holt algebra 1 2-10 percent increase and decrease 2-10 percent increase and decrease holt algebra 1...

Holt Algebra 1

2-10 Percent Increase and Decrease2-10 Percent Increase and Decrease

Holt Algebra 1

Lesson QuizLesson Quiz

Lesson PresentationLesson Presentation

Warm UpWarm Up

Holt Algebra 1

2-10 Percent Increase and Decrease

Warmup: Which is a better deal?

A DVD costs $20. Sales tax is 8% and you receive a 10% discount. Should you calculate the tax first then the discount or the other way around?

Get Your Calculator

Holt Algebra 1


Tax first:

($20)(.08) = $1.60

20 + 1.60 = $21.60

Now Discount:

($21.60)(.10) = $2.16

21.60 – 2.16 = $19.44

Now Tax:

($18)(.08) = $1.44

18 + 1.44 = $19.44

Discount first:

($20)(.10) = $2

20 – 2 = $18

Which is a better deal for you?Which is a better deal for the business?

Holt Algebra 1


Warm Up

1. Find 30% of 40.

2. Find 28% of 60. Solve for x.

3. 22 = x(50)

4. 17.2 = x(86)

5. 20 is what percent of 80?

6. 36 is what percent of 30?

16.8

12

38

0.44

25%

120%

Holt Algebra 1


Find percent increase and decrease.

Objective

Holt Algebra 1


percent changepercent increasepercent decreasediscountmarkup

Vocabulary

Holt Algebra 1


A percent change is an increase or decrease given as a percent of the original amount. Percent increase describes an amount that has grown and percent decrease describes an amount that has be reduced.

Notes on next slide

Holt Algebra 1


Percent of Change

Using this formula, your answer comes out as a decimal. Just multiply by 100 to change to a percent

Percent of Change = Difference Original

% Increase % Decrease

Which Means:

or

Definition: (write this down)

Holt Algebra 1


Example 1A: Finding Percent Increase and Decrease

Find each percent change. Tell whether it is a percent increase or decrease.

From 8 to 10

= 0.25

= 25% Write the answer as a percent.

Simplify the numerator.Simplify the fraction.

8 to 10 is an increase, so a change from 8 to 10 is a 25% increase.

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Helpful Hint

Before solving, decide what is a reasonable answer. For Example 1A, 8 to 16 would be a 100% increase. So 8 to 10 should be much less than 100%.

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From 75 to 30

= 0.6

= 60% Write the answer as a percent.

Simplify the numerator.Simplify the fraction.

75 to 30 is a decrease, so a change from 75 to 30 is a 60% decrease.

Example 1B: Finding Percent Increase and Decrease

Find the percent change. Tell whether it is a percent increase or decrease.

Holt Algebra 1


Example 2: Finding Percent Increase and Decrease

A. Find the result when 12 is increased by 50%.

0.50(12) = 6 Find 50% of 12. This is the amount of increase.

12 + 6 =18 It is a percent increase, so add 6 to the original amount.

12 increased by 50% is 18.

B. Find the result when 55 is decreased by 60%.

0.60(55) = 33 Find 60% of 55. This is the amount of decrease.

55 – 33 = 22 It is a percent decrease so subtract 33 from the the original amount.

55 decreased by 60% is 22.

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Common application of percent change are discounts and markups.

A discount is an amount by which an original price is reduced.

discount = % of original price

final price = original price – discount

A markup is an amount by which a wholesale price is increased.

final price = wholesale cost markup+

markup wholesale cost= % of

Holt Algebra 1


Example 3: Discounts The entrance fee at an amusement park is

$35. People over the age of 65 receive a 20% discount. What is the amount of the discount? How much do people over 65 pay?

Method 1 A discount is a percent decrease. So find $35 decreased by 20%.

0.20(35) = 7 Find 20% of 35. This is the amount of the discount.

35 – 7 = 28 Subtract 7 from 35. This is the entrance fee for people over the age of 65.

Holt Algebra 1


Example 3A: Discounts

Method 2 Subtract the percent discount from 100%.

100% – 20% = 80% People over the age of 65 pay 80% of the regular price, $35.

0.80(35) = 28 Find 80% of 35. This is the entrance fee for people over the age of 65.

35 – 28 = 7 Subtract 28 from 35. This is the amount of the discount.

By either method, the discount is $7. People over the age of 65 pay $28.00.

Holt Algebra 1


Helpful Hint

Before solving, decide what is a reasonable answer. For example 3A, a 10% discount is $3.50 off. So a 20% discount would be more than $2 off.

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Example 3B: Discounts

A student paid $31.20 for art supplies that normally cost $52.00. Find the percent discount .

$52.00 – $31.20 = $20.80 Think: 20.80 is what percent of 52.00? Let x represent the percent.20.80 = x(52.00)

0.40 = x

40% = x

The discount is 40%

Since x is multiplied by 52.00, divide both sides by 52.00 to undo the multiplication.

Write the answer as a percent.

Holt Algebra 1


Example 4: Markups The wholesale cost of a DVD is $7. The markup is 85%. What is the amount of the markup? What is the selling price?Method 1A markup is a percent increase. So find $7 increased by 85%.0.85(7) = 5.95

7 + 5.95 = 12.95

Find 85% of 7. This is the amount of the markup.

Add to 7. This is the selling price.

Subtract from 12.95. This is the amount of the markup.

12.95 7 = 5.95

By either method, the amount of the markup is $5.95. The selling price is $12.95.

Method 2Add percent markup to 100%

The selling price is 185% of the wholesale price, 7.

100% + 85% = 185%

Find 185% of 7. This is the selling price.

1.85(7) = 12.95

Holt Algebra 1


Lesson Quiz: Part 1

1. from 20 to 28.

2. from 80 to 62.

3. from 500 to 100.

4. find the result when 120 is increased by 40%.

5. find the result when 70 is decreased by 20%.


40% increase

22.5% decrease

80% decrease

168

56

Holt Algebra 1

2-10 Percent Increase and DecreaseLesson Quiz: Part 2


3. A movie ticket costs $9. On Mondays, tickets are 20% off. What is the amount of discount? How much would a ticket cost on a Monday?

4. A bike helmet cost $24. The wholesale cost was $15. What was the percent of markup?

$1.80; $7.20

60%

Find the percent change. Tell whether it is a percent increase or decrease.

1. from 500 to 100. 80% decrease

2. find the result when 120 is increased by 40%. 168

holt algebra 1 2-10 percent increase and decrease 2-10 percent increase and decrease holt algebra 1...

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