- •Study Skills Workshop
- •1.1 An Introduction to the Whole Numbers
- •1.2 Adding Whole Numbers
- •1.3 Subtracting Whole Numbers
- •1.4 Multiplying Whole Numbers
- •1.5 Dividing Whole Numbers
- •1.6 Problem Solving
- •1.7 Prime Factors and Exponents
- •1.8 The Least Common Multiple and the Greatest Common Factor
- •1.9 Order of Operations
- •THINK IT THROUGH Education Pays
- •2.1 An Introduction to the Integers
- •THINK IT THROUGH Credit Card Debt
- •2.2 Adding Integers
- •THINK IT THROUGH Cash Flow
- •2.3 Subtracting Integers
- •2.4 Multiplying Integers
- •2.5 Dividing Integers
- •2.6 Order of Operations and Estimation
- •Cumulative Review
- •3.1 An Introduction to Fractions
- •3.2 Multiplying Fractions
- •3.3 Dividing Fractions
- •3.4 Adding and Subtracting Fractions
- •THINK IT THROUGH Budgets
- •3.5 Multiplying and Dividing Mixed Numbers
- •3.6 Adding and Subtracting Mixed Numbers
- •THINK IT THROUGH
- •3.7 Order of Operations and Complex Fractions
- •Cumulative Review
- •4.1 An Introduction to Decimals
- •4.2 Adding and Subtracting Decimals
- •4.3 Multiplying Decimals
- •THINK IT THROUGH Overtime
- •4.4 Dividing Decimals
- •THINK IT THROUGH GPA
- •4.5 Fractions and Decimals
- •4.6 Square Roots
- •Cumulative Review
- •5.1 Ratios
- •5.2 Proportions
- •5.3 American Units of Measurement
- •5.4 Metric Units of Measurement
- •5.5 Converting between American and Metric Units
- •Cumulative Review
- •6.2 Solving Percent Problems Using Percent Equations and Proportions
- •6.3 Applications of Percent
- •6.4 Estimation with Percent
- •6.5 Interest
- •Cumulative Review
- •7.1 Reading Graphs and Tables
- •THINK IT THROUGH The Value of an Education
- •Cumulative Review
- •8.1 The Language of Algebra
- •8.2 Simplifying Algebraic Expressions
- •8.3 Solving Equations Using Properties of Equality
- •8.4 More about Solving Equations
- •8.5 Using Equations to Solve Application Problems
- •8.6 Multiplication Rules for Exponents
- •Cumulative Review
- •9.1 Basic Geometric Figures; Angles
- •9.2 Parallel and Perpendicular Lines
- •9.3 Triangles
- •9.4 The Pythagorean Theorem
- •9.5 Congruent Triangles and Similar Triangles
- •9.6 Quadrilaterals and Other Polygons
- •9.7 Perimeters and Areas of Polygons
- •THINK IT THROUGH Dorm Rooms
- •9.8 Circles
- •9.9 Volume
- •Cumulative Review
66.1 t 5(t 2) 10
67.30x 12 1,338
68.40y 19 1,381
69.7 37 r 14
70.21 25 f 19
71.10 2y 8
72.7 7x 21
73.9 5(r 3) 6 3(r 2)
74.2 3 (n 6) 4(n 2) 21
2
75. 3 z 4 8
7
76. 5 x 9 5
77. 2(9 3s) (5s 2) 25
78. 4(x 5) 3(12 x) 7
79. 9a 2.4 7a 4.6
80. 4c 1.6 7c 3.2
8.5 Using Equations to Solve Application Problems |
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WRITING
81.To solve 3x 4 5x 1, one student began by subtracting 3x from both sides. Another student solved the same equation by first subtracting 5x from both sides. Will the students get the same solution? Explain why or why not.
82.Explain the error in the following solution.
Solve: |
2x 4 30 |
22x 4 302
x 4 15
x 4 4 15 4 x 11
REVIEW
Name the property that is used.
