California math triumphs ratios, rates, and percents, volume 3b

Trang 1

Authors Basich Whitney • Brown • Dawson • Gonsalves • Silbey • Vielhaber

Trang 2

Photo Credits

Cover Peter Sterling/Getty Images; iv (tl bl br) File Photo, (tc tr) The McGraw-Hill

Companies, (cl c) Doug Martin, (cr) Aaron Haupt; v (1 2 3 4 6 7 8 9 11 12) The

McGraw-Hill Companies, (5 10 13 14) File Photo; vii Digital Vision/PunchStock;

viii CORBIS; ix Larry Brownstein/Getty Images; x CORBIS; 2–3 Michael A Keller/

CORBIS; 27 CORBIS; 36 Rachel Epstein/PhotoEdit; 44 Getty Images;

51 Stockdisc/SuperStock; 57 Darwin Wiggett/Getty Images; 58 David Buffington/

Getty Images; 60 Darren McCollester/Getty Images; 67 Brand X Pictures/

PunchStock; 76 Ryan McVay/Getty Images; 81 Getty Images

permitted under the United States Copyright Act, no part of this publication may be

reproduced or distributed in any form or by any means, or stored in a database or

retrieval system, without prior permission of the publisher.

Send all inquiries to:

Printed in the United States of America

California Math Triumphs Volume 3B

Trang 3

California Math Triumphs

Volume 1 Place Value and Basic Number Skills 1A Chapter 1 Counting

1A Chapter 2 Place Value

1A Chapter 3 Addition and Subtraction

2A Chapter 2 Equivalence of Fractions

2B Chapter 3 Operations with Fractions

2B Chapter 4 Positive and Negative Fractions and Decimals

Volume 3 Ratios, Rates, and Percents 3A Chapter 1 Ratios and Rates

3A Chapter 2 Percents, Fractions, and Decimals

3B Chapter 3 Using Percents

3B Chapter 4 Rates and Proportional Reasoning

Volume 4 The Core Processes of Mathematics 4A Chapter 1 Operations and Equality

4A Chapter 2 Math Fundamentals

4B Chapter 3 Math Expressions

4B Chapter 4 Linear Equations

4B Chapter 5 Inequalities

Volume 5 Functions and Equations 5A Chapter 1 Patterns and Relationships

5A Chapter 2 Graphing

5B Chapter 3 Proportional Relationships

5B Chapter 4 The Relationship Between

Graphs and Functions

Volume 6 Measurement 6A Chapter 1 How Measurements Are Made

6A Chapter 2 Length and Area in the Real World

Trang 4

Authors and Consultants

AUTHORS

Frances Basich Whitney

Project Director, Mathematics K–12

Santa Cruz County Offi ce of Education

Capitola, California

Kathleen M Brown

Math Curriculum Staff Developer Washington Middle School Long Beach, California

Dixie Dawson

Math Curriculum Leader Long Beach Unifi ed Long Beach, California

Dinah-Might Activities, Inc.

San Antonio, Texas

Trang 5

California Advisory Board

Carol Cronk

Mathematics Program Specialist

San Bernardino City Unifi ed

School District

San Bernardino, California

Audrey M Day

Classroom Teacher Rosa Parks Elementary School San Diego, California

Jill Fetters

Math Teacher Tevis Jr High School Bakersfi eld, California

Grant A Fraser, Ph.D.

Professor of Mathematics California State University, Los Angeles

Los Angeles, California

Eric Kimmel

Mathematics Department Chair

Frontier High School

Bakersfi eld, California

Donna M Kopenski, Ed.D.

Math Coordinator K–5 City Heights Educational Collaborative San Diego, California

Michael A Pease

Instructional Math Coach Aspire Public Schools Oakland, California

Chuck Podhorsky, Ph.D.

Math Director City Heights Educational Collaborative San Diego, California

Arthur K Wayman, Ph.D.

