Download Finding a Percent

7.1
Percents and Fractions
Goal: Use a fraction to find the percent of a number.
Vocabulary
Percent:
Writing Percents
Words In the area model shown,
85 of the 100 squares are shaded.
You can say that 85 percent of the
squares are shaded.
85
100
Numbers 85%
p
100
Algebra p%
Example 1
Writing Percents as Fractions, Fractions as Percents
Write 31% and 60% as fractions in simplest form.
a. 31% 3
10
b. 60% 4
5
Write and as percents.
3
10
3p
10 p
a. 4p
b. 4 5
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5p
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143
7.1
Percents and Fractions
Goal: Use a fraction to find the percent of a number.
Vocabulary
A percent is a ratio whose denominator is 100. The
symbol for percent is %.
Percent:
Writing Percents
Words In the area model shown,
85 of the 100 squares are shaded.
You can say that 85 percent of the
squares are shaded.
85
100
Numbers 85%
p
100
Algebra p%
Example 1
Writing Percents as Fractions, Fractions as Percents
Write 31% and 60% as fractions in simplest form.
31
a. 31% 100
3
10
3
60
b. 60% 5
100
4
5
Write and as percents.
10
30
3
3p
a. 1
00 30%
10
10 p 10
20
80
4p
4
b. 1
00 80%
5 p 20
5
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143
Checkpoint Write the percent as a fraction in simplest form,
or write the fraction as a percent.
1. 73%
Example 2
2. 40%
9
10
4
25
3. 4. Writing a Probability as a Percent
Random Number A computer randomly generates an integer from
1 to 10. Find the probability that 8 is the integer generated.
Solution
There are
P(8) possible outcomes, and
outcome is favorable.
Write probability as a fraction.
Write fraction as percent.
Answer: The probability that 8 is the integer generated is
.
Checkpoint A computer randomly generates an integer from
1 to 10. Find the probability of the given event. Write your answer
as a percent.
5. P(2)
144
Chapter 7 • Pre-Algebra Notetaking Guide
6. P(prime number)
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Checkpoint Write the percent as a fraction in simplest form,
or write the fraction as a percent.
1. 73%
2. 40%
2
5
73
100
Example 2
9
10
4
25
3. 4. 90%
16%
Writing a Probability as a Percent
Random Number A computer randomly generates an integer from
1 to 10. Find the probability that 8 is the integer generated.
Solution
There are 10 possible outcomes, and 1 outcome is favorable.
1
P(8) 1
0
Write probability as a fraction.
10%
Write fraction as percent.
Answer: The probability that 8 is the integer generated is 10% .
Checkpoint A computer randomly generates an integer from
1 to 10. Find the probability of the given event. Write your answer
as a percent.
5. P(2)
6. P(prime number)
10%
144
Chapter 7 • Pre-Algebra Notetaking Guide
40%
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Example 3
Finding a Percent of a Number
Crackers In a survey of 85 people, 20% of them said they usually
eat crackers with soup. How many people in the survey said they
usually eat crackers with soup?
Solution
To find 20% of 85, use the fact that 20% 20% of 85 Answer:
with soup.
p
. Then multiply.
Write percent as a fraction.
Simplify.
people said they usually eat crackers
Checkpoint Find the percent of the number.
7. 30% of 80
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8. 60% of 105
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145
Example 3
Finding a Percent of a Number
Crackers In a survey of 85 people, 20% of them said they usually
eat crackers with soup. How many people in the survey said they
usually eat crackers with soup?
Solution
1
To find 20% of 85, use the fact that 20% 5 . Then multiply.
1
20% of 85 5 p 85
17
Write percent as a fraction.
Simplify.
Answer: Seventeen people said they usually eat crackers
with soup.
Checkpoint Find the percent of the number.
7. 30% of 80
8. 60% of 105
24
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63
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145
7.2
Percents and Proportions
Goal: Use proportions to solve percent problems.
Solving Percent Problems
You can represent “a is p percent of b” using the proportion
p
a
100
b
p
100
where a is a part of the base b and p%, or , is the percent.
