Page 1 of 5
Writing Expressions
and Equations
BEFORE
Now
WHY?
You evaluated variable
expressions.
You’ll write variable expressions
and equations.
So you can find the altitude of
a hot air balloon, as in Ex. 34.
In the Real World
Word Watch
verbal model, p. 318
Caves You are exploring a cave in
which rock formations called
stalagmites grow up from the cave
floor. The tour guide informs you
that the tallest stalagmite in the
cave is in a pool of water 55 feet
deep, and the distance between
the tip of the stalagmite and the
surface of the water is 41 feet.
How tall is the stalagmite? You’ll
find the answer in Example 3.
Translating Phrases and Sentences To solve real-world problems, you
need to translate verbal phrases and sentences into variable expressions
and equations. Look for key words that indicate addition, subtraction,
multiplication, and division.
tch Out!
Wa
Order is important
in subtraction and division
expressions. For example,
“2 less than a number” is
written as x 2, not
2 x. Similarly, “a number
divided by 5” is written as
x 5, not 5 x.
Addition
Subtraction
Multiplication
Division
plus
the sum of
increased by
total
more than
added to
minus
the difference of
decreased by
fewer than
less than
subtracted from
times
the product of
multiplied by
of
divided by
the quotient of
EXAMPLE
1
Translating Verbal Phrases
Verbal phrase
Expression
a. A number increased by 5
x5
b. 7 less than a number
x7
c. 3 more than twice a number
2x 3
d. 4 decreased by the quotient of a number and 7
4 Lesson 7.1
x
7
Writing Expressions and Equations
317
Page 2 of 5
EXAMPLE
with
Solving
2
Translating Verbal Sentences
Verbal sentence
When translating verbal
sentences into equations,
look for the key words “is”
and “equals,” which can
be represented by the
symbol .
Equation
a. 16 increased by a number is 27.
16 y 27
b. The difference of twice a number and 3 equals 4.
2y 3 4
c. The product of 2 and a number is 36.
1
1
y 36
2
d. 3 is equal to twice the sum of a number and 2.
3 2(y 2)
Your turn now
Write the verbal phrase or sentence as a variable
expression or equation. Let n represent the number.
1. 14 added to a number
1
2. of a number decreased by 22
2
3. 42 divided by a number equals 7.
4. 5 minus twice a number is 17.
You can use verbal models to solve real-world problems. A verbal model
uses words to describe ideas and math symbols to relate the words.
EXAMPLE
3
Writing and Solving an Equation
To find the height of the stalagmite described at
the top of page 317, you can write and solve an
equation. First write a verbal model.
with
Solving
Let h represent the height of the stalagmite.
Assign a meaningful
variable to represent what
you need to find. In
Example 3, h is chosen to
represent the height of
the stalagmite.
Distance between
Height of
Depth of
tip of stalagmite stalagmite
water
and water surface
h
41
41 f t
55 ft
55
Use mental math: Because 14 41 55, h 14.
h
ANSWER The height of the stalagmite is 14 feet.
Your turn now
Use mental math to solve the following problem.
5. While hiking you descend 2000 feet from the start of a trail to an
elevation of 5200 feet. Write and solve an equation to find the
elevation at the start of the trail.
318
Chapter 7
Equations, Inequalities, and Functions
Page 3 of 5
INTERNET
Exercises
eWorkbook Plus
CLASSZONE.COM
More Practice, p. 711
Getting Ready to Practice
1. Vocabulary Copy and complete: A(n) _?_ uses words to describe ideas
and math symbols to relate the words.
Match the verbal phrase with its variable expression.
2. 4 more than a number
A. 4 x
3. The quotient of a number and 4
B. x 4
4. The difference of 4 and a number
C. x 4
5. 4 less than a number
D. x 4
6. Guided Problem Solving The Colorado River, which is 1450 miles long,
is 450 miles shorter than the Rio Grande River. How long is the Rio
Grande River?
1 Reread the problem. Decide what you know and what you are asked
to find.
2 Write a verbal model that represents the situation. Then write
an equation.
3 Use mental math to solve the equation.
Practice and Problem Solving
with
Homework
Example Exercises
1
7–12, 26–29,
36–40
2
13–17, 36–40
3
31–35, 42
Online Resources
Write the verbal phrase as a variable expression. Let x represent
the number.