Professor Emeritus

California State University, Long

Beach

Long Beach, California

Frances Basich Whitney

Project Director, Mathematics K–12 Santa Cruz County Offi ce of Education

Capitola, CA

Mario Borrayo

Teacher Rosa Parks Elementary San Diego, California

Melissa Bray

K–8 Math Resource Teacher Modesto City Schools Modesto, California

CALIFORNIA ADVISORY BOARD

Glencoe wishes to thank the following professionals for their invaluable

feedback during the development of the program They reviewed

the table of contents, the prototype of the Student Study Guide, the

prototype of the Teacher Wraparound Edition, and the professional

Bonnie Awes

Teacher, 6th Grade Math Monroe Clark Middle School San Diego, California

Kathleen M Brown

Math Curriculum Staff Developer Washington Middle School Long Beach, California

Trang 6

California Reviewers

CALIFORNIA REVIEWERS

Each California Reviewer reviewed at least two chapters of the Student

Study Guides, providing feedback and suggestions for improving the

effectiveness of the mathematics instruction

Bobbi Anne Barnowsky

Monica S Patterson

Educator Aspire Public Schools Modesto, California

Rechelle Pearlman

4th Grade Teacher Wanda Hirsch Elementary School Tracy, California

Armida Picon

5th Grade Teacher Mineral King School Visalia, California

Anthony J Solina

Lead Educator Aspire Public Schools Stockton, California

Trang 7

Volume 3A Ratios, Rates, and Percents

6NS1.2 Interpret and use ratios

in different contexts (e.g., batting averages, miles per hour) to show the relative size of two quantities, using appropriate notations

(a/b, a to b, a:b).

6AF2.2 Demonstrate an

understanding that rate is a measure of

one quantity per unit value of another quantity.

probabilities as ratios, proportions, decimals between 0 and 1, and percentages between 0 and 100 and verify that the probabilities computed are

reasonable; know that if P is the probability

of an event, 1 - P is the probability of an event not occurring.

Chapters 1 and 2 are contained in Volume 3A Chapters 3 and 4 are contained in Volume 3B.

Chapter

1 Ratios and Rates

Joshua Tree National Park

in This Chapter

Trang 8

5SDAP1.3 Use fractions and percentages to compare data sets of different sizes.

6NS1.2 Interpret and use ratios

in different contexts (e.g., batting averages, miles per hour) to show the relative size of two quantities, using appropriate notations

(a/b, a to b, a:b).

Merced River near Yosemite National Park

Trang 9

Manhattan Beach Pier

Chapters 1 and 2 are contained in Volume 3A Chapters 3 and 4 are contained in Volume 3B.

6NS1.3 Use proportions to solve problems (e.g., determine the value of

7 = _N

21 , fi nd the length of a side of

a polygon simiular to a known polygon) Use cross-multiplication as a method for solving such problems, understanding it

as the multiplication of both sides of an equation by a multiplicative inverse.

6NS1.4 Calculate given percentages of quantities and solve problems involving discounts at sales, interest earned, and tips.

7NS1.6 Calculate the percentage of increases and decreases of a quantity

7NS1.7 Solve problems that involve discounts, markups, commissions, and profi t and compute simple and compound interest.

Trang 10

4-3 Solve Rate Problems 61

3AF2.1, 3AF2.2, 6AF2.3

4-4 Solve Problems Using Proportions 69

3AF1.4 Express simple unit conversions

in symbolic form (e.g., _ inches = _ feet × 12).

3AF2.1 Solve simple problems involving a functional relationship between two quantities (e.g., fi nd the total cost of multiple items given the cost per unit).

3AF2.2 Extend and recognize a linear pattern by its rules (e.g., the number of legs on a given number of horses may

be calculated by counting by 4s or by multiplying the number of horses by 4).

3MG1.4 Carry out simple unit conversions within a system of measurement (e.g., centimeters and meters, hours and minutes).

6NS1.3 Use proportions to solve problems (e.g., determine the value of

7 = _21N , fi nd the length of a side of

a polygon simiular to a known polygon)

Use cross-multiplication as a method for solving such problems, understanding it

as the multiplication of both sides of an equation by a multiplicative inverse.

