GUIDED PRACTICE
Concept Check
✓
1.
3 APPLY
YEARBOOK DESIGN In Example 1, the top and bottom margins are each
7
3
ᎏᎏ inch. There are 5 rows of pictures, with ᎏᎏ inch of vertical space between
8
16
ASSIGNMENT GUIDE
pictures. Draw a diagram and label all the heights on your diagram.
Then write and solve an equation to find the height of each picture.
Day 1: p. 163 Exs. 6–16, 22, 30–40
AVERAGE
1.7 in.; See margin for sample diagram and equation.
Skill Check
✓
3. Rate your friend is driving
= 52 (mi/h); Time after you
start driving = t (h);
Friend’s distance when
you leave = 32 (mi); rate
you are driving = 60 (mi/h);
52t + 32 = 60t
4. 4; 4 hours after you leave,
you and your friend are
side by side. Her distance
in miles from Los Angeles
is 4(52) + 32 = 240 and
yours is 60(4) = 240.
2. Show how unit analysis can help you check the verbal model for Example 3.
Examine the units in the equation: feet + feet = feet.
DISTANCE PROBLEM In Exercises 3–5, use the following problem.
You and your friend are each driving 379 miles from Los Angeles to San
Francisco. Your friend leaves first, driving 52 miles per hour. She is 32 miles
from Los Angeles when you leave, driving 60 miles per hour. How far do each of
you drive before you are side by side? Use the following verbal model.
Rate your
Time after
Friend’s distance
friend is • you start +
when you leave =
driving
driving
Rate
you are
driving
Time after
you start
driving
•
3. Assign labels to each part of the verbal model. Use the labels to translate the
verbal model into an algebraic model. See margin.
4. Solve the equation. Interpret your solution. How far do each of you drive
before you are side by side? See margin.
5. Make a table or a graph to check your solution.
See margin.
PRACTICE AND APPLICATIONS
STUDENT HELP
Extra Practice
to help you master
skills is on p. 799.
6. Sample answer : B since
it shows the length,
width, and height of the
3-dimensional box.
PACKAGE SIZE In Exercises 6–8, use this U.S.
postal regulation: a rectangular package can have
a combined length and girth of 108 inches. Suppose
a package that is 36 inches long and as wide as it is
high just meets the regulation.
Girth is the
distance
around the
end of the
package.
6. USING A DIAGRAM Which diagram do you find most helpful for
understanding the relationships in the problem? Explain. See margin.
A.
B.
x
36 in.
36 in.
x
C.
x
36 in.
x
x
x
STUDENT HELP
HOMEWORK HELP
Example 1: Exs. 6–7,
14–16
Example 2: Exs. 8–12,
17–21
Example 3: Exs. 9–13,
17–21
BASIC
Day 1: p. 163 Exs. 6–17, 22, 30–40
ADVANCED
Day 1: p. 163 Exs. 6–26, 30–40
BLOCK SCHEDULE WITH 3.6
p. 163 Exs. 6–17, 22, 30–40
EXERCISE LEVELS
Level A: Easier
27–30
Level B: More Difficult
6–16, 22, 31–40
Level C: Most Difficult
17–21, 23–26
HOMEWORK CHECK
To quickly check student understanding of key concepts, go
over the following exercises:
Exs. 6, 8, 12, 13, 16. See also the
Daily Homework Quiz:
• Blackline Master (Chapter 3
Resource Book, p. 80)
•
Transparency (p. 24)
TEACHING TIP
EXERCISE 5 You may wish to
have students who created a table
to check their solution also create a
graph and vice versa. Students
could then compare the two methods of checking solutions.
1, 5, 8. See Additional Answers
beginning on page AA1.
x
7. CHOOSING A MODEL Choose the equation you would use to find the width
of the package. Then find its width. C; 18 in.
A. x + 36 = 108
B. 2x + 36 = 108
C. 4x + 36 = 108
8. MAKING A TABLE Make a table showing possible dimensions, girth, and
combined length and girth for a “package that is 36 inches long and as wide
as it is high.” Which package in your table just meets the postal regulation?
See margin.
3.5 Linear Equations and Problem Solving
163
163
UNIT ANALYSIS In Exercises 9–12, find the resulting unit of measure.
9. (hours per day) • (days) hours
11. (inches) ÷ (inches per foot) ft
10. (feet) ÷ (minute) ft/min
12. (miles per hour) • (hours per minute)
mi/min
13. A VISUAL CHECK Use the graph to check the answer to the problem below.
Is the solution correct? Explain.
