CONFIDENTIAL 1

Algebra1Algebra1

Percent IncreasePercent Increaseand Decreaseand Decrease

CONFIDENTIAL 2

Warm UpWarm Up

1) What percent of 64 is 48?

2) What percent of 90 is 54?

3) What percent of 36 is 72?

4) What percent of 6 is 7.5?

1) 75%

2) 60%

3) 200%

4) 125%

CONFIDENTIAL 3

Applications of Percent

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

been reduced.

Percent Change

percent change = amount of increase or decrease original amount , expressed as a percent

CONFIDENTIAL 4

A) from 25 to 56

= 0.96

SOLUTION:

Simplify the numerator.

Write the answer as a percent.

Finding Percent Increase or Decrease

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

percent change = amount of increase original amount

= 56 - 25 25

= 31 25

= 96%

CONFIDENTIAL 5

B) from 25 to 17

= 0.32

SOLUTION:

Simplify the numerator.

Write the answer as a percent.

percent change = amount of decrease original amount

= 25 - 17 25

= 8 25

= 32%

CONFIDENTIAL 6

1) from 200 to 110

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

Now you try!

2) from 25 to 30

1) 45% decrease

2) 20% increase

CONFIDENTIAL 7

Finding the Result of a Percent Increase or Decrease

A) Find the result when 20 is increased by 40%.

0.40 (20) = 8

20 + 8 = 28

20 increased by 40% is 28.

Find 40% of 20. This is the amount of the increase.

It is a percent increase, so add 8 to the original amount.

B) Find the result when 75 is decreased by 60%.

0.60 (75) = 45

75 - 45 = 30

75 decreased by 60% is 30.

Find 60% of 75. This is the amount of the decrease.

It is a percent decrease, so subtract 45 from the original amount.

CONFIDENTIAL 8

1) Find the result when 72 is increased by 25%.

Now you try!

2) Find the result when 10 is decreased by 40%.

1) 90

2) 6

CONFIDENTIAL 9

Common applications of percent change are discounts and markups.

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

discount = % of original price

final price = original price - discount

markup = % of wholesale cost

final price = wholesale cost + markup

A markup is an amountby which a wholesale costis increased.

CONFIDENTIAL 10

Discounts

A) Admission to the museum is $8. Students receive a 15% discount. How much is the discount? How much do

students pay?

0.15 (8) = 1.20

8 - 1.20 = 6.80

Find 15% of 8. This is the amount of the discount.

Subtract 1.20 from 8. This is the student price.

Method 1: A discount is a percent decrease. So find $8 decreased by 15%.

Next Page

CONFIDENTIAL 11

By either method, the discount is $1.20. Students pay $6.80.

100% - 15% = 85%

0.85 (8) = 6.80

Students pay 85% of the regular price, $8.

Find 85% of 8. This is the student price.

Method 2: Subtract percent discount from 100%.

8 - 6.80 = 1.20 Subtract 6.80 from 8. This is the amount of the discount.

CONFIDENTIAL 12

B) Christie used a coupon and paid $7.35 for a pizza that normally costs $10.50. Find the percent discount.

3.15 = x (10.50)

0.3 = x

Since x is multiplied by 10.50, divide both sides by 10.50 to undo the multiplication.

Write the answer as a percent.

$10.50 - $7.35 = $3.15 3.15 is what percent of 10.50? Let x represent the percent.

3.15 = x . (10.50)10.50 10.50

30% = x

The discount is 30%.

CONFIDENTIAL 13

Now you try!

1) A $220 bicycle was on sale for 60% off. Find the sale price.

Solve:

2) Ray paid $12 for a $15 T-shirt. What was the percent discount?

1) $88

2) 20%

CONFIDENTIAL 14

Markups

48 + 36 = 84Add to 48. This is the selling price.

0.75 (48) = 36 Find 75% of 48. This is the amount of the markup.

A) Kale buys necklaces at a wholesale price of $48 each. He then marks up the price by 75% and sells the necklaces. What is the amount of the markup?

What is the selling price?

Method 1: A markup is a percent increase. So find $48 increased by 75%.

Next Page

Solution:

CONFIDENTIAL 15

By either method, the amount of the markup is $36. The selling price is $84.

100% + 75% = 175%

1.75 (48) = 84

The selling price is 175% of the wholesale price, $48.

Find 175% of 48. This is the selling price.

Method 2: Add percent markup to 100%.

84 - 48 = 36 Subtract from 84. This is the amount of the markup.

CONFIDENTIAL 16

B) Lars purchased a daily planner for $32. The wholesale cost was $25. What was the percent markup?

The markup was 28%.

32 - 25 = 7

7 = x (25)

Find the amount of the markup.

7 is what percent of 25? Let x represent the percent.

0.28 = x

Since x is multiplied by 25, divide both sides by 25 toundo the multiplication.

7 = x . (25)25 25

Write the answer as a percent.28% = x

Solution:

CONFIDENTIAL 17

Now you try!

1) A video game has a 70% markup. The wholesale cost is $9. What is the selling price?

Solve:

2) What is the percent markup on a car selling for $21,850 that had a wholesale cost of $9500?