6AF2.1 Convert one unit of measurement to another (e.g., from feet to miles, from centimeters to inches).

6AF2.3 Solve problems involving rates, average speed, distance, and time.

7AF4.2 Solve multistep problems involving rate, average speed, distance, and time or a direct variation.

Reconstructed house in a restored Hoopa

Valley Tribe village, Humboldt County

Trang 11

HUNT

SCAVENGER

HUNT

Let’s Get Started

Use the Scavenger Hunt below to learn where things are

located in each chapter

1 What is the title of Chapter 4?

Rates and Proportional Reasoning

2 What is the Key Concept of Lesson 4-4?

Solve Problems Using Proportions

3 In Example 1 on page 12, how much did Theresa’s

coat cost? $42

4 What are the vocabulary words for Lesson 4-3?

unit cost, unit rate, proportion

5 How many Examples are presented in Lesson 3-4? 3

6 What are the California Standards covered in Lesson 4-3?

3AF2.1, 3AF2.2, 6AF2.3

7 From Lesson 3-3, write the formula for simple interest I = prt

8 How many problems are in the Standard Practice on

pages 82–83? 12

9 On what pages will you find the Study Guide for Chapter 3?

pages 37–39

10 In Chapter 3, find the logo and Internet address that tells

you where you can take the Online Readiness Quiz It is

found on page 3 The URL is ca.mathtriumphs.com

Trang 13

STEP 1 Quiz Are you ready for Chapter 3? Take the Online Readiness

Quiz at ca.mathtriumphs.com to find out

STEP 2 Preview Get ready for Chapter 3 Review these skills and compare

them with what you’ll learn in this chapter

You know how fractions, decimals, and percents are related

is called interest To calculate simple

interest, follow this formula:

Trang 14

The word percent means

hundredths or out of 100

(Lesson 2-1, p 34)

ratio

a comparison of two numbers by division Example: The ratio of 2 to

3 can be stated as 2 out

KEY Concept

Calculate Percents

Percents can be less than 1% or more than 100% A percent

that is less than 1% is written as a fraction or decimal A

percent more than 100% is expressed with a number greater

than 100

Use the equation below to solve percent problems Express

the percent as a decimal or a fraction before you multiply

1 Write the percent equation

2 Substitute the given numbers and a variable (unknown

number) into the equation Write 15% as a decimal

3 Solve for the variable

4 Check your answer

compute a given percent of a whole number.

of quantities and solve problems involving discounts at sales, interest

earned, and tips.

Trang 15

Example 2

What is 35% of 1,050?

2 Substitute the known numbers and variable into

the equation

4 Check your answer

2 Substitute the known numbers and

variable into the equation

4 Check your answer

2 Substitute the known numbers and

variable into the equation

4 Check your answer

Trang 16

Example 3

What percent of 500 is 125?

2 Substitute the given numbers and a variable into

the equation

4 Change the decimal to a percent by multiplying by 100

5 Check your answer

2 Substitute the given numbers and

a variable into the equation

4 Change the decimal to a percent by

Trang 17

Guided Practice

Write each percent as a decimal

Remember that to write a percent as a decimal, you divide by 100.

Step 1 Write the percent equation

percent · whole = partStep 2 Substitute the given numbers and a variable into

Step 4 Change the decimal to a percent by multiplying by 100 0.2%

Step 5 Check your answer

5IJTNFBOTNPWF UIFEFDJNBMQPJOUUP UIFSJHIUUXPQMBDFT

Step by Step Practice

Solve using the percent equation Check each answer

6 What is 140% of 60?

Check: 1.4 · 60 = 84

7 20% of what number is 55? 275 8 40% of what number is 130? 325

percent · whole = part

Trang 18

Solve using the percent equation Check each answer.

9 What is 175% of 28? 49 10 What is 45% of 80? 36

11 What percent of 3,000 is 12? 0.4% 12 What percent of 8,000 is 16? 0.2%

Solve.