13. No; according to the
graph the solution is
5 weeks, not 25 weeks.
You have $320 and save $10 each week.
Your brother has $445 and spends his
income, plus $15 of his savings each week.
When will you and your brother have
the same amount in savings?
EXERCISES 17 AND 21 As
with Exercise 5, you may wish to
have students who checked their
solutions with a table go back and
draw a graph and vice versa
320 + 10t = 445 º 15t
320 = 445 º 5t
º125 = º5t
14. See Additional Answers beginning on page AA1.
25 = t
1
4
in 25 weeks
Comparing Savings
Dollars in savings
TEACHING TIPS
EXERCISE 13 Most students will
see from the graph that the solution
of 25 weeks is incorrect. Ask students to go a step further and find
the error in the computation. This
may help them avoid making similar
errors in their work.
460
440
420
400
380
360
340
320
300
0
0 1 2 3 4 5 6 t
Time (weeks)
16. 2}} ; each photo should
1
4
be 2}} in. wide.
1
2
1
2
3
inches wide, and the left and right margins are each }} inch. The space
4
1
between the photos is }} inch. How wide should you make the photos?
2
media guide to show two photos across its width. The cover is 6}}
1
2
19. }} mi; x + }}
20. Sample equation:
1
2
COVER DESIGN In Exercises 14–16, you want the cover of a sports
5 1
6 3
x + }} = }}; }} mi
FOCUS ON
APPLICATIONS
14. Draw a diagram of the cover. See margin.
15. Write an equation to model the problem. Use your diagram to help.
1
Let x = the width in inches of the photos; 2x + 2 = 6 }}.
2
16. Solve the equation and answer the question. See margin.
17.
LANGUAGE CLASSES At Barton High School, 45 students are taking
Japanese. This number has been increasing at a rate of 3 students per year. The
number of students taking German is 108 and has been decreasing at a rate of
4 students per year. At these rates, when will the number of students taking
Japanese equal the number taking German? Write and solve an equation to
answer the question. Check your answer with a table or a graph.
BIOLOGY
CONNECTION
Sample equation: 45 + 3x = 108 º 4x; in 9 years
In Exercises 18–21, use the following information.
A migrating elephant herd started moving at a rate of 6 miles per hour. One
elephant stood still and was left behind. Then this stray elephant sensed danger
and began running at a rate of 10 miles per hour to reach the herd. The stray
caught up in 5 minutes.
For Lesson 3.5:
• Practice Levels A, B, and C
(Chapter 3 Resource Book, p. 70)
• Reteaching with Practice
(Chapter 3 Resource Book, p. 73)
•
See Lesson 3.5 of the
Personal Student Tutor
For more Mixed Review:
•
Search the Test and Practice
Generator for key words or
specific lessons.
164
18. How long (in hours) did the stray run to catch up? How far did it run? }1} h; }5} mi
RE
L
AL I
FE
ADDITIONAL PRACTICE
AND RETEACHING
12
ELEPHANTS need
a supply of fresh
water, some shade, and
plentiful food such as
grasses and leaves. To find
these, elephants may make
yearly migrations of a few
hundred miles.
164
6
19. Find the distance that the herd traveled while the stray ran to catch up. Then
write an expression for the total distance the herd traveled. Let x represent the
distance (in miles) that the herd traveled while the stray elephant stood still.
See margin.
20. Use the distances you found in Exercises 18 and 19. Write and solve an
equation to find how far the herd traveled while the stray stood still. See margin.
21. Make a table or a graph to check your answer. Check tables and graphs.
Chapter 3 Solving Linear Equations
22. c. The sum of the
distances they’ve
ridden must be 60 mi;
2
21t + 15t = 60; 1}} h.
3
d. Sample answer: It
would be relatively
convenient in that it
would take Sally about
1.6 h to get there and
Teresa about 1.7 h.;
Check data displays.