Finding a Percent
Example 1
What percent of 9 is 5?
a
p
b
100
Write proportion.
p
100
5
9
p Substitute for a and for b.
p
100
p p
Answer: 5 is
Multiply each side by
.
Simplify.
% of 9.
Checkpoint Use a proportion to answer the question.
1. What percent of 28 is 4?
146
Chapter 7 • Pre-Algebra Notetaking Guide
2. What percent of 80 is 30?
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7.2
Percents and Proportions
Goal: Use proportions to solve percent problems.
Solving Percent Problems
You can represent “a is p percent of b” using the proportion
p
a
100
b
p
100
where a is a part of the base b and p%, or , is the percent.
Finding a Percent
Example 1
What percent of 9 is 5?
a
p
b
100
5
p
9
100
5
p
100 p 100 p 9
100
5
55 p
9
Write proportion.
Substitute for a and for b.
Multiply each side by 100 .
Simplify.
5
Answer: 5 is 55 9 % of 9.
Checkpoint Use a proportion to answer the question.
1. What percent of 28 is 4?
2
7
14 %
146
Chapter 7 • Pre-Algebra Notetaking Guide
2. What percent of 80 is 30?
1
2
37 %
Copyright © Holt McDougal. All rights reserved.
Finding a Part of a Base
Example 2
What number is 15% of 300?
a
p
b
100
Write proportion.
a
100
a
p Substitute for b and for p.
p 100
a
Answer:
Multiply each side by
.
Simplify.
is 15% of 300.
Example 3
Finding a Base
Student Council Election You receive 189 votes, or 45%, of the
votes in the student council election. How many students voted?
Solution
189 is a part of the total number of voters, which is the base.
a
p
b
100
Write proportion.
b
100
p
Answer:
p
Substitute for a and for p.
Cross products property
Multiply.
b
Divide each side by
.
students voted in the election.
Checkpoint Use a proportion to answer the question.
3. What number is 62% of 200?
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4. 117 is 78% of what number?
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147
Example 2
Finding a Part of a Base
What number is 15% of 300?
a
p
b
100
15
a
100
300
15
a
300 p 300 p 100
300
a 45
Write proportion.
Substitute for b and for p.
Multiply each side by 300 .
Simplify.
Answer: 45 is 15% of 300.
Example 3
Finding a Base
Student Council Election You receive 189 votes, or 45%, of the
votes in the student council election. How many students voted?
Solution
189 is a part of the total number of voters, which is the base.
a
p
b
100
45
189
b
100
189 p 100 45 p b
18,900 45b
420 b
Write proportion.
Substitute for a and for p.
Cross products property
Multiply.
Divide each side by 45 .
Answer: 420 students voted in the election.
Checkpoint Use a proportion to answer the question.
3. What number is 62% of 200?
4. 117 is 78% of what number?
124
150
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147
7.3
Percents and Decimals
Goal: Use decimals to solve percent problems.
Percents and Decimals
• To write a decimal as a percent, move the decimal point two
places to the
and
.
• To write a percent as a decimal, move the decimal point two
places to the
and
.
Example 1
Writing Decimals as Percents
Write 0.17, 2, and 3.2 as percents.
a. 0.17 0.17
b. 2 2.00
Example 2
c. 3.2 3.20
Writing Percents as Decimals
Write 63%, 0.7%, and 129% as decimals.
a. 63% 63%
b. 0.7% 00.7%
c. 129% 129%
Checkpoint Write the decimal as a percent or the percent
as a decimal.
148
1. 0.54
2. 4
3. 1.75
4. 0.03
5. 41%
6. 147%
7. 9%
8. 12.5%
Chapter 7 • Pre-Algebra Notetaking Guide
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7.3
Percents and Decimals
Goal: Use decimals to solve percent problems.
Percents and Decimals
• To write a decimal as a percent, move the decimal point two
places to the right and write a percent sign .
• To write a percent as a decimal, move the decimal point two
places to the left and remove the percent sign .
Example 1
Writing Decimals as Percents
Write 0.17, 2, and 3.2 as percents.
a. 0.17 0.17
b. 2 2.00
17%
Example 2
c. 3.2 3.20
200%
320%
Writing Percents as Decimals
Write 63%, 0.7%, and 129% as decimals.
a. 63% 63%
b. 0.7% 00.7%
c. 129% 129%
0.007
1.29
0.63
Checkpoint Write the decimal as a percent or the percent
as a decimal.
