MTH 100 CBI
Applications of Linear Equations
Formulas and Problem Solving
Objectives
1. Solve a Formula for a Given Variable.
2. Solve Application Problems Involving
Geometric Formulas
3. Solve Application Problems Involving Money
4. Solve Application Problems Involving
Mixtures
Objective 1
• Solving a formula for a specific variable
involves isolating that variable.
• All of the techniques used in solving a linear
equation are valid.
Objective 1 Examples
1. Solve the formula C = tm for t.
2. Solve the formula C  1 f (s  b) for s.
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Objective 2
• The three most commonly-used formulas
involve perimeter of a triangle (P = a + b + c),
perimeter of a rectangle (P = 2l + 2w), and
area of a triangle (A = ½ bh).
• In many cases, drawing a picture will help to
illustrate the problem situation.
Objective 2 Examples
1. An athletic field is twice as long as it is wide.
If the perimeter of the field is 78 meters,
determine the dimensions of the field.
2. The area of a triangular sail for a boat is 96
square feet. If the base of the sail is 8 feet
long, find its height.
Objective 3
• Important: simple interest is calculated by
multiplying the amount invested by the
interest rate (expressed as a decimal).
• In many cases, a table is used to set up the
equations needed to solve the problem.
Objective 3 Example
• Juanita has $39,000 to invest in two accounts
that pay simple interest on an annual basis.
One pays 6% simple interest and the other
pays 5% simple interest. How much would she
have to invest in each account to earn a total
of $2,150 after one year?
Objective 4
• Mixture problems are very similar to money
problems in the way they are set up.
Objective 4 Examples
1. Suppose 2 pints of a 5% alcohol solution are
mixed with 8 pints of a 90% alcohol solution.
What is the concentration of alcohol in the
next 10-pint mixture?
2. How much of an 80% orange juice drink must
be mixed with 55 gallons of a 20% orange
juice drink to obtain a mixture that is 50%
orange juice?