OBJECTIVE 1 Solve a formula for a specified variable. The formula
says that interest on a loan or investment equals principal (amount borrowed or in-
vested) times rate ( percent) times time at interest (in years). To determine how long it
will take for an investment at a stated interest rate to earn a predetermined amount of
interest, it would help to first solve the formula for t. This process is called solving
for a specified variableor solving a literal equation.
When solving for a specified variable, the key is to treat that variable as if it
were the only one. Treat all other variables like numbers (constants).The steps used
in the following examples are very similar to those used in solving linear equations
from Section 2.1.
Solving for a Specified VariableSolve the formula for t.
We solve this formula for tby treating I, p, and ras constants (having fixed val-
ues) and treating tas the only variable.
Associative propertyDivide by pr.t=
I
pr
1 pr 2 t
pr
=
I
pr
1 pr 2 t= I
prt= I
I= prt
EXAMPLE 1
I=prt
SECTION 2.2 Formulas and Percent 57
We solve the formula for Wby isolating Won one side of the equals symbol.
NOW TRY
EXERCISE 1
Solve the formula
for p.
I=prtNOW TRY ANSWER
- p=rtI
The result is a formula for t, time in years. NOW TRY
Our goal is to
isolate t.Solving for a Specified VariableStep 1 If the equation contains fractions, multiply both sides by the LCD to
clear the fractions.
Step 2 Transform so that all terms containing the specified variable are on one
side of the equation and all terms without that variable are on the other
side.
Step 3 Divide each side by the factor that is the coefficient of the specified
variable.
Solving for a Specified VariableSolve the formula for W.
This formula gives the relationship between perimeter of a rectangle, P, length of
the rectangle, L, and width of the rectangle, W. See FIGURE 2.
P= 2 L+ 2 W
EXAMPLE 2
LWWLPerimeter, P, distance around a
rectangle, is given by
P = 2L + 2 W.FIGURE 2