1. 0.54
54%
5. 41%
0.41
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Chapter 7 • Pre-Algebra Notetaking Guide
2. 4
3. 1.75
400%
6. 147%
1.47
175%
7. 9%
0.09
4. 0.03
3%
8. 12.5%
0.125
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Example 3
4
9
Writing Fractions as Percents
7
4
Write and as percents.
4
9
a. Write fraction as a decimal.
Write decimal as a percent.
b. Write fraction as a decimal.
Write decimal as a percent.
7
4
Checkpoint Write the fraction as a percent.
5
8
9. Example 4
8
9
11
5
10. 13
6
11. 12. Finding a Percent of a Number
Day of Dread In a survey of 1300 adults, 18% said the day they
dread the most is Monday. How many adults chose Monday?
Solution
Find 18% of 1300.
18% of 1300 p 1300
Write percent as decimal.
Multiply.
Answer: The number of adults that chose Monday is
.
Checkpoint Find the percent of the number.
13. 25% of 76
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14. 110% of 65
15. 0.7% of 500
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149
Example 3
4
9
Writing Fractions as Percents
7
4
Write and as percents.
4
9
a. 0.444 . . .
Write fraction as a decimal.
44.4 %
Write decimal as a percent.
7
4
b. 1.75
Write fraction as a decimal.
175%
Write decimal as a percent.
Checkpoint Write the fraction as a percent.
5
8
8
9
9. 11
5
10. 88.8
%
62.5%
Example 4
13
6
11. 12. 216.6%
220%
Finding a Percent of a Number
Day of Dread In a survey of 1300 adults, 18% said the day they
dread the most is Monday. How many adults chose Monday?
Solution
Find 18% of 1300.
18% of 1300 0.18 p 1300
234
Write percent as decimal.
Multiply.
Answer: The number of adults that chose Monday is 234 .
Checkpoint Find the percent of the number.
13. 25% of 76
19
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14. 110% of 65
71.5
15. 0.7% of 500
3.5
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149
7.4
The Percent Equation
Goal: Use equations to solve percent problems.
The Percent Equation
You can represent “a is p percent of b” using the equation
a p% p b
where a is a part of the base b and p% is the percent.
Finding a Part of a Base
Example 1
In a newspaper’s survey, 1100 adults were asked to name their
favorite condiment. The most frequent response was ketchup,
which was given by 47% of the adults. How many adults
chose ketchup?
Solution
To find how many adults chose ketchup as their favorite condiment,
use the percent equation.
a p% p b
Write percent equation.
p
Substitute for p and for b.
p
Write percent as a decimal.
Multiply.
Answer: The number of adults who chose ketchup as their
favorite condiment was
.
Checkpoint Use the percent equation to answer the question.
1. What number is 15% of 60?
150
Chapter 7 • Pre-Algebra Notetaking Guide
2. What number is 78% of 105?
Copyright © Holt McDougal. All rights reserved.
7.4
The Percent Equation
Goal: Use equations to solve percent problems.
The Percent Equation
You can represent “a is p percent of b” using the equation
a p% p b
where a is a part of the base b and p% is the percent.
Example 1
Finding a Part of a Base
In a newspaper’s survey, 1100 adults were asked to name their
favorite condiment. The most frequent response was ketchup,
which was given by 47% of the adults. How many adults
chose ketchup?
Solution
To find how many adults chose ketchup as their favorite condiment,
use the percent equation.
a p% p b
Write percent equation.
47% p 1100
Substitute for p and for b.
0.47 p 1100
Write percent as a decimal.
517
Multiply.
Answer: The number of adults who chose ketchup as their
favorite condiment was 517 .
Checkpoint Use the percent equation to answer the question.
150
1. What number is 15% of 60?
2. What number is 78% of 105?
9
81.9
Chapter 7 • Pre-Algebra Notetaking Guide
Copyright © Holt McDougal. All rights reserved.