7. A number added to 7
1
9. of a number
3
8. The product of a number and 2
10. A number divided by 16
11. 50 decreased by a number
12. Twice a number
CLASSZONE.COM
• More Examples
• eTutorial Plus
Write the verbal sentence as an equation. Let y represent the
number.
13. The sum of a number and 9 equals 24.
14. The product of a number and 5 is 10.
15. 13 is equal to 5 minus a number.
1
16. of the difference of 6 and a number is 200.
4
17. The sum of 4 times a number and 3 is 27.
Lesson 7.1
Writing Expressions and Equations
319
Page 4 of 5
Write a verbal phrase for the variable expression.
18. 3 a
19. 13b
20. c 2
21. 10 d
Write a verbal sentence for the equation.
22. 4p 16
23. q 8 34
24. 9 2r 15
25. 90 s 1
Write the real-world phrase as a variable expression. Be sure to
identify what the variable represents.
26. 3 years older than Theo
27. Twice a team’s score
28. Half of your class
29. 5 inches shorter than Ann
30. Writing Describe real-world situations that can be represented by the
expressions n 3, n 3, 3n, and n 3.
In Exercises 31–35, write an equation to represent the situation
described. Then use mental math to solve the equation.
31. Temperature The temperature decreased by 24F, and it is now 75F.
What was the original temperature?
32. Shopping A sweater is on sale for half off the regular price, and it is
now $16. What was the regular price of the sweater?
Sports
33. Savings You deposit $30 into your savings account, and your new
balance is $100. What was your previous balance?
34. Hot Air Balloon You are in a hot air balloon, and you descend 200 feet
to an altitude of 1000 feet. What was your original altitude?
35. Swimming In 1994, Tammy and John Van Wisse became the first
brother and sister to swim across the English Channel. Tammy’s
crossing time, 8 hours 32 minutes, or 512 minutes, was 15 minutes
longer than her brother’s crossing time. How long, in hours and
minutes, did it take John to swim across the English Channel?
Write the verbal phrase or sentence as a variable expression or
equation. Let n represent the number.
36. The quotient of a number plus 6 and 3
■
Swimming
37. 4 added to the square of a number
By 2001, Tammy Van Wisse
had swum enough races to
circle Earth 1.5 times. The
circumference of Earth is
about 25,000 miles. About
how many miles had she
swum in races by 2001?
38. 8 multiplied by the difference of 9 and a number
1
39. of a number is equal to 8 plus the number.
3
40. The product of 3 and a number is twice the sum of the number and 5.
41. Critical Thinking Is “three less than a number” equivalent to
“the difference of three and a number”? Explain your reasoning.
320
Chapter 7
Equations, Inequalities, and Functions
Page 5 of 5
42. Braces Amy has an orthodontist’s appointment to get her braces
checked every 6 weeks. About how many times does she have to
go to the orthodontist in 1 year?
43. Geometry Write an expression for the area of a rectangle whose length
is 5 inches longer than its width. Evaluate this expression to find the
area of such a rectangle whose width is 3 inches.
1
44. Challenge You walk at 4 miles per hour for hour, and then jog at
2
6 miles per hour for h hours. The total distance that you cover both
walking and jogging is 6 miles. Write an equation that represents
this situation.
Mixed Review
Plot the point and describe its location in a coordinate plane.
(Lesson 6.8)
45. A(3, 2)
47. C(5, 1)
46. B(9, 2)
Choose a Strategy Use a strategy from
the list to solve the following problem.
Explain your choice of strategy.
48. D(6, 8)
Problem Solving Strategies
Draw a Diagram
Guess, Check, and Revise
■ Make a List
■
■
49. There are 60 houses on Independence
Road, numbered from 1 to 60. How
many houses on Independence Road
have at least one 2 as a digit?
Basic Skills Find the perimeter.
50.
51.
3 ft
2 ft
4 in.
4 in.
52.
25 cm
2 ft
15 cm
6 in.
20 cm
3 ft
Test-Taking Practice
INTERNET
State Test Practice
CLASSZONE.COM
53. Multiple Choice A vehicle rental company charges $25 to rent a
moving van plus $.50 for each mile traveled. Which expression
represents the total cost of renting a van and driving d miles?
A. 25 d
B. 25 0.50d
C. 25 0.50d
D. 25d 0.50
54. Multiple Choice The perimeter of a square is 20 inches. Which
equation can you use to find the length s of a side of the square?
F. s 2 20
G. 5s 20
Lesson 7.1
H. 4s 20
I. 20s 4
Writing Expressions and Equations
321