83.x 9 9x
84.x 99 99 x
85.(x 1) 2 x (1 2)
86.2(30y) (2 30)y
S E C T I O N 8.5
Using Equations to Solve Application Problems
Throughout this course, we have used the steps Analyze, Form, Solve, State, and Check as a strategy to solve application problems. Now that you have had an introduction to algebra, we can modify that strategy and make use of your newly learned skills.
1 Solve application problems to find one unknown.
To become a good problem solver, you need a plan to follow, such as the following fivestep strategy.You will notice that the steps are quite similar to the strategy first introduced in Chapter 1. However, this new approach uses the concept of variable, the translation skills from Section 8.1, and the equation solving methods of Sections 8.3 and 8.4.
Strategy for Problem Solving
1.Analyze the problem by reading it carefully to understand the given facts. What information is given? What are you asked to find? What vocabulary is given? Often, a diagram or table will help you visualize the facts of the problem.
2.Form an equation by picking a variable to represent the numerical value to be found. Then express all other unknown quantities as expressions involving that variable. Key words or phrases can be helpful. Finally, translate the words of the problem into an equation.
3.Solve the equation.
4.State the conclusion clearly. Be sure to include the units (such as feet, seconds, or pounds) in your answer.
5.Check the result using the original wording of the problem, not the equation that was formed in step 2 from the words.
Objectives
1Solve application problems to find one unknown.
2Solve application problems to find two unknowns.
676 |
Chapter 8 An Introduction to Algebra |
Self Check 1
APARTMENT BUILDINGS Owners of a newly constructed apartment building would have to sell 34 more units before all of the 510 units were sold. How many of the apartment units have been sold to date?
Now Try Problem 19
Systems Analysis A
company’s telephone use would have to increase by 350 calls per hour before the system would reach the maximum capacity of 1,500 calls per hour. Currently, how many calls are being made each hour on the system?
Analyze
• If the number of calls increases by |
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Find |
Caution! Unlike an arithmetic approach, you do not have to determine whether to add, subtract, multiply, or divide at this stage. Simply translate the words of the problem to mathematical symbols to form an equation that describes the situation. Then solve the equation.
© iStockphoto.com/Neustockimages
Form
Let n the number of calls currently being made each hour. To form an equation involving n, we look for a key word or phrase in the problem.
Key phrase: increase by 350 |
Translation: addition |
The key phrase tells us to add 350 to the current number of calls to obtain an expression for the maximum capacity of the system. Now we translate the words of the problem into an equation.
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n 350 1,500 |
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n 350 350 1,500 350 |
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State
Currently, 1,150 calls per hour are being made.
Check
If the number of calls currently being made each hour is 1,150, and we increase that number by 350, we should obtain the maximum capacity of the system.
1,150350
1,500 This is the maximum capacity.
The result, 1,150, checks.
Caution! Always check the result in the original wording of the problem, not by substituting it into the equation. Why? The equation may have been solved correctly, but the danger is that you may have formed it incorrectly.
Small Businesses Last
year, a stylist lost 17 customers who moved away. If she now has 73 customers, how many did she have originally?
Analyze
• She lost 17 customers. Given
8.5 Using Equations to Solve Application Problems |
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Self Check 2 |
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GASOLINE STORAGE A tank |
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currently contains 1,325 gallons |
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of gasoline. If 450 gallons were |
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•She now has 73 customers. Given
•How many customers did she originally have? Find
Form
We can let c the original number of customers. To form an equation involving c, we look for a key word or phrase in the problem.
Key phrase: moved away |
Translation: subtraction |
Now we translate the words of the problem into an equation.
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the number of |
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of customers |
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c 17 73 |
We need to isolate c on the left side. |
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c 17 17 73 17 |
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subtraction of 17. |
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Do the addition. |
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State
She originally had 90 customers.
Check
If the hair stylist originally had 90 customers, and we decrease that number by the 17 that moved away, we should obtain the number of customers she has now.
8 10
90
17
73 This is the number of customers the hair stylist now has.
The result, 90, checks.