13 ASTRONOMY On Mars an object weighs 38% as much as

it weighs on Earth How much would a person who

weighs 150 pounds on Earth weigh on Mars?

Understand Read the problem Write what you know

On Mars something weighs 38% of what it does on Earth

Plan Pick a strategy One strategy is to solve a simpler

problem

Divide 38% into percents that are easier to compute

38% = 30% + 5% + 3%

Solve 30%: What is 10% of 150 pounds? 15 pounds

Multiply this by 3 because 30 = 10 · 3 45

So, 30% of 150 is 45

5%: 10% of 150 is 15 Divide the amount of 10% in half to find 5%

So, 5% of 150 is 1

2 · 15 , or 7.5 .3%: What is 1% of 150 pounds? 1.5 pounds

Multiply this by 3 4.5

So, 3% of 150 is 3 · 1.5 , or 4.5 .38%: Add the smaller percents to find 38% of 150 pounds.

Step by Step Problem-Solving Practice Problem-Solving Strategies

Use a table.

Look for a pattern.

Guess and check.

✓ Solve a simpler problem.

Act it out.

Trang 19

14 TENNIS In the city of Bridgeport, 75% of the parks have tennis

courts If 18 parks have tennis courts, how many parks does

Bridgeport have altogether? 24 parks

Check off each step

✔ Understand

✔ Plan

✔ Solve

✔ Check

15 SCHOOL There are 175 students in seventh grade at Silverado

Middle School A survey shows that 84% of them plan to volunteer

during the summer How many students plan to volunteer?

147 students

16 Write the percent equation in three different ways:

1 when n is the part

2 when n is the whole

3 when n is the percent.

Explain when to use each form

See TWE margin

Skills, Concepts, and Problem Solving

Write each percent as a decimal.

17 33% 0.33 18 3

Solve using the percent equation Check each answer

20 2% of what number is 5? 250 21 6% of what number is 21? 350

22 What is 110% of 60? 66 23 What is 175% of 28? 49

24 What is 250% of 40? 100 25 What is 120% of 55? 66

Trang 20

Solve.

28 CHESS The chess club has 60 members Twenty-four of the

members are younger than 20 years old What percent of the total

number of members are younger than 20?

40%

29 EATING OUT Trevor and Marina’s restaurant bill came to $36

They plan to leave a 20% tip How much should they leave?

$7.20

30 SPORTS In a recent season, the Los Angeles Angels won 95

games and lost 67 games What percent of games played did the

Angels win? Round to the nearest tenth if necessary

58.6%

Vocabulary Check Write the vocabulary word that completes each

sentence.

31 A(n) ratio is a comparison of two quantities by division

32 A ratio that compares a number to 100 is a(n) percent

33 Writing in Math Write out how you would calculate a 15% tip

Answers may vary First calculate 10% Then calculate 5% Finally, add the

two values together.

Spiral Review

The letters of the words United States are placed in a bag Find the

following probabilities (Lesson 1-3, p 19)

34 Pulling out the letter t 1 _ 6 , or 17%

35 Pulling out a vowel 5 _ 12 , or 42%

36 Not pulling out the letter e 5 _ 6 , or 83%

Solve (Lesson 1-2, p 11; Lesson 2-1, p 34)

37 FASHION Ruby can get three hats for a total cost of $45 At that

rate, how much would five hats cost? $75

Trang 21

The word percent means hundredths or out of 100

(Lesson 2-1, p 34)

ratio

a comparison of two numbers by division

of the other ratio

KEY Concept

Solve Percent Problems

A proportion is an equation stating that two ratios are equal

In a proportion, a cross product is the product of the

numerator of one ratio and the denominator of the other ratio

Finding both cross products is called cross multiplying

In this proportion, a common

denominator of the two fractions _ 2.4

On the left side, you can cancel the 4s

On the right side, you can cancel the 5s 5 · 2.4 = 3 · 4

Notice that 5 · 2.4 and 3 · 4 are the same as the two cross

products of the original proportion This demonstrates how

cross products of a proportion are equal

Cross multiply to find the unknown value in a proportion

percent × whole = part

The percent is always the ratio of

This is a proportion because two ratios are equal The percent

is one ratio, and the part-to-whole is the other ratio.

