# 1.1: Variables in Algebra ```1.1 Variables in Algebra
What you should learn
GOAL
1
Evaluate a variable expression.
GOAL
2
Write a variable expression that models a
real-life situation.
Why you should learn it
To express real-life number relationships.
1.1 Variables in Algebra
GOAL
1
EVALUATING VARIABLE EXPRESSIONS
VOCABULARY
•variable
•values
•variable expression
•evaluating an expression
To evaluate a variable expression, follow these three steps:
•Write the variable expression.
•Substitute values for variables.
•Simplify the numerical expression.
EXAMPLE 1
Extra Example 1
Evaluate each expression when y = 3. Click for solutions.
1. 4y
4(3)
12
2.
12
y
12
3
4
EXAMPLE 2
3. y + 8
4. 18 - y
38
11
18  3
15
Extra Example 2
d
Find the average speed, , of a car that traveled 89 miles in
t
2 hours.
Solution:
d
average speed 
t
89 miles

2 hours
 44.5 mi/h
EXAMPLE 3
Extra Example 3
Find the perimeter, a + b + c, of the triangle. The
dimensions are in centimeters.
b = 1.75
Click to see the solution.
a=1
c = 2.25
Perimeter = a + b + c
= 1 + 1.75 + 2.25
= 5 cm
Checkpoint
1. Find the average speed of a car that travels 225 miles in
4.5 hours.
50 mi/h
2. Find the perimeter of the triangle. The dimensions are in
inches.
c = 6.7
a=8
EXAMPLE 4
b=8
22.7 in
Extra Example 4
Find the simple interest, Prt, you will earn in two years on a
deposit of \$870 at a rate of 5% per year.
Click for the solution.
Simple interest = Prt
Did you remember
to
convert the interest
rate
to a decimal
number?
 0.05 
(2 years)
= (\$870) 

 year 
= \$87
These units
cancel.
1.1 Variables in Algebra
GOAL
2
MODELING A REAL-LIFE SITUATION
VOCABULARY
•Unit Analysis
•Verbal Model
EXAMPLE 5
Extra Example 5
You plan to ride your bicycle to school and back at an
average rate of 6 miles per hour for a distance of 10.5 miles.
How long will it take you?
Click to see the solution.
VERBAL
MODEL
LABELS
ALGEBRAIC
MODEL
Time
Distance
=
Rate
Time = t
Distance = 10.5 miles
Rate = 6 mi/h
10.5 miles
t
6 mi/h
 1.75 hours
 mi
 mi/h  mi

h

h 
mi 


Checkpoint
1. Find the simple interest you will earn after one half of a
year with a deposit of \$1250 at a rate of 6% per year.
\$37.50
2. Your parents drive to the grocery store 9 miles away at
12:30 p.m. and return at 2:00 p.m. If the grocery shopping
took 45 minutes, what was the average speed of their car?
24 mi/h