 17.99 = 12.00

The sale price is only $12.00.

Not so fast. We almost forgot to pay the tax. If the sales tax is 6.25%, we must now add the tax to the sale price.

Amount of tax: 12 \times .0625 = .75

Add tax to the sale price: 12 + .75 = 12.75

The sale price with tax is $12.75.

Example

A local bookstore has a 30% off everything sale. The sales tax is 5%. What is the total price on a book whose cover price is $15.99?

Amount of discount: 15.99 \times .30 = 4.80

Subtract discount from original price: 15.99 - 4.80 = 11.19

The sale price is $11.19.

Don’t forget the sales tax!

Amount of tax: 11.19 \times .05 = .56

Add tax to the sale price: 11.19 + .56 = 11.75

The sale price with tax is $11.75.

Notice that with a discount you subtract the amount and with sales tax you add the cost.

Absolutely! A lot of this math you are probably able to figure out in your head. However, it is a good idea to understand the steps and how the pricing is figured out!

III. Find Original Prices Given Total Receipt Amounts

Calculating a price with tax is the same as increasing by a percent. What if you know the total price including the tax and want to know the original price of a product?

Example

A store clerk charges you $78.75 for a DVD player. The tax in your area is 5%. So how much was the original price of the DVD player?

We can find this out by using an equation.

In order to get the total cost, the cash register computes the 5% tax and adds the tax to the original price like we did three sections ago. In other words:

\text{original price} + 5\% \ \text{of original price} = \text{total cost}

Now let’s use variables and convert the percent to decimal.

p+.05p = c

In this equation, we p and .05p are like terms so they can be combined.

1.05p = c

In this case, if we are given p, we can solve for c. Or if we are given c, we can solve for p. In our example, we paid a total cost c of $78.75. Substitute c in the equation and solve for p.

1.05p &= 78.75\\1.05p \div 1.05 &= 78.75 \div 1.05\\p &= 75

The original price was $75.00.

Example

You are charged $29.10 for an item with 7% tax included. What was the original price of the item?

1.07p &= 29.10\\p &= 27.20

The original price of the item was $27.20.

IV. Solve Real – World Problems Involving Discounts, Markups, Sales Tax and Tips

Now let’s see more examples from the real-world where discounts and markups, tax and tips all come together.

Example

You purchase some plants for your gardens. Two trees have a price of $55.00 each. Six tulips cost $2.50 each. The tax on your purchase is 5.75% but there is an early-bird special of 10% off your entire purchase to those who show up before 10am. What is the total cost?

Add up all of the products: 55.00 \cdot 2 = 110.00

2.50 \cdot 6 = 15.00

Total price of products: 125.00

Calculate the tax of 5.75%: 125 \times .0575 = 7.19

Add the tax to the price: 125.00 + 7.19 = 132.19

Calculate the 10% discount: 132.19 \times .10 = 13.22

Subtract the discount from the price: 132.19 - 13.22 = 118.97

The grand total is $118.97.

Now let’s return to the problem in the introduction and use what we have learned.

Real-Life Example Completed

A Student Council Meal

Here is the original problem once again. Reread it and then solve the problem for the total cost of the meal. Show your work for each piece.

After the student council meeting, Cameron’s Mom offered to take all of the students out for lunch. They went to their favorite restaurant, “Howie’s Burger Place” for a lunch of burgers and fries. From the restaurant menu, each student ordered the burger special which costs $12.95 each but includes a drink, and a dessert. After eating, Cameron looked at the bill. He saw that 5 students ordered the burger special.

The sales tax is 7%. The food server was particularly attentive so Cameron’s Mom decided to give her an 18% tip. Cameron began to work through the math in his head. How much was the total bill?

Now figure out the total bill. Remember to show each part of the solution.

Solution to Real – Life Example

Here is the solution to the problem. Notice each part of the bill and how it is calculated.

First, add up all of the meals. 12.95 \times 7 = \$90.65

Calculate the tax of 7%: 90.65 \times .07 = 6.35

Add the tax to the price: 90.65 + 6.35 = 97.00

Calculate the 18% tip: 97.00 \times .18 = 17.46

Add the tip to the price: 97.00 + 17.46 = \$114.46

The total bill is $114.46. You could round up to $114.50 to make the numbers even too.

Vocabulary

Here are the vocabulary words used in this lesson.

Wholesale price
the price that a merchant pays when they purchase a product from a manufacturer.
Markup
the amount that the merchant charges retail to the customer. The difference between wholesale and retail is the markup and also the profit.
Sales Tax
a percentage charged on purchases, and that goes to the government.
Discounts
when merchants have a sale a percent of the decrease is calculated to sell the product at a lower price.

Time to Practice

Directions: Calculate the retail price given the wholesale price and percent markup.

  1. Wholesale price: $6.43 markup: 38%
  2. Wholesale price: $612.00 markup: 70%
  3. Wholesale price: $.22 markup: 55%

Directions: Find the total cost after adding the tax.

  1. Retail price: $76.50 tax: 8%
  2. Retail price: $399 tax: 4.75%
  3. Retail price: $8.79 tax: 7.25%
  4. Retail price $44.56 tax: 5%
  5. Retail price $345.00 tax 11%

Directions: Find the total cost after computing the wholesale price and the tax.

  1. wholesale price: $4.15 markup: 100% tax: 6%
  2. wholesale price: $116.21 markup: 33% tax: 5.5%
  3. wholesale price: $51.55 markup: 61.3% tax: 3.75%

Directions: Find the price after a discount and the tax.

  1. original price: $3.29 discount: 50% tax: 0%
  2. original price: $108.75 discount: 25% tax: 5.25%
  3. original price: $45 discount: 33.3% tax: 7.5%

Directions: If your food bill at a restaurant is $85.77, what your total cost be after the tip for:

  1. service 10%
  2. decent service 15%
  3. great service 20%

Directions: What was the original price given total cost and tax rate?

  1. total cost: $1475.68 tax rate: 7%
  2. total cost: $63.80 tax rate: 4.5%

Directions: Solve each problem. There are several steps to solving each problem.

  1. You take a taxi ride in a foreign country where they add 20% to your total for late night travel. The driver expects an additional 15% tip. How much do you owe for the taxi ride if the meter shows $45?
  2. You take your mother out for lobster for Mother’s Day. The lobster platters are $24.95 each but include the drink and dessert buffet. Your waitress is a mother, too, so you leave her a 20% tip. However, you did bring a coupon for 25% off. What is your total cost for 2 people?

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Date Created:

Jan 14, 2013

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Sep 23, 2014
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CK.MAT.ENG.SE.1.Middle-School-Math-Grade-8.5.5

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