Transcript EXAMPLE 1 Translate verbal phrases into expressions Verbal Phrase Expression a. 4 less than the quantity 6 times a number n 6n – 4 b.

EXAMPLE 1
Translate verbal phrases into expressions
Verbal Phrase
Expression
a. 4 less than the quantity 6 times a number n
6n – 4
b. 3 times the sum of 7 and a number y
3(7 + y)
c. The difference of 22 and the square of a
number m
22 – m2
GUIDED PRACTICE
for Example 1
1. Translate the phrase “the quotient when the
quantity 10 plus a number x is divided by 2” into an
expression.
ANSWER
1.
Expression
10 + x
2
EXAMPLE 2
Write an expression
Cutting A Ribbon
A piece of ribbon l feet long is cut from a ribbon 8
feet long. Write an expression for the length (in feet)
of the remaining piece.
SOLUTION
Draw a diagram and use a specific case to help you
write the expression.
Suppose the piece cut is
Suppose the piece cut is
L feet long.
2 feet long.
The remaining piece is
(8 – 2) feet long.
The remaining piece is
(8 – l) feet long.
EXAMPLE 2
Write an expression
ANSWER
The expression 8 – l represents the length (in feet) of
the remaining piece.
EXAMPLE 3
Use a verbal model to write an expression
Tips
You work with 5 other people at an ice cream stand.
All the workers put their tips into a jar and share the
amount in the jar equally at the end of the day. Write
an expression for each person’s share (in dollars) of
the tips.
SOLUTION
STEP 1
Write a verbal model.
STEP 2
Translate the verbal
model into an algebraic
expression. Let a represent the
amount (in dollars) in the jar.
Amount
in jar

Number
of people
a

6
EXAMPLE 3
Use a verbal model to write an expression
ANSWER
An expression that represents each person’s share
(in dollars) is a .
6
GUIDED PRACTICE
for Examples 2 and 3
WHAT IF? In Example 2, suppose that you cut the
original ribbon into p pieces of equal length. Write an
expression that represents the length (in feet) of each
piece.
ANSWER
l
p
GUIDED PRACTICE
for Examples 2 and 3
WHAT IF? In Example 3, suppose that each of the 6
workers contributes an equal amount for an afterwork celebration. Write an expression that represents
the total amount (in dollars) contributed.
ANSWER
6d, where d represents the amount contributed by
each worker.
EXAMPLE 4
Find a unit rate
A car travels 110 miles in 2 hours. Find the unit rate.
110 miles
2 hours =
110 miles
2 hours
2
55 miles
2 = 1 hour
ANSWER
The unit rate is 55 miles per hour, or 55 mi/h.
EXAMPLE 5
Solve a multi-step problem
Cell Phones
Your basic monthly charge for cell phone service is
$30, which includes 300 free minutes. You pay a fee
for each extra minute you use. One month you paid
$3.75 for 15 extra minutes. Find your total bill if you
use 22 extra minutes.
SOLUTION
STEP 1 Calculate the unit rate.
3.75 0.25
=
= $.25 per minute
15
1
EXAMPLE 5
Solve a multi-step problem
STEP 2
Write a verbal model and then an expression. Let m be
the number of extra minutes.
30
+
0.25
m
Use unit analysis to check that the expression
30 + 0.25m is reasonable.
dollars
dollars +
minutes = dollars + dollars = dollars
minute
Because the units are dollars, the expression is
reasonable.
EXAMPLE 5
Solve a multi-step problem
STEP 3
Evaluate the expression when m = 22.
30 + 0.25(22) = 35.5
ANSWER
The total bill is $35.50.
EXAMPLE 5
Solve a multi-step problem
STEP 3
Evaluate the expression when m = 22.
30 + 0.25(22) = 35.5
ANSWER
The total bill is $35.50.