Example 2
Finding a Commission
Commission A sales person earns 5.5% commission on every
car sold. The sales person sells a car for $41,200. What is
the commission?
Solution
a p% p b
Write percent equation.
p
Substitute for p and for b.
p
Write percent as decimal.
Multiply.
Answer: The commission is $
.
Checkpoint
3. In Example 2, find the commission if a car is sold for $45,000.
Example 3
Finding a Percent
What percent of 24 is 84?
a p% p b
p% p
Substitute for a and for b.
p%
Divide each side by
p%
Write decimal as a percent.
Answer: 84 is
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Write percent equation.
.
% of 24.
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151
Example 2
Finding a Commission
Commission A sales person earns 5.5% commission on every
car sold. The sales person sells a car for $41,200. What is
the commission?
Solution
a p% p b
Write percent equation.
5.5% p 41,200
Substitute for p and for b.
0.055 p 41,200
Write percent as decimal.
2266
Multiply.
Answer: The commission is $ 2266 .
Checkpoint
3. In Example 2, find the commission if a car is sold for $45,000.
$2475
Example 3
Finding a Percent
What percent of 24 is 84?
a p% p b
Write percent equation.
84 p% p 24
Substitute for a and for b.
3.5 p%
Divide each side by 24 .
350% p%
Write decimal as a percent.
Answer: 84 is 350 % of 24.
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151
Checkpoint Use the percent equation to answer the question.
4. What percent of 15 is 21?
Example 4
5. What percent of 72 is 45?
Finding a Base
Football Your friend paid $48 for a ticket to a professional football
game. This amount was 64% of the total amount your friend spent
at the game. How much money did your friend spend?
Solution
a p% p b
Write percent equation.
%pb
Substitute for a and for p.
pb
Write percent as decimal.
b
Divide each side by
Answer: Your friend spent $
.
at the game.
Checkpoint Use the percent equation to answer the question.
6. 33 is 30% of what number?
152
Chapter 7 • Pre-Algebra Notetaking Guide
7. 90 is 37.5% of what number?
Copyright © Holt McDougal. All rights reserved.
Checkpoint Use the percent equation to answer the question.
4. What percent of 15 is 21?
5. What percent of 72 is 45?
140%
Example 4
62.5%
Finding a Base
Football Your friend paid $48 for a ticket to a professional football
game. This amount was 64% of the total amount your friend spent
at the game. How much money did your friend spend?
Solution
a p% p b
Write percent equation.
48 64 % p b
Substitute for a and for p.
48 0.64 p b
Write percent as decimal.
75 b
Divide each side by 0.64 .
Answer: Your friend spent $ 75 at the game.
Checkpoint Use the percent equation to answer the question.
6. 33 is 30% of what number?
110
152
Chapter 7 • Pre-Algebra Notetaking Guide
7. 90 is 37.5% of what number?
240
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7.5
Percent of Change
Goal: Find a percent of change in a quantity.
Vocabulary
Percent
of change:
Percent
of increase:
Percent
of decrease:
Percent of Change
The percent of change is the ratio of the amount of increase or
decrease to the original amount.
Amount of increase or decrease
Original amount
Percent of change, p% Example 1
Finding a Percent of Increase
Enrollment A school had 720 students enrolled last year. This
year, 745 students are enrolled. By about what percent did the
number of students change from last year to this year?
Amount of increase
Original amount
p% Write formula for percent of increase.
Substitute.
Subtract.
≈
Divide. Then write
decimal as a percent.
Answer: The number of students increased by about
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%.
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153
7.5
Percent of Change
Goal: Find a percent of change in a quantity.
Vocabulary
A percent of change indicates how much a quantity
Percent
of change: increases or decreases with respect to the original
amount.
The percent of change in a quantity when the new
Percent
of increase: amount of the quantity is greater than the original
amount.
The percent of change in a quantity when the new
Percent
of decrease: amount of the quantity is less than the original
amount.
Percent of Change
The percent of change is the ratio of the amount of increase or
decrease to the original amount.
Amount of increase or decrease
Original amount
Percent of change, p% Example 1
Finding a Percent of Increase
Enrollment A school had 720 students enrolled last year. This
year, 745 students are enrolled. By about what percent did the
number of students change from last year to this year?