solve problems Use multiplication as a method for solving such problems, understanding

cross-it as the multiplication of both sides

of an equation by a multiplicative inverse

of quantities and solve problems involving discounts at sales, interest

earned, and tips

discounts, markups, commissions, and

profit and compute simple and

compound interest

Trang 22

Example 1

Theresa bought a coat that cost $42 She

paid 6% sales tax How much did she pay

in tax?

1 Write the percent proportion

_ percent

100 = _ wholepart

2 Substitute what you know into the

proportion Let x = the amount of the tax.

tax

rate

amount of taxprice of coat

1 Write the percent proportion

_ percent

100 = _ wholepart :PVDPVMEBMTPVTF

UIFQFSDFOUFRVBUJPO

2 Substitute the known numbers into the

proportion Let x = the tip amount

Tyler earns a 5% commission on sales of computer games

Last week he earned $25 in commission How much did Tyler

sell last week?

1 Write the percent equation percent · whole= part

You could also use a percent proportion.

2 The part is the amount earned in commission

The whole is the amount of sales

Substitute the known numbers into the equation 0.05 · n= 25

Let n = the amount of sales _ 0.05n

0.05 = _ 0.0525

3 Solve for Tyler’s amount of sales n = 500

Percents are used in discounts, tips, taxes, commissions, and

circle graphs

Trang 23

YOUR TURN!

Mrs Halen earns 3.5% on sales of furniture Last week she earned $630 in commission How much did Mrs Halen sell last week?

1 Write the percent equation percent · whole= part

2 The part is the amount earned in commission

The whole is the amount of sales

Substitute the known numbers into the equation

A skateboard that normally sells for $129 is on sale for $90.30

What is the percent of the discount?

1 Find the amount of the discount $129 - $90.30 = $38.70

2 Use the percent equation to find the percent of discount

The percent of discount is about 30%

A shirt that normally sells for $18.99 is on sale for $15.19.

What is the percent of the discount?

1 Find the amount of the discount

The percent of discount is about 20%

Trang 24

7 TAXES Danielle had to pay an 11% “dine in” tax If Danielle’s

food order came to $6.29, how much additional did she have to

pay in tax?

$0.69

8 TIPPING Tom’s lunch is $6.83 If Tom wants to leave an 18% tip,

how much tip should Tom leave?

$1.23

9 TIPPING The Evans family’s dinner is $42.23 If Mrs Evans wants

to leave a 20% tip, how much tip should she leave?

$8.45

Trang 25

10 Find the amount of commission on $315 sales if the

Substitute the values that you know

Let n = the amount of commission

6

_

100 = n _ 315 Step 3 Cross multiply and solve

6 · 315 = 100 · n 1,890 = 100n 18.90 = n

Step 4 The amount of commission is $ 18.90

Step by Step Practice

Find the amount of commission on each sales amount at the rate

given Round to the nearest cent.

Trang 26

Solve using the percent equation or proportion.

17 TAXES What is the sales tax on an $899 television if the tax rate is

6.5%? $58.44

18 TAXES What is the sales tax of a $14.99 book if the tax rate

is 5.75%? $0.86

19 TIPPING Pearl wants to tip 15% of the restaurant bill If

her bill came to $14.67, how much should she leave as a tip?

$2.20

20 TIPPING John wants to tip 18% of the restaurant bill If his bill

came to $22.34, how much should he leave as a tip? $4.02

21 DISCOUNT A pair of jeans that normally sells for $59.99 is on sale

for $44.99 What is the percent of discount? 25%

22 DISCOUNT A video game that normally sells for $54.99 is on sale

for $46.74 What is the percent of discount? 15%

Solve

23 COMPUTERS Andrea ordered a computer online The

computer cost $1,000 plus 7% sales tax What was the

total amount Andrea paid for her computer?

