Beginning Algebra, 11th Edition

2.5 Formulas and Additional Applications from Geometry

from Geometry

To find the value of one of the variables in a formula,
given values for the others, substitute the known values
into the formula.

To solve a formula for one of the variables, isolate that
variable by treating the other variables as numbers and
using the steps for solving equations.

Find Lif given that and

Divide by 3.

Solve for b.

Subtract 2a.

Combine like terms.

Divide by 2.

P- 2 a

2

=b, or b=

P- 2 a

2

P- 2 a

2

=

2 b

2

P- 2 a= 2 b

P- 2 a= 2 a+ 2 b- 2 a

P= 2 a+ 2 b

8 =L

24

3

=

L# 3

3

24 =L# 3 a=24, W= 3

a=LW, a= 24 W=3.

CONCEPTS EXAMPLES

2.6 Ratio, Proportion, and Percent

To write a ratio, express quantities in the same units.

To solve a proportion, use the method of cross products.

To solve a percent problem, use the percent equation.

amountpercent (as a decimal)#base

2.7 Further Applications of Linear

Equations

Step 1 Read. Two cars leave from the same point, traveling in opposite directions.
One travels at 45 mph and the other at 60 mph. How long will it take
them to be 210 mi apart?

166 CHAPTER 2 Linear Equations and Inequalities in One Variable

Step 2 Assign a variable. Make a table and/or draw
a sketch to help solve the problem.
The three forms of the formula relating
distance, rate, and time are

and t

d

r

r.

d

t

drt, ,

Let time it takes for them to be 210 mi apart.

210 mi

t=

(continued)

4 ftto 8 in. 48 in. to 8 in.

Solve.

Cross products

Multiply.

Divide by 60.

Solution set:

65 is what percent of 325?

65 p 325

p

0.2 p,or20% p

65 is 20%of 325.

= =

=

65

325

= #

576

x= 7

60 x= 420

60 x= 12 # 35

x

12

=

35

60

=

48

8

=

6

1

=

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