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EXAMPLE 3 |
Traffic Fines For speeding |
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in a construction zone, a motorist had to pay a fine of |
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$592. The violation occurred on a highway posted |
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with signs like the one shown on the right.What would |
CONSTRUCTION ZONE |
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the fine have been if such signs were not posted? |
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Find |
Form
We can let f the amount that the fine would normally have been. To form an equation, we look for a key word or phrase in the problem or analysis.
Key word: double Translation: multiply by 2
Now Try Problem 20
Self Check 3
SPEED READING A speed reading course claims it can teach a person to read four times faster. After taking the course, a student can now read 700 words per minute. If the company’s claims are true, what was the student’s reading rate before taking the course?
Now Try Problem 21
678 |
Chapter 8 An Introduction to Algebra |
Now we translate the words of the problem into an equation.
Self Check 4
CLASSICAL MUSIC A woodwind quartet was hired to play at an art exhibit. If each member made $85 for the performance, what fee did the quartet charge?
Now Try Problem 22
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speeding fine |
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2f 592 |
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If the normal fine was $296, and we double it, we should get the new fine.
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296
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592 This is the new fine.
The result, $296, checks.
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EXAMPLE 4 |
Entertainment Costs A five-piece band worked on |
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New Year’s Eve. If each player earned $120, what fee did the band charge? |
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Analyze |
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Given |
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• What fee did the band charge? |
Find |
Form
We can let f the band’s fee. To form an equation, we look for a key word or phrase. In this case, we find it in the analysis of the problem. If each player earned the same amount ($120), the band’s fee must have been divided into 5 equal parts.
Key phrase: divided into 5 equal parts |
Translation: division |
Now we translate the words of the problem into an equation.
The |
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share. |
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120 |
Solve
f
5 120
f
5 5 5 120
f 600
State
We need to isolate f on the left side.
To isolate f, multiply both sides by 5 to undo the |
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division by 5. |
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Do the multiplication. |
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The band’s fee was $600.
679
Check
If the band’s fee was $600, and we divide it into 5 equal parts, we should get the amount that each player earned.
120
5 600 This is the amount each band member earned.
5
1010
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How many more 3-hour shifts must she work? |
Find |
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Form
Let x the number of shifts needed to complete the service requirement. Since each shift is 3 hours long, multiplying 3 by the number of shifts will give the number of additional hours the student needs to volunteer.
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135 87 |
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Check
The student has already completed 87 hours. If she works 16 more shifts, each 3 hours long, she will have 16 3 48 more hours. Adding the two sets of hours, we get:
8748
135 This is the total number of hours needed.
The result, 16, checks.
Self Check 5
SERVICE CLUBS To become a member of a service club, students at one college must complete 72 hours of volunteer service by working 4-hour shifts at the tutoring center. If a student has already volunteered 48 hours, how many more 4- hour shifts must she work to meet the service requirement for membership in the club?
Now Try Problem 23
680 |
Chapter 8 An Introduction to Algebra |
Self Check 6
YARD SALES A husband and wife split the money equally that they made on a yard sale. The husband gave $75 of his share to charity, leaving him with $210. How much money did the couple make at their yard sale?
Now Try Problem 24
In return for her services, an attorney and her client split the jury’s cash award equally. After paying her assistant $1,000, the attorney ended up making $10,000 from the case. What was the amount of the award?
Analyze
• The attorney and client split the award equally. |
Given |
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• The attorney’s assistant was paid $1,000. |
Given |
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The attorney made $10,000. |
Given |
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What was the amount of the award? |
Find |
Form
Let x the amount of the award. Two key phrases in the problem help us form an equation.
Key phrase: |
split the award equally |
Translation: |
divide by 2 |
Key phrase: |
paying her assistant $1,000 |
Translation: |
subtract $1,000 |
Now we translate the words of the problem into an equation.
The award |
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Solve
x
2 1,000 10,000
x2 1,000 1,000 10,000 1,000
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2 11,000
2 x2 2 11,000
x 22,000
We need to isolate x on the left side.
To isolate the variable term 2x , add 1,000 to both sides to undo the subtraction of 1,000.
Do the addition. |
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multiply both sides by 2 |
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to undo the division by 2. |
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Do the multiplication.