Amount of increase
Original amount
p% Write formula for percent of increase.
745 720
720
Substitute.
25
720
Subtract.
≈ 0.035 3.5%
Divide. Then write
decimal as a percent.
Answer: The number of students increased by about 3.5 %.
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153
Example 2
Finding a Percent of Decrease
Find the percent of decrease from 576 to 216.
Write formula for percent
of decrease.
Amount of decrease
Original amount
p% Substitute.
Subtract.
Simplify fraction.
Then write the
fraction as a percent.
Answer: The percent of decrease is
Example 3
%.
Using a Percent of Increase
Ticket Prices A professional baseball team announces that the
average ticket price to one of their games will be 8% more than
last year. If the average price of a ticket was $12 last year, how
much will the average ticket cost this year?
Solution
To find the average ticket cost this year, you need to increase the
average ticket cost last year by 8%.
Amount of
Ticket cost
Ticket cost
increase
this year
last year
p
Substitute.
p
Write percent as
a decimal.
Evaluate.
Answer: This year, the average ticket will cost $
154
Chapter 7 • Pre-Algebra Notetaking Guide
.
Copyright © Holt McDougal. All rights reserved.
Example 2
Finding a Percent of Decrease
Find the percent of decrease from 576 to 216.
Amount of decrease
Original amount
p% Write formula for percent
of decrease.
576 216
576
Substitute.
360
576
Subtract.
5 62.5%
Simplify fraction.
Then write the
fraction as a percent.
8
Answer: The percent of decrease is 62.5 %.
Example 3
Using a Percent of Increase
Ticket Prices A professional baseball team announces that the
average ticket price to one of their games will be 8% more than
last year. If the average price of a ticket was $12 last year, how
much will the average ticket cost this year?
Solution
To find the average ticket cost this year, you need to increase the
average ticket cost last year by 8%.
Amount of
Ticket cost
Ticket cost
increase
this year
last year
12 8% p 12
Substitute.
12 0.08 p 12
Write percent as
a decimal.
Evaluate.
12.96
Answer: This year, the average ticket will cost $ 12.96 .
154
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Example 4
Finding a New Amount
Tuna In 1990, the average price per pound of light chunk tuna
was $2.11. By 2001, the average price per pound had decreased
by 7.1%. What was the average price per pound in 2001?
To find a new
amount, do one of
the following.
For a p% increase,
multiply the original
amount by
(100% p%).
For a p% decrease,
multiply the original
amount by
(100% p%).
Solution
Price in 2001 Price in 1990 p (100% p%)
(
p 100% p
p
)
%
Substitute.
Subtract percents.
Write percent as
a decimal.
Multiply.
Answer: The average price per pound in 2001 was about $
.
Checkpoint Find the percent of increase.
1. Original: 25
New: 31
2. Original: 150
New: 195
Find the new amount.
3. Increase 54 by 25%.
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4. Decrease 78 by 40%.
Chapter 7 • Pre-Algebra Notetaking Guide
155
Example 4
Finding a New Amount
Tuna In 1990, the average price per pound of light chunk tuna
was $2.11. By 2001, the average price per pound had decreased
by 7.1%. What was the average price per pound in 2001?
To find a new
amount, do one of
the following.
For a p% increase,
multiply the original
amount by
(100% p%).
For a p% decrease,
multiply the original
amount by
(100% p%).
Solution
Price in 2001 Price in 1990 p (100% p%)
(
)
2.11 p 100% 7.1 %
Substitute.
2.11 p 92.9%
2.11 p 0.929
Subtract percents.
Write percent as
a decimal.
1.96019
Multiply.
Answer: The average price per pound in 2001 was about $ 1.96 .
Checkpoint Find the percent of increase.
1. Original: 25
New: 31
24%
2. Original: 150
New: 195
30%
Find the new amount.
3. Increase 54 by 25%.
67.5
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4. Decrease 78 by 40%.
46.8
Chapter 7 • Pre-Algebra Notetaking Guide
155
7.6
Percent Applications
Goal: Find markups, discounts, sales tax, and tips.