Understand Read the problem Write what you know

The computer cost $1,000 The sales tax rate is 7% Plan Pick a strategy One strategy is to solve a simpler

Andrea paid a total amount of $1,070

Check Does the answer seem reasonable? Is your answer

about 10% greater than the cost of the computer?

Step by Step Problem-Solving Practice

5IF-FH FOETP G$BTUM FT

Guess and check.

✓ Solve a simpler problem.

Trang 27

24 MOVIES A video store is having a sale DVDs are on sale for 20%

off During this sale, what is the cost of 3 DVDs that regularly cost

$20 each? $48 Check off each step

✔ Understand

✔ Plan

✔ Solve

✔ Check

25 CELL PHONES Justin is buying a cell phone that has a regular

price of $150 The cell phone is on sale for 15% off the regular price

What will be the sale price? $127.50

26 Explain the difference between solving a problem about

10% off a price and paying 10% sales tax on an item

You calculate the 10% of the price in about the same way for both problems

For the 10%-off problem, you subtract from the price For the sales-tax

problem, you add to the price.

Find the amount of commission on each sales amount at the rate

given Round to the nearest cent.

27 $2,018 at 8% $161.44

28 $388 at 5.75% $22.31

29 $16,500 at 11% $1,815

30 $538 at 4.5% $24.21

Trang 28

Use the percent equation or a proportion to solve.

31 TESTS On the written portion of her driving test, Nadina

answered 84% of the questions correctly If Nadina answered 42

questions correctly, how many questions were on the driving test?

50

32 TAXES A property tax of 2% of a home’s value is billed to

residents of the city each year How much property tax would the

owner of a $115,000 home owe?

$2,300

33 COMMISSION Mr Faccinto earns 3% on sales of cars Last week

he earned $870 in commission How much did Mr Faccinto sell

last week?

$29,000

34 DISCOUNT Marcus is buying a DVD that normally sells for $18.99

If the DVD is on sale for 20% off, how much will Marcus pay for

the DVD?

$15.19

Use the receipt at the right for Exercises 35–37

35 TIPPING Find the total cost of Leanne’s bill with a 7.5% tax

$11.58

36 TIPPING Leanne wants to tip 18% of the restaurant bill before tax

How much would she leave as a tip?

$1.94

37 TIPPING Suppose Leanne pays with a $20 bill How much change

should there be after tax and tip are included?

%BUF

5BY 5PUBM 5IBOL:PVo1MFBTF$PNF"HBJO

%BUF

5BY 5PUBM 5IBOL:PVo1MFBTF$PNF"HBJO 5BCMF 4FSWFS $MBJN

Trang 29

43 FASHION In Mae’s class, 6 of the students wear earrings If there

are 24 students in her class, what percent do not wear earrings?

Trang 30

Chapter

3 Progress Check 1 (Lessons 3-1 and 3-2)

Solve using the percent equation 5NS1.2

1 13% of what number is 52? 400 2 What is 12.5% of 88? 11

3 What is 31.5% of 200? 63 4 What percent of 200 is 86? 43%

Solve using the percent proportion 6NS1.3

5 3 is what percent of 10? 30% 6 What is 65% of 120? 78

7 81 is 54% of what number? 150 8 What is 44% of 55? 24.2

Solve 5NS1.2, 5SDAP1.3, 6NS1.3, 6NS1.4, 7NS1.7

9 MOVIES Fourteen of the students in Rosa’s class prefer animated

movies above all other types of movies The rest of the students

like action or mystery movies better If there are 25 students in

Rosa’s class, what percent do not prefer animated movies?

44%

10 MONEY Reina earns 7% commission on her sales each day The

table shows her sales for last week Fill in the table to show the

amount of commission Reina earned each day How much total

commission did Reina earn last week?

Trang 31

principal

the amount of money deposited or invested

compound interest

when interest is earned

on both the principal and any interest already in an account

KEY Concept

Interest Problems

When you have a savings account, the bank pays you money

This money is called interest The amount of money that you

save is called the principal When you invest money, you

receive interest When you borrow money, you pay interest

A common form of borrowing money is a loan.