State
The amount of the award was $22,000.
Check
If the award of $22,000 is split in half, the attorney’s share is $11,000. If $1,000 is paid to her assistant, we subtract to get:
$11,0001,000
$10,000 This is what the attorney made.
The result, $22,000, checks.
2 Solve application problems to find two unknowns.
When solving application problems, we usually let the variable stand for the quantity we are asked to find. In the next two examples, each problem contains a second unknown quantity. We will look for a key word or phrase in the problem to help us describe it using an algebraic expression.
8.5 Using Equations to Solve Application Problems |
681 |
Civil Service A candidate for a position with the FBI scored 12 points higher on the written part of the civil service exam than she did on her interview. If her combined score was 92, what were her scores on the interview and on the written part of the exam?
Analyze
• She scored 12 points higher on the written part than on the |
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interview. |
Given |
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Her combined score was 92. |
Given |
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What were her scores on the interview and on the written part? |
Find |
Form
Since we are told that her score on the written part was related to her score on the interview, we let x her score on the interview.
There is a second unknown quantity—her score on the written part of the exam. We look for a key phrase to help us decide how to represent that score using an algebraic expression.
Key phrase: 12 points higher on the |
Translation: add 12 points to the |
written part than on |
interview score |
the interview |
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So x 12 her score on the written part of the test. Now we translate the words of the problem into an equation.
The score on |
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Solve
x x 12 92 2x 12 92
2x 12 12 92 12
2x 80
22x 802
x 40
We need to isolate x on the left side.
On the left side, combine like terms: x x 2x.
To isolate the variable term, 2x, subtract 12 from both sides to undo the addition of 12.
Do the subtraction.
To isolate the variable x, divide both sides by 2 to undo the multiplication by 2.
Do the division. This is her score on the interview.
To find the second unknown, we substitute 40 for x in the expression that represents her score on the written part.
x 12 40 12
52 |
This is her score on the written part. |
Self Check 7
CIVIL SERVICE A candidate for a position with the IRS scored 15 points higher on the written part of the civil service exam than he did on his interview. If his combined score was 155, what were his scores on the
interview and on the written part?
Now Try Problem 25
State
Her score on the interview was 40 and her score on the written part was 52.
Check
Her score of 52 on the written exam was 12 points higher than her score of 40 on the interview. Also, if we add the two scores, we get:
40 |
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This is her combined score. |
The results, 40 and 52, check.
682 |
Chapter 8 An Introduction to Algebra |
Self Check 8
CRIME SCENES Police used
800 feet of yellow tape to fence off a rectangular-shaped lot for an investigation. Fifty less feet of tape was used for each width as for each length. Find the length and the width of the lot.
Playgrounds After
receiving a donation of 400 feet of chain link fencing, the staff of a preschool decided to use it to enclose a playground that is rectangular. Find the length and the width of the playground if the length is three times the width.
The perimeter is 400 ft. |
Width |
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The length is three times as long as the width.
Analyze
Now Try Problem 26 |
• The perimeter is 400 ft. |
Given |
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• What is the length and what is the width of the rectangle? |
Find |
Form
We will let w the width of the playground. There is a second unknown quantity: the length of the playground. We look for a key phrase to help us decide how to represent it using an algebraic expression.
Key phrase: length three times the width Translation: multiply width by 3
So 3w the length of the playground.
The formula for the perimeter of a rectangle is P 2l 2w. In words, we can
write |
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We need to isolate w on the left side.
Do the multiplication: 2 3w 6w.
On the left side, combine like terms: 6w 2w 8w.
To isolate w, divide both sides by 8 to undo the multiplication by 8.
Do the division.
50
8 400
40
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0
0
To find the second unknown, we substitute 50 for w in the expression that represents the length of the playground.
3w 3(50) Substitute 50 for w.
150 This is the length of the playground.
State
The width of the playground is 50 feet and the length is 150 feet.
Check
If we add two lengths and two widths, we get 2(150) 2(50) 300 100 400. Also, the length (150 ft) is three times the width (50 ft). The results check.
