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Solving Problems With Formulas

Evaluating Formulas

A formula describes a known relationship among quantities. For
example, the formula Abh relates the area A of a triangle to
the length so fits base b and height h.

If A=20ft2 and b=5ft,what is the value of h?

Substitute the values for A and b.
Clear the fraction.
Solve the equation for h.

Solving Formulas

The formula Abh is solved for A because A is alone on one side
of the formula. We can solve the formula for b or h by applying the
same strategy we use to solve an equation.

To solve the formula for h, first we clear the fraction:

Next, we divide both sides by b to get h alone on one side:

Comparing Equations and Formulas


Solve: 42 = 2x + 10

To solve the equation for x, we
subtract 10 on both sides, and then
we divide both sides by 2:


Solve the formula for x: y = mx + b

To solve the formula for x, we
subtract b on both sides, and then we
divide both sides by m:

Solving Problems With Formulas

To evaluate a formula, substitute the given value(s) for the
variable(s) and solve for the unknown variable.

To solve a formula for a specified variable,

1.Clear fractions and decimals if necessary.
2.Remove parentheses.
3.Combine like terms on the same side.
4.Add opposites to get the specified variable alone on one side
of the formula.
5.Multiply or divide to solve for the specified variable

Example 1(a) and (b)

a) Write a formula for the
perimeter of a rectangle. Use
L for the length, W for the
width and P for the perimeter.

P = 2L + 2W

b) Use the formula to find the
perimeter of a rectangular pool
that has a length of 24 feet
and a width of 16feet


P = 80 feet

Example 1(c) and (d)

c) A rectangular car lot has a
perimeter of 60 meters. Find
the length of the lot when the
width measures 12 meters.

L = 18 meters

d) Solve the formula P = 2L + 2W
for W.



Example 2

The length of an oil painting is 4 meters longer than twice its  width.
If the perimeter of the painting is 56 meters, find the length.

Read the problem:


Perimeter = 56 meters

Unknown: Width

Assign a variable: Width=x
Translate: Length=2x+4
Equation: Use the formula to write the equation:

Solve the equation:


State the answer:

Width = x = 8 meters
Length = 2(8) + 4 = 20 meters

Practice Exercise 1

Substitute the given values into the formula and solve for the
unknown variable.

A. t = 9.72

B. t = 97.2

C. t = 0.3

D. t = 3

Practice Exercise 2

Ted drove to his grand parents' house for a holiday weekend. The
total distance (one way) was 216 miles. If the trip took 8 hours,
how fast was he driving? Use the distance formula d=rt.

A.27 mph

B.29 mph

C.37 mph

D.17 mph

Practice Exercise 3

Solve the formula for A

Practice Exercise 4

Solve the formula for y: 2x + 3y = 6

Practice Exercise 5

Solve the formula for b

Practice Exercise 6

Find the length of a rectangular garden with a perimeter of 94
meters if the length is 5 meters more than the width.

A.52 meters

B.26 meters

C.21 meters

D.47 meters