The formula I = p × r × t is used to find simple interest

Write the interest rate as a decimal Drop the % sign and

move the decimal to the left two places Time must be

expressed in years If the time is part of a year, write it as

a decimal or fraction

When interest is paid on both the principal and on any

interest already in the account, it is called compound interest

Write the interest rate as a decimal

In the simple interest formula, you have to add the principal to

the amount of interest earned to find the amount in the account In the

compound interest formula, you have to subtract the principal to find

the amount of the interest earned

per-centages of quantities and solve problems involving discounts at

sales, interest earned, and tips

discounts, markups, commissions, and

profit and compute simple and

compound interest.

Trang 32

Example 1

Find the simple interest earned on an

investment of $600 at 8.5% for 6 months

1 Write the simple interest formula I = prt

2 Write the decimal for 8.5% 0.085

The time is not given in years

Find the value of an investment of $2,500

for 1 year at 6% interest compounded

quarterly Round to the nearest cent.

1 Write the compound interest formula

3 Substitute the principal, rate, number of

times per year and number of years into

to help you Round to the nearest cent.

A = 3,600 ⎛ ⎪

⎝1 + 0.07 _ 4 ⎞ ⎥

⎠ 4(2)

= 3,600(1 + 0.0175)4(2)

= 3,600(1.0175)4(2)

= 3,600(1.0175)8

= 4,135.97

Trang 33

Example 3

Charliqua borrowed $1,500 from her bank

The loan was for 5 years The bank charged

8% interest compounded monthly How

much money will Charliqua have paid back

at the end of the loan? Use a calculator or

spreadsheet to help you Round to the

To find the interest in a compounded formula, you need to subtract the principal.

YOUR TURN!

Royale borrowed $3,000 from his bank His loan was for 10 years The bank charged 6% compounded monthly How much money will Royale have paid back at the end of the loan? Use a calculator or spreadsheet to help you Round to the nearest cent.

Trang 34

5 Find the value of an investment of $1,000 for 5 years at 8% interest

compounded semiannually Use a spreadsheet or calculator to help

you Round the answer to the nearest cent

Step 1 Write the compound interest formula A = P(1 + r _ n )nt

Step 2 How many times is interest paid per year? n = 2

How many years is the investment? t = 5

Step 3 Substitute the values that you know A = 1,000(1 + 0.08 _ 2 )2(5)

Semiannually means two times a year.

Step by Step Practice

Trang 35

Find the value of each investment using the compound interest formula

Use a spreadsheet or calculator to help you Round each answer to

the nearest cent.

6 $2,000 invested for 6 years at 12% interest compounded quarterly

= $ 4,065.59

7 $10,000 invested for 10 years at 9% interest compounded annually

$23,673.64

Solve

8 MONEY Deepak put $1,000 into a savings account The

simple interest rate is 3.5% How much interest will

Deepak earn in 1 month? in 6 months? in 12 months?

Understand Read the problem Write what you know

Deepak invests $1,000 at an interest rate of 3.5% .

Plan Pick a strategy One strategy is

to solve a simpler problem

Use the simple interest formula

to find the interest earned foreach time period

Solve Use the simple interest formula

to calculate the interest for

1 month, 6 months, and 1 year

1 month I = 1,000 · 0.035 · 1 _ 12 = $2.92

6 months I = 1,000 · 0.035 · 1 _ 2 = $17.50

12 months I = 1,000 · 0.035 · 1 = $35Check The amount of interest should increase as the

number of months increases

Make a table to help you write the time as a ratio in simplest form.

Ratio of number of months to 12 months

1_

12 6 _ 12 12 _ 12 Ratio in simplest

1_

12 6 _ 12 12 _ 12 Ratio in simplest

1_

12 1 _ 2 1

Step by Step Problem-Solving Practice

Quarterly means four times a year.