ANSWERS TO SELF CHECKS
1. 476 units have been sold. 2. The tank originally contained 1,775 gallons of gasoline. 3. The student used to read 175 words per minute. 4. The quartet charged $340 for the performance. 5. The student needs to complete 6 more 4-hour shifts of volunteer service. 6. The couple made $570 at the yard sale. 7. His score on the interview was 70 and his score on the written part was 85. 8. The length of the lot is 225 feet and the width of the lot is 175 feet.
S E C T I O N 8.5 STUDY SET
VOCABULARY
Fill in the blanks.
1.The five-step problem-solving strategy is:
•the problem
•Form an
•the equation
•State the
•the result
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CONCEPTS
In each of the following problems, find the key word or phrase and tell how it translates. You do not have to solve the problem.
7.FAST FOOD The franchise fee and startup costs for a Taco Bell restaurant total $1,324,300. If an entrepreneur has $550,000 to invest, how much money will she need to borrow to open her own Taco Bell restaurant? (Source: yumfranchises.com)
Key word:
Translation:
8.GRADUATION ANNOUNCEMENTS Six of Tom’s graduation announcements were returned by the post office stamped “no longer at this address,” but 27 were delivered. How many announcements did he send?
Key word:
Translation:
9.WORKING IN GROUPS When a history teacher had the students in her class form equal-size discussion groups, there were seven complete groups, with five students in a group. How many students were in the class?
Key word:
Translation:
8.5 Using Equations to Solve Application Problems |
683 |
10.SELF-HELP BOOKS An author book claimed that the information in his book could double a salesperson’s monthly income. If a medical supplies salesperson currently earns $5,000 a month, what monthly income can she expect to make after reading the book?
Key word:
Translation:
11.SCHOLARSHIPS See the illustration. How many scholarships were awarded this year?
Last year, s scholarships |
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were awarded. |
were awarded this year |
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12.OCEAN TRAVEL See the illustration. How many miles did the passenger ship travel?
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13.SERVICE STATIONS See the illustration. How many gallons does the smaller tank hold?
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14.Complete this statement about the perimeter of the rectangle shown.
2 2 240
The perimeter is 240 ft. |
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5w
684Chapter 8 An Introduction to Algebra
15.HISTORY A 1,700-year-old scroll is 425 years older than the clay jar in which it was found. How old is the jar?
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16.BANKING After a student wrote a $1,500 check to pay for a car, he had a balance of $750 in his account. How much did he have in the account before he wrote the check?
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Key phrase: wrote a check |
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Solve
1,500 750
x 1,500 750 x
State The account balance before writing the check was .
Check
1,500
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The result checks. |
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17.AIRLINE SEATING An 88-seat passenger plane has ten times as many economy seats as first-class seats. Find the number of first-class seats and the number of economy seats.
Analyze
•There are seats on the plane.
•There are times as many economy as first-class
seats. |
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• Find the number of |
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seats and the |
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Form Since the number of economy seats is related to the number of first-class seats, we let x the number of
seats.
To represent the number of economy seats, look for a key phrase in the problem.
Key phrase: ten times as many
Translation: multiply by
So the number of economy seats.
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Solve
x 10x
88 11x 88
x
State There are first-class seats and economy seats.
Check The number of economy seats, 80, is times the number of first-class seats, 8. Also, if we add the numbers of seats, we get:
8
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The results check.
18.THE STOCK MARKET An investor has seen the value of his stock double in the last 12 months. If the current value of his stock is $274,552, what was its value one year ago?
Analyze
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equation. |
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State
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Check
2
This is the current
value of the stock.
The result checks.
GUIDED PRACTICE
Form an equation and solve it to answer each question.
See Example 1.
19.FAST FOOD The franchise fee and startup costs for a Pizza Hut restaurant are $316,500. If an entrepreneur has $68,500 to invest, how much money will she need to borrow to open her own Pizza Hut restaurant?
See Example 2.
8.5 Using Equations to Solve Application Problems |
685 |
See Example 3.
