MTH 091

Section 9.5Formulas and Problem Solving

What Is A Formula?

• A formula is an equation in which variables are used to describe a relationship.

• We have two objectives for working with formulas:

1.Solve a formula for one variable, given the values of the other variables

2.Solve a formula for a specified variable

Solving A Formula When Numbers Are Given

• Similar to evaluating an expression• When you substitute the given values into the

equation, one variable will be left over.• Isolate this variable using the techniques

previously discussed

Examples

1. Using the formula d = rt, find the unknown variable if d = 195 and t = 3.

2. Using the formula , find the unknown variable if A = 60, B = 7, and b = 3.

3. The world’s largest sign for Coca-Cola is located in Arica, Chile. The rectangular sign has a length of 400 feet and an area of 52400 square feet. Find the width of the sign.

)(2

1bBhA

More Examples

4. Using the formula S = 4LW + 2WH, solve for H if S = 300, L = 10, and W = 5.

5. Using the formula P = a + b + c, solve for b if P = 37, a = 15, and c = 9.

Solving A Formula When Numbers Are Not Given

• Isolate the required variable using the same techniques as when you had numbers.

• If your formula has a fraction, multiply both sides by the LCD.

Solve each formula for the specified variable.

fkD

yx

yx

4

1

1352

4

for y

for y

for k

More Examples

cbaP

PRTPA

for T

for c