Vocabulary
Markup:
Discount:
Example 1
Finding a Retail Price
Pillows A store buys decorative pillows from a manufacturer
for $2 each. The store marks up the price by 400%. What is the
retail price?
Solution
Method 1 Add the markup to the wholesale price.
Retail price Wholesale price Markup
p
Substitute.
Write
decimal.
Multiply.
p
as a
Add.
Method 2 Multiply the wholesale price by (100% Markup
percent).
Retail price Wholesale price p (100% Markup percent)
(
)
p 100% p
Add percents.
p
Write
decimal.
Multiply.
Substitute.
Answer: The retail price of a decorative pillow is $
156
Chapter 7 • Pre-Algebra Notetaking Guide
as a
.
Copyright © Holt McDougal. All rights reserved.
7.6
Percent Applications
Goal: Find markups, discounts, sales tax, and tips.
Vocabulary
Markup:
An increase from the wholesale price of an item to the
retail price is a markup.
Discount:
A decrease from the original price of an item to the
sale price is a discount.
Example 1
Finding a Retail Price
Pillows A store buys decorative pillows from a manufacturer
for $2 each. The store marks up the price by 400%. What is the
retail price?
Solution
Method 1 Add the markup to the wholesale price.
Retail price Wholesale price Markup
2 400% p 2
Substitute.
2 4 p 2
2 8
Write 400% as a
decimal.
Multiply.
10
Add.
Method 2 Multiply the wholesale price by (100% Markup
percent).
Retail price Wholesale price p (100% Markup percent)
(
2 p 100% 400%
)
Substitute.
2 p 500%
Add percents.
2 p 5
Write 500% as a
decimal.
Multiply.
10
Answer: The retail price of a decorative pillow is $ 10 .
156
Chapter 7 • Pre-Algebra Notetaking Guide
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Example 2
Finding a Sale Price
Backpack You buy a backpack that is on sale for 25% off the
original price of $20. What is the sale price?
Solution
Method 1 Subtract the discount from the original price.
Sale price Original price Discount
p
Substitute.
p
Write
as a decimal.
Multiply.
Subtract.
Method 2 Multiply the original price by (100% Discount percent).
Sale price Original price p (100% Discount percent)
(
)
p 100% p
Subtract percents.
p
Write
Substitute.
as a decimal.
Multiply.
Answer: The sale price of the backpack is $
.
Checkpoint
1. In Example 1, what is the retail price of a decorative pillow if the
markup percent is 250%?
2. A pair of shorts that originally costs $15 is 40% off. Find the
sale price.
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Chapter 7 • Pre-Algebra Notetaking Guide
157
Example 2
Finding a Sale Price
Backpack You buy a backpack that is on sale for 25% off the
original price of $20. What is the sale price?
Solution
Method 1 Subtract the discount from the original price.
Sale price Original price Discount
20 25% p 20
Substitute.
20 0.25 p 20
Write 25% as a decimal.
20 5
Multiply.
15
Subtract.
Method 2 Multiply the original price by (100% Discount percent).
Sale price Original price p (100% Discount percent)
(
20 p 100% 25%
)
Substitute.
20 p 75%
Subtract percents.
20 p 0.75
Write 75% as a decimal.
15
Multiply.
Answer: The sale price of the backpack is $ 15 .
Checkpoint
1. In Example 1, what is the retail price of a decorative pillow if the
markup percent is 250%?
$7
2. A pair of shorts that originally costs $15 is 40% off. Find the
sale price.
$9
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Chapter 7 • Pre-Algebra Notetaking Guide
157
Example 3
Using Sales Tax and Tips
Pizza You order pizza to be delivered. The bill is $18. You give the
delivery person a 15% tip. The sales tax is 5%. What is the total
cost of the pizza?
Solution
Sales tax and tips are calculated using a percent of the purchasing
price. These amounts are then added to the purchase price.
Total Food bill Sales tax Tip
p
p
p
Substitute.
Write percents
as decimals.
p
Evaluate.
Answer: The total cost of the pizza is $
.