Problem-Solving Strategies

Use a table.

Look for a pattern.

Guess and check.

✓ Solve a simpler problem Work backward.

Trang 36

9 FINANCE How much interest will Hannah earn in 4 years if she

deposits $630 in a savings account at 6.5% simple interest?

10 FINANCE Kelly’s inheritance was $220,000 after taxes The money

is invested in an account that earns $9,900 in simple interest every

year What is the interest rate on her account?

4.5%

11 Write the formulas for simple interest and compound

interest Explain what each variable stands for

See TWE margin.

Find the amount of simple interest earned to the nearest cent

Trang 37

Find the value of each investment using the compound interest

formula Use a calculator or spreadsheet to help you Round each

answer to the nearest cent

18 $500 invested for 1 year at 5% interest compounded semiannually

21 LOANS Refer to the photo caption at the right The interest

rate on the loan was 8% compounded monthly How much

interest did Pul’s father pay if he took 2 years to repay the loan?

Remember to subtract the principal to find interest

$207.47

22 BUSINESS Raj invested $900 for 4 years at an interest rate

of 8% How much interest did he earn?

$288.00

23 FINANCE In 2002, a $5 bank note from 1886 was sold to a

collector for $103,500 Suppose a person had deposited the $5

in a bank in 1886 with an interest rate of 4% compounded quarterly

After 116 years, how much money would be in the account?

$505.93

LOANS Pul’s father borrowed $1,200 from the bank for a riding lawn mower

Trang 38

sentence.

24 The amount of money deposited or invested is the

principal

25 When interest is earned on both the principal and any interest

already in the account, it is called compound interest .

26 Writing in Math Another form of borrowing is to use credit cards

Consider the following two credit cards One has a compound

interest rate of 18% that is compounded annually The other has a

compound interest rate of 21% that is compounded quarterly

Which interest rate is better? Explain (If $1,000 is charged onto

each card and no payments are made, what will the balance be in

31 SCHOOL Out of 459 students at Breckinridge Junior High, only

30% take the bus to school How many students take the bus?

138 students

32 FASHION Becky tipped her hair stylist 15% for a haircut If the tip

was $6.30, how much was the haircut?

$42

Trang 39

The word percent means

hundredths or out of 100

(Lesson 2-1, p 34)

ratio

a comparison of two numbers by division Example: The ratio of 2 to

3 can be stated as 2 out

of 3, 2 to 3, 2:3, or 2/3

(Lesson 1-1, p 4)

KEY Concept

Percent of Change

A percent of change is a ratio that compares the change in an

amount to the original amount

When the change is positive, it is a percent of increase

When the change is negative, it is a percent of decrease

Convert your decimal answer to a percent If it is positive,

label it “percent of increase.” If it is negative, drop the

negative sign and label it “percent of decrease.”

Example 1

Find the percent of change

At 1 year old, a tree was 3 feet tall At

7 years old, the same tree was 7.5 feet

tall What is the percent of change in

the tree’s height?

1 The original amount is 3

The new amount is 7.5

2 Substitute the values in the formula

new

original amount original amount =

At 4 years old, Yonnie was 40 inches tall At

12 years old, she was 54 inches tall What is the percent of change in her height?

1 The original amount is 40 The new amount is 54 .

discounts, markups, commissions, and profit and compute simple and

compound interest

Trang 40

Example 2

Find the percent of change.

A car that was worth $10,500 in 2004 is now

worth $9,030 What is the percent of change

in the car’s worth?

1 The original amount is $10,500

The new amount is $9,030

Kieran’s winter coat was originally priced

$135 He bought the coat on clearance and paid $74.25 What is the percent of change in the price Kieran paid?

1 The original amount was $135 The new amount is $74.25

Warren got a score of 60 on his science exam He was able to

retake the test and scored a 63.5 Find the percent of change in

the test scores Round to the nearest whole percent.

1 The original amount is 60

The new amount is 63.5

new

original amount original amount =

Định dạng
Số trang	95
Dung lượng	8,26 MB