1) $15.3

2) 130%

CONFIDENTIAL 18

Some more examples

A) A trader marks his goods 40% above cost price and allows a discount of 25% .What gain percent does he make?

SOLUTION:

Let the cost price be $100.

Then marked price = $140.

Discount = 25% of marked price = $140 × 25 = $35 100

Hence, the trader gains 5%.

Therefore, net selling price = Marked price – Discount = $(140 – 35) = $105

Therefore, gain = 5%

CONFIDENTIAL 19

B) By allowing a discount of 10% on the marked price of an article, a dealer gains 8%. By what percent is the marked

price above cost price?

SOLUTION:

Let the cost price be $100.

Then, selling price = $108.

When selling price is $1, then marked price = $100 90

Hence, the marked price is 20% above the cost price.

When marked price $100, then $100 is the discount and $90 is the selling price.

Thus, when selling price is $90, then marked price = $100.

When selling price is $108, then marked price = $108 ×100= $120 90

CONFIDENTIAL 20

Now you try!

1) A dealer marked his goods 35% above the cost price and allows a discount of 20% on the marked

price. Find his gain or loss percent.

Solve:

1)Gain = 8%

CONFIDENTIAL 21

Assessment

1) 80% of a number is the same as a --% decrease from that number.

2) Find the result when 40 is increased by 85%.

3) Find the result when 60 is increased by 3%.

4) What is the final price on a $185 leather jacket that is on sale for 40% off?

1) 20%

2) 74

3) 78

4) $111

CONFIDENTIAL 22

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

5) 25 to 45

6) 10 to 8

7) 400 to 300

5) 80% increase

6) 20% decrease

7) 25% decrease

CONFIDENTIAL 23

8) Robert finds a shirt on a sale rack. All items on the rack are 40% off. The price on his shirt is missing.

When the clerk scans the bar code, he tells Robert that the sale price of shirt is $18. What percent of the

original price is 18?

9) A can of soup had 480 mg of sodium per serving. The sodium was reduced to 360 mg per serving so that the soup could be advertised as “low sodium.”What was the percent change in sodium content?

10) Last summer, Duncan charged $20 to mow a lawn in his neighborhood. This summer, he’ll charge $23. What is the percent increase in Duncan’s price?

Show that your answer is reasonable.

8) 60%

9) 25% decrease

10) 15%

CONFIDENTIAL 24

Applications of Percent

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

been reduced.

Percent Change

percent change = amount of increase or decrease original amount , expressed as a percent

Let’s review

CONFIDENTIAL 25

A) from 25 to 56

= 0.96

SOLUTION:

Simplify the numerator.

Write the answer as a percent.

Finding Percent Increase or Decrease

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

percent change = amount of increase original amount

= 56 - 25 25

= 31 25

= 96%

review

CONFIDENTIAL 26

Finding the Result of a Percent Increase or Decrease

A) Find the result when 20 is increased by 40%.

0.40 (20) = 8

20 + 8 = 28

20 increased by 40% is 28.

Find 40% of 20. This is the amount of the increase.

It is a percent increase, so add 8 to the original amount.

B) Find the result when 75 is decreased by 60%.

0.60 (75) = 45

75 - 45 = 30

75 decreased by 60% is 30.

Find 60% of 75. This is the amount of the decrease.

It is a percent decrease, so subtract 45 from the original amount.

review

CONFIDENTIAL 27

Common applications of percent change are discounts and markups.

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

discount = % of original price

final price = original price - discount

markup = % of wholesale cost

final price = wholesale cost + markup

A markup is an amountby which a wholesale costis increased.

review

CONFIDENTIAL 28

Markups

48 + 36 = 84Add to 48. This is the selling price.

0.75 (48) = 36 Find 75% of 48. This is the amount of the markup.

A) Kale buys necklaces at a wholesale price of $48 each. He then marks up the price by 75% and sells the necklaces. What is the amount of the markup?

What is the selling price?

Method 1: A markup is a percent increase. So find $48 increased by 75%.

Next Page

Solution:

review

CONFIDENTIAL 29

By either method, the amount of the markup is $36. The selling price is $84.

100% + 75% = 175%

1.75 (48) = 84

The selling price is 175% of the wholesale price, $48.

Find 175% of 48. This is the selling price.

Method 2: Add percent markup to 100%.

84 - 48 = 36 Subtract from 84. This is the amount of the markup.

review

CONFIDENTIAL 30

B) Lars purchased a daily planner for $32. The wholesale cost was $25. What was the percent markup?

The markup was 28%.

32 - 25 = 7

7 = x (25)

Find the amount of the markup.

7 is what percent of 25? Let x represent the percent.

0.28 = x

Since x is multiplied by 25, divide both sides by 25 toundo the multiplication.

7 = x . (25)25 25

Write the answer as a percent.28% = x

Solution:

review

CONFIDENTIAL 31

Some more examples

A) A trader marks his goods 40% above cost price and allows a discount of 25% .What gain percent does he make?

SOLUTION:

Let the cost price be $100.

Then marked price = $140.

Discount = 25% of marked price = $140 × 25 = $35 100

Hence, the trader gains 5%.

Therefore, net selling price = Marked price – Discount = $(140 – 35) = $105

Therefore, gain = 5%

review

CONFIDENTIAL 32

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