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Percent Change - Percent Decrease

Answers and Explanations

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Percent increase and percent decrease are the two types of percent change. This article focuses on percent decrease. Answers and Explanations for the Worksheet, Percent Change - Percent Decrease are on this page.

What is Percent Decrease?

Percent decrease is a ratio that compares 2 values. It describes the decline in value of something by a specific rate. Percent decrease is evident anytime a number or amount decreases.

When is Percent Decrease Calculated in the Real World?

  • A school principal is comparing student attendance from one semester to another.
  • A cell phone company is comparing the number of February text messages to March text messages.

Example:  The original price for a bag of apples is $3. On Tuesday, the bag of apples sells for $1.80. What is the percent decrease?

Careful, do not find the difference between $3 and $1.80 and say that the percent decrease is $1.20.

Use this formula to find the percent decrease.

Percent decrease = (Older – Newer) ÷ Older.

= (3 – 1.80) ÷ 3

= .40 = 40%

Note: To convert a decimal into a percent, move the decimal point twice and stick a percent sign (%) at the end.

Percent Decrease is Given

In other situations, the percent decrease is known, but the newer value is unknown.

Example 1: Best Bargain wants to sell a laptop computer for $600 to Alan. J’s Electronics will sell the computer to Alan for 20% less than Best Bargain.

1. How much money will Alan save when he buys the computer from J’s Electronics instead of Best Bargain?
Multiply .20 and $600. Alan will save $120.

2. How much will Alan pay for the computer at J’s Electronics?
$600 – $120 = $480

Example 2:  A dress regularly sells for $150. A green tag, marked 40% off, is attached to the dress.

1. What is the discount? .40 * $150 = $60

2. What is the sale price? $150 - $60 = $90

Exercises

1. A silk blouse regularly costs $45. It’s on sale for 33% off.

A. What is the discount? $15
.33 * $45 = $15

B. What is the sale price? $30
$45 - $30

2. A leather purse regularly costs $84. It’s on sale for 25% off.
A. What is the discount? $21
.25 * $84 = $21

B. What is the sale price? $63
$84 - $21 = $63

3. A scarf regularly costs $85. It’s on sale for 15% off.
A. What is the discount? $12.75
$85 * .15 = $12.75

B. What is the sale price? $72.25
$85 - 12.75 = $72.25

4. A sundress regularly costs $30. It’s on sale for 10% off.
A. What is the discount? $3.00
$30 * .10

B. What is the sale price? $27.00
$30 - $3.00 = $27.00

5. A woman’s silk romper regularly costs $250. It’s on sale for 40% off.
A. What is the discount? $100
$250 * .40 = $100

B. What is the sale price? $150
$250 - $100 = $150

6. A pair of women’s platform heels regularly costs $90. It’s on sale for 60% off.
A. What is the discount? $54
$90 * .60 = $54

B. What is the sale price? $36
$90 - $54 = $36

7. A floral skirt regularly costs $240. It’s on sale for 50% off.
A. What is the discount? $120
$240 * .50 = $120

B. What is the sale price? $120
$240 - $120 = $120

 

 

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