★ Challenge
23. rabbit: 1.2 sec;
x + 30
50
coyote: }} sec
x + 30
50
24. }} = 1.2; 30 ft
22. MULTI-STEP PROBLEM Two friends are 60 miles apart. They decide to ride
their bicycles to meet each other. Sally starts from the college and heads east,
riding at a rate of 21 miles per hour. At the same time Teresa starts from the
river and heads west, riding at a rate of 15 miles per hour.
a. Draw a diagram showing the college and the river 60 miles apart and the
two cyclists riding toward each other. Check diagrams.
b. How far does each cyclist ride in t hours? Sally: 21t mi; Teresa: 15t mi
c. When the two cyclists meet, what must be true about the distances they
have ridden? Write and solve an equation to find when they meet. See margin.
d. CHOOSING A DATA DISPLAY Would a park that is 26 miles west of the
river be a good meeting place? Explain. Use a diagram, a table, or a graph
to support your answer.
RABBIT AND COYOTE
In Exercises 23–26, use this
information. A rabbit is 30 feet
from its burrow. It can run
25 feet per second. A coyote
that can run 50 feet per
second spots the rabbit and
starts running toward it.
30 ft
x ft
Burrow
Rabbit
Coyote
25. If the coyote is 30 ft from
the rabbit, the rabbit and
the coyote will reach the
burrow at the same time.
If x is less than 30 ft, the 23. Write expressions for the time it will take the rabbit to get to its burrow and
coyote should be able to
for the time it will take the coyote to get to the burrow. See margin.
overtake the rabbit. If x
24. Write and solve an equation that relates the two expressions in Exercise 23.
is greater than 30 ft, the
See margin.
rabbit should be able to
25.
C
RITICAL THINKING Interpret your results from Exercise 24. Include a
escape the coyote.
description of what happens for different values of x. See margin.
EXTRA CHALLENGE
www.mcdougallittell.com
x
35. 18 + ᎏᎏ = 9 º27
3
10 0
30. ᎏᎏ 0.50; 50%
201
3
ᎏᎏx º y when x = º25 and y = º10
5
º5
ab
ᎏᎏ when a = 8 and b = 7
3a º 10
4
(Review 3.3 and 3.4 for 3.6)
2
36. 8 = ºᎏᎏ(2x º 6) º3
3
3
4
37. 4(2 º n) = 1 1}}
1
38. º3y + 14 = º5y º7 39. º4a º 3 = 6a + 2 º}2} 40. 5x º (6 º x) = 2(x º 7)
º2
3.5 Linear Equations and Problem Solving
Train B
Train A
0
2
4
6
Time (min)
x
8
EXTRA CHALLENGE NOTE
EVALUATING EXPRESSIONS Evaluate the expression. (Review 2.5 and 2.7)
º6
31. ᎏᎏ º 2r when q = 2 and r = 11
32.
q
º25
x+y
33. ᎏᎏ when x = º24 and y = 6
34.
12
º1.5
SOLVING EQUATIONS Solve the equation.
y
12
10
8
6
4
2
0
Challenge problems for
Lesson 3.5 are available in
blackline format in the Chapter 3
Resource Book, p. 77 and at
www.mcdougallittell.com.
FRACTIONS, DECIMALS, AND PERCENTS Write as a decimal rounded to the
nearest hundredth. Then write as a percent. (Skills Review, pages 784–785)
25
29. ᎏᎏ 0.81; 81%
31
Transparency Available
1. Train A leaves the downtown
station headed for the other end
of the line at 55 mi/h. Train B
leaves the other end of the line
on a parallel route and heads
downtown at 65 mi/h. Use the
graph to tell how many minutes
it will be before the trains pass
one another. 6 min
55
65
}} t = 12 – }} t; 6 min
60
60
MIXED REVIEW
11
28. ᎏᎏ 0.92; 92%
12
DAILY HOMEWORK QUIZ
2. Write and solve an equation to
check your answer for Ex. 1.
26. Use a table or a graph to check your conclusions. Check tables and graphs.
3
27. ᎏᎏ 0.27; 27%
11
4 ASSESS
Distance from
downtown (mi)
Test
Preparation
165
ADDITIONAL TEST
PREPARATION
1. WRITING You are personalizing
sweatshirts to sell at a fund
raiser. Each sweatshirt requires
3
1
ᎏᎏ h to paint and 1 ᎏᎏ h to dry. It
4
2
3
4
will also require a total of 2 ᎏᎏ h
to prepare the sweatshirts. If
you have a total of 32 h to spend
on the sweatshirts and you can
work on only one at a time, how
many can you make to sell?
Write an equation to model the
problem. Then solve the problem.
3
1
3
}}x + 1 }}x + 2 }} = 32; 13 sweatshirts
4
2
4
165