21.SPEED READING An advertisement for a speed reading program claimed that successful completion of the course could triple a person’s reading rate.
After taking the course, Alicia can now read 399 words per minute. If the company’s claims are true, what was her reading rate before taking the course?
See Example 4.
22.PHYSICAL EDUCATION A high school PE teacher had the students in her class form
three-person teams for a basketball tournament. Thirty-two teams participated in the tournament. How many students were in the PE class?
See Example 5.
23.BUSINESS After beginning a new position with 15 established accounts, a salesman made it his objective to add 5 new accounts every month. His goal was to reach 100 accounts. At this rate, how many months would it take to reach his goal?
See Example 6.
24.TAX REFUNDS After receiving their tax refund, a husband and wife split the refunded money equally. The husband then gave $50 of his money to charity, leaving him with $70. What was the amount of the tax refund check?
See Example 7.
25.SCHOLARSHIPS Because of increased giving, a college scholarship program awarded six more scholarships this year than last year. If a total of
20 scholarships were awarded over the last two years, how many were awarded last year and how many were awarded this year?
See Example 8.
26.GEOMETRY The perimeter of a rectangle is 150 inches. Find the length and the width if the length is four times the width.
APPLICATIONS
20.PARTY INVITATIONS Three of Mia’s party invitations were lost in the mail, but 59 were delivered. How many invitations did she send?
Form an equation and solve it to answer each question.
27.LOANS A student plans to pay back a $600 loan with monthly payments of $30. How many
payments has she made if she now only owes $420?
686Chapter 8 An Introduction to Algebra
28.ANTIQUES A woman purchases 8 antique spoons each year. She now owns 56 spoons. In how many years will she have 200 spoons in her collection?
29.HIP HOP Forbes magazine estimates that in 2008, Shawn “Jay-Z” Carter earned $82 million. If this was $68 million less than Curtis “50 Cent” Jackson’s earnings, how much did 50 Cent earn in 2008?
30.BUYING GOLF CLUBS A man needs $345 for a new set of golf clubs. How much more money does he need if he now has $317?
31.INTERIOR DECORATING As part of redecorating, crown molding was installed around the ceiling of a room. Sixty feet of molding was needed for the project. Find the length and the width of the room if its length is twice the width.
Molding
Paint
Wallpaper
32.SPRINKLER SYSTEMS A landscaper buried a water line around a rectangular lawn to serve as a supply line for a sprinkler system. The length of the lawn is 5 times its width. If 240 feet of pipe was used to do the job, what is the length and the width of the lawn?
Lawn
33.GRAVITY The weight of an object on Earth is 6 times greater than what it is on the moon. The situation shown below took place on Earth. If it took place on the moon, what weight would the scale register?
300
330
Pounds
360
34.INFOMERCIALS The number of orders received each week by a company selling skin care products increased fivefold after a Hollywood celebrity was added to the company’s infomercial. After adding the celebrity, the company received about 175 orders each week. How many orders were received each week before the celebrity took part?
35.THEATER The play Romeo and Juliet, by William Shakespeare, has 5 acts and a total of 24 scenes. The second act has the most scenes, 6. The third and fourth acts both have 5 scenes. The last act has the least number of scenes, 3. How many scenes are in the first act?
36.U.S. PRESIDENTS As of December 31, 1999, there had been 42 presidents of the United States. George Washington and John Adams were the only presidents in the18th century (1700-1799). During the 19th century (1800-1899), there were 23 presidents. How many presidents were there during the 20th cenury (1900-1999)?
37.HELP WANTED From the following ad from the classified section of a newspaper, determine the value of the benefit package. ($45K means $45,000.)
ACCOUNTS PAYABLE
2-3 yrs exp as supervisor. Degree a +. High vol company. Good pay, $45K & xlnt benefits; total compensation worth $52K. Fax resume.
38.POWER OUTAGES The electrical system in a building automatically shuts down when the meter shown reads 85. By how much must the current reading increase to cause the system to shut down?
50
30 70
1090
39.VIDEO GAMES After a week of playing Sega’s Sonic Adventure, a boy scored 11,053 points in one game— an improvement of 9,485 points over the very first
time he played. What was his score for his first game?
