Problem: In a video store, a DVD that sells for $15 is marked "10% off." What is the discount? What is the sale price of the DVD?
Analysis: Stores often sell goods for a discounted price. Typically, a store will discount an item by a percent of the original price. In this problem, an item that originally costs $15 is being discounted by 10%. So "10% off" refers to the rate of discount. To solve this problem, we need a procedure.
Procedure:
- The rate is usually given as a percent.
- To find the discount, multiply the rate by the original price.
- To find the sale price, subtract the discount from original price.
Now that we have a procedure, we can solve the problem above.
Problem: In a video store, a DVD that sells for $15 is marked, "10% off". What is the discount? What is the sale price of the DVD?
Solution: The rate is 10%.
The discount is: 0.10 x $15.00 = $1.50
The sale price is calculated as follows:
$15.00 | original price |
- 1.50 | - discount |
$13.50 | sale price |
Answer: The discount is $1.50 and the sale price is $13.50.
Let's take a look at some more examples of calculating discount and sale price.
Example 1: In a department store, a $40 dress is marked, "Save 25%." What is the discount? What is the sale price of the dress?
Analysis: The phrase, "Save 25%," refers to the rate.
The original price of the dress is $40.
Solution: The rate is 25%.
The discount is: 0.25 x $40.00 = $10.00
The sale price is calculated as follows:
$40.00 | original price |
- 10.00 | - discount |
$30.00 | sale price |
Answer: The discount is $10.00 and the sale price is $30.00.
Example 2: In a grocery store, a $12 case of soda is labeled, "Get a 20% discount." What is the discount? What is the sale price of the case of soda?
Analysis: The phrase, "Get a 20% discount," refers to the rate.
Solution: The rate is 20%.
The discount is: 0.20 x $12.00 = $2.40
The sale price is calculated as follows:
$12.00 | original price |
- 2.40 | - discount |
$ 9.60 | sale price |
Answer: The discount is $2.40 and the sale price is $9.60.
Example 3: In a candy store, a $5.00 jar of candy is labeled, "50% off." What is the discount? What is the sale price of the jar of candy?
Analysis: The phrase, "50% off," refers to the rate.
Solution: The rate is 50%.
The discount is: 0.50 x $5.00 = $2.50
The sale price is calculated as follows:
$5.00 | original price |
- 2.50 | - discount |
$2.50 | sale price |
Answer: The discount is $2.50 and the sale price is $2.50.
In Example 3, note that the discount and the sale price are the same amount! Do you know what fraction is equal to 50%? Could you have done this problem using mental math? The phrase, "50% off," is the same as, "1/2 off". So using mental math, you would get that one-half of $5.00 is $2.50. Let's look at another example that uses a fraction.
Example 4: A pizzeria has a coupon that reads, "Get off a $9.00 cheese pizza." What is the discount? What is the sale price of the cheese pizza?
Analysis: The phrase, " off," refers to the rate. It is expressed as a fraction.
Solution: The rate is given as the fraction .
The discount is: x $9.00 = $3.00
The sale price is calculated as follows:
$9.00 | original price |
- 3.00 | - discount |
$6.00 | sale price |
Answer: The discount is $3.00 and the sale price is $6.00.
Once again, you could calculate the discount and sale price using mental math. Let's look at another way of calculating the sale price of an item. Below is a modified version of the problem from the top of this page.
Example 5: In a video store, a DVD that sells for $15 is marked, "10% off." What is the sale price of the DVD?
Solution: The rate is 10%. Thus, the customer is paying 90% for the DVD.
The sale price is: 0.90 x $15.00 = $13.50
Answer: The sale price is $13.50.
Note that we calculated the sale price in the above problem, but we did not calculate the discount.
Summary: Stores often sell goods for a discounted price. Typically, a store will discount an item by a percent of the original price. The rate of discount is usually given as a percent, but may also be given as a fraction. The phrases used for discounted items include, " off," "Save 50%," and "Get a 20% discount."
Procedure:
- To calculate the discount, multiply the rate by the original price.
- To calculate the sale price, subtract the discount from original price.
Exercises
Directions: Solve each problem below by entering a dollar amount with cents. For each exercise below, click once in the ANSWER BOX, type in your answer and then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR.
1. | In a boutique, a $14 scarf is marked, "20% off." What is the sale price of the scarf? |
2. | In an electronics store, a $75 iPod is labeled, "Save 15%." What is the sale price of the iPod? |
3. | What is the discount for the iPod in Exercise 2? |
4. | A $30 shirt is marked, "Get off." What is the sale price of the shirt? |
5. | In a bicycle store, a $500 bicycle is marked, "Get a 30% discount." What is the sale price of the bicycle? |