Checkpoint
3. In Example 3, find the total cost of the pizza if the tip is 20%.
Example 4
Finding an Original Amount
Blender A store marks up the wholesale price of a blender by
125%. The retail price is $30. What is the wholesale price?
Solution
Let x represent the wholesale price.
Retail price Wholesale price p (100% Markup percent)
(
x p 100% )
Substitute.
xp
Add percents.
xp
Write
≈x
Divide each side by
as a decimal.
Answer: The wholesale price of the blender is about $
158
Chapter 7 • Pre-Algebra Notetaking Guide
.
.
Copyright © Holt McDougal. All rights reserved.
Example 3
Using Sales Tax and Tips
Pizza You order pizza to be delivered. The bill is $18. You give the
delivery person a 15% tip. The sales tax is 5%. What is the total
cost of the pizza?
Solution
Sales tax and tips are calculated using a percent of the purchasing
price. These amounts are then added to the purchase price.
Total Food bill Sales tax Tip
18 5% p 18 15% p 18
18 0.05 p 18 0.15 p 18
Substitute.
Write percents
as decimals.
21.6
Evaluate.
Answer: The total cost of the pizza is $ 21.60 .
Checkpoint
3. In Example 3, find the total cost of the pizza if the tip is 20%.
$22.50
Example 4
Finding an Original Amount
Blender A store marks up the wholesale price of a blender by
125%. The retail price is $30. What is the wholesale price?
Solution
Let x represent the wholesale price.
Retail price Wholesale price p (100% Markup percent)
(
30 x p 100% 125%
)
Substitute.
30 x p 225%
Add percents.
30 x p 2.25
Write 225% as a decimal.
13.33 ≈ x
Divide each side by 2.25 .
Answer: The wholesale price of the blender is about $ 13.33 .
158
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7.7
Simple and Compound Interest
Goal: Calculate interest earned and account balances.
Vocabulary
Interest:
Principal:
Simple
interest:
Annual
interest rate:
Balance:
Compound
interest:
Simple Interest Formula
Simple interest I is given by the formula
I Prt
where P is the principal, r is the annual interest rate (written as a
decimal), and t is the time in years.
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Chapter 7 • Pre-Algebra Notetaking Guide
159
7.7
Simple and Compound Interest
Goal: Calculate interest earned and account balances.
Vocabulary
Interest:
Principal:
Interest is the amount earned or paid for the use of
money.
The amount of money deposited or borrowed is the
principal.
Simple Interest that is earned or paid only on the principal is
interest: called simple interest.
Annual
The percent of the principal earned or paid per
interest rate: year is the annual interest rate.
Balance:
The balance A of an account that earns simple annual
interest is the sum of the principal P and the interest
Prt. In symbols this means A P Prt, or A P(1 rt).
Compound interest is interest that is earned on both
Compound the principal and any interest that has been earned
interest:
previously.
Simple Interest Formula
Simple interest I is given by the formula
I Prt
where P is the principal, r is the annual interest rate (written as a
decimal), and t is the time in years.
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Chapter 7 • Pre-Algebra Notetaking Guide
159
Example 1
Finding Simple Interest
A $2000 bond earns 3% simple interest per year on its purchase
price. Find the interest earned after 5 years.
Solution
I Prt
Write simple interest formula.
Substitute.
Multiply.
Answer: The bond will earn $
Example 2
in interest after 5 years.
Finding an Interest Rate
You deposit $900 into an account that earns simple annual
interest. After 8 months, the balance is $913.20. Find the
annual interest rate.
Solution
Because t in the formula A P(1 rt) is the time in years,
8
12
2
3
write 8 months as , or year. Then solve for r after substituting
values for A, P, and t in A P(1 rt).
A P(1 rt)
1 r
r
r
Write formula for finding balance.
r
Substitute.
Distributive property
Subtract
Divide each side by
Answer: The annual interest rate is
160
Chapter 7 • Pre-Algebra Notetaking Guide
from each side.
.
%.
Copyright © Holt McDougal. All rights reserved.
Example 1
Finding Simple Interest
A $2000 bond earns 3% simple interest per year on its purchase
price. Find the interest earned after 5 years.
Solution
I Prt
Write simple interest formula.
2000(0.03)(5)
Substitute.