On Earth
40.AUTO REPAIR A woman paid $29 less to have her car fixed at a muffler shop than she would have paid at a gas station. At the gas station, she would have paid $219. How much did she pay to have her car fixed?
41.For a half-hour time slot on television, a producer scheduled 18 minutes more time for the program than time for the commercials. How many minutes of commercials and how many minutes of the program were there in that time slot? (Hint: How many minutes are there in a half hour?)
from Campus to Careers
Broadcasting
© iStockphoto.com/Dejan Ljami´c
42.SERVICE STATIONS At a service station, the underground tank storing regular gas holds 100 gallons less than the tank storing premium gas. If the total storage capacity of the tanks is 700 gallons, how much does the premium gas tank and how much does the regular gas tank hold?
43.CLASS TIME In a biology course, students spend a total of 250 minutes in lab and lecture each week. The lab time is 50 minutes shorter than the lecture time. How many minutes do the students spend in lecture and how many minutes do students spend in lab per week?
44.OCEAN TRAVEL At noon, a passenger ship and a freighter left a port traveling in opposite directions. By midnight, the passenger ship was
3 times farther from port than the freighter was. How far was the freighter and how far was the passenger ship from port if the distance between the ships was 84 miles?
45.ANIMAL SHELTERS The number of phone calls to an animal shelter quadrupled after the evening news aired a segment explaining the services the shelter offered. Before the publicity, the shelter received 8 calls a day. How many calls did the shelter receive each day after being featured on the news?
46.OPEN HOUSES The attendance at an elementary school open house was only half of what the principal had expected. If 120 people visited the school that evening, how many had she expected to attend?
47.BUS RIDERS A man had to wait 20 minutes for a bus today. Three days ago, he had to wait 15 minutes longer than he did today, because four buses passed by without stopping. How long did he wait three days ago?
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8.5 Using Equations to Solve Application Problems |
687 |
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48. |
HIT RECORDS The |
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oldest artist to have a |
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was Louis Armstrong, |
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number one single |
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Dolly. He was 55 |
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with the song Hello |
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years older than the |
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Courtesy |
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youngest artist to |
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have a number one |
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single, 12-year-old Jimmy Boyd, with I Saw Mommy |
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Kissing Santa Claus. How old was Louis Armstrong |
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when he had the number one song? (Source: The Top |
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10 of Everything, 2000.) |
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49. |
COST OVERRUNS Lengthy delays and skyrocketing |
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costs caused a rapid-transit construction project to |
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go over budget by a factor of 10. The final audit |
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showed the project costing $540 million. What was |
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the initial cost estimate? |
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50. |
LOTTO WINNERS The grocery store employees |
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listed below pooled their money to buy $120 worth |
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of lottery tickets each week, with the understanding |
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that they would split the prize equally if they |
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happened to win. One week they did have the |
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winning ticket and won $480,000. What was each |
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employee’s share of the winnings? |
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Sam M. Adler |
Ronda Pellman |
Manny Fernando |
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Lorrie Jenkins |
Tom Sato |
Sam Lin |
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Kiem Nguyen |
H. R. Kinsella |
Tejal Neeraj |
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Virginia Ortiz |
Libby Sellez |
Alicia Wen |
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51.RENTALS In renting an apartment with two other friends, Enrique agreed to pay the security deposit of $100 himself. The three of them agreed to contribute equally toward the monthly rent. Enrique’s first check to the apartment owner was for $425. What was the monthly rent for the apartment?
52.BOTTLED WATER DELIVERY A truck driver left the plant carrying 300 bottles of drinking water. His delivery route consisted of office buildings, each of which was to receive 3 bottles of water. The driver returned to the plant at the end of the day with
117 bottles of water on the truck. To how many office buildings did he deliver?
53.CONSTRUCTION To get a heavy-equipment operator’s certificate, 48 hours of on-the-job training are required. If a woman has completed 24 hours, and the training sessions last for 6 hours, how many more sessions must she take to get the certificate?