300
Multiply.
Answer: The bond will earn $ 300 in interest after 5 years.
Example 2
Finding an Interest Rate
You deposit $900 into an account that earns simple annual
interest. After 8 months, the balance is $913.20. Find the
annual interest rate.
Solution
Because t in the formula A P(1 rt) is the time in years,
8
12
2
3
write 8 months as , or year. Then solve for r after substituting
values for A, P, and t in A P(1 rt).
A P(1 rt)
913.2 900 1 r
Write formula for finding balance.
23 913.2 900 600 r
13.2 600 r
0.022 r
Substitute.
Distributive property
Subtract 900 from each side.
Divide each side by 600 .
Answer: The annual interest rate is 2.2 %.
160
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Checkpoint
1. A $1200 bond earns 5% simple interest per year on its purchase
price. Find the interest earned after 3 years.
Find the unknown quantity for an account that earns simple
annual interest.
2. A __
? , P $1300,
r 4%, t 4 years
3. A $1116.50, P $1100,
r 3%, t __
?
Compound Interest Formula
When an account earns interest compounded annually, the
balance A is given by the formula
A P(1 r)t
where P is the principal, r is the annual interest rate (written as a
decimal), and t is the time in years.
Example 3
Calculating Compound Interest
You deposit $1250 into an account that earns 2.25% interest
compounded annually. Find the balance after 4 years.
Solution
A P(1 r)t
≈
(1 Write formula.
)
Substitute.
Use a calculator.
Answer: The balance of the account after 4 years is about
$
.
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Chapter 7 • Pre-Algebra Notetaking Guide
161
Checkpoint
1. A $1200 bond earns 5% simple interest per year on its purchase
price. Find the interest earned after 3 years.
$180
Find the unknown quantity for an account that earns simple
annual interest.
2. A __
? , P $1300,
r 4%, t 4 years
3. A $1116.50, P $1100,
r 3%, t __
?
$1508
6 months
Compound Interest Formula
When an account earns interest compounded annually, the
balance A is given by the formula
A P(1 r)t
where P is the principal, r is the annual interest rate (written as a
decimal), and t is the time in years.
Example 3
Calculating Compound Interest
You deposit $1250 into an account that earns 2.25% interest
compounded annually. Find the balance after 4 years.
Solution
A P(1 r)t
(
1250 1 0.0225
≈ 1366.35
Write formula.
)
4
Substitute.
Use a calculator.
Answer: The balance of the account after 4 years is about
$ 1366.35 .
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Chapter 7 • Pre-Algebra Notetaking Guide
161
7
Words to Review
Give an example of the vocabulary word.
Percent
Percent of change
Percent of increase
Percent of decrease
Markup
Discount
Interest
Principal
Simple interest
Annual interest rate
Balance
Compound interest
Review your notes and Chapter 7 by using the Chapter Review on
pages 384–387 of your textbook.
162
Chapter 7 • Pre-Algebra Notetaking Guide
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7
Words to Review
Give an example of the vocabulary word.
Percent
25
25%
100
Percent of increase
The percent of change in a
quantity when the new
amount is greater than the
original amount
Markup
The increase from the
wholesale price of an item
to the retail price
Interest
For a $2000 bond that earns
3% simple interest per year
on its purchase price, 3% is
the interest.
Simple interest
For a $2000 bond that earns
3% simple interest per year
on its purchase price, 3% is
the simple interest.
Balance
After 4 years, a $1250 deposit
that earns 2.25% interest
compounded annually has a
balance of about $1366.35.
Percent of change
p% Amount of increase or decrease
Original amount
Percent of decrease
The percent of change in a
quantity when the new
amount is less than the
original amount
Discount
The decrease from the original
price of an item to the sale
price
Principal
For a $2000 bond that earns
3% simple interest per year
on its purchase price, $2000
is the principal.
Annual interest rate
For a $1250 deposit that earns
2.25% interest compounded
annually, 2.25% is the annual
interest rate.
Compound interest
Interest earned on both the
principal and any interest
earned previously
Review your notes and Chapter 7 by using the Chapter Review on
pages 384–387 of your textbook.
162
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