Chapter 5
Using Equations to Solve Business Problems
Student Performance Objectives
Section I Solving Basic Equations
5-1 Understanding the Concepts, Terminology, and Rules of Equations
Section II Using Equations to Solve Business-Related Word Problems
5-4 Setting Up and Solving Business-Related Word Problems by Using Equations
Chapter Notes, Teaching Tips and Lecture Launchers
• Equations may give some students a problem if they haven’t taken algebra recently, or at all.
I usually cover this material quite meticulously; being sure that students understand the
fundamentals of creating and solving equations.
• Spotlight: This is an important chapter for business math success since a number of other
• Spotlight: Students often ask of geometry and trigonometry, “What do I need this for? –
When am I ever going to use this stuff?” Trying to explain the practical value of calculating
the volume of a tetrahedron can be difficult. Some basic knowledge of equations, on the
• This chapter lends itself to extra practice. Remind students, the MathCue.Business software,
used in the tutorial mode, can provide students with an endless supply of practice exercises
for any Performance Objective they choose.
• The Collaborative Learning Activity, “Using Formulas in Business,” is a good opportunity for
Section I Solving Basic Equations
• Be sure students know the difference between an expression (no equal sign) and an equation,
(contains an equal sign).
• Remind students that in equations, a letter which stands alone, such as M, is assumed to have
a coefficient of “one” before it.
• For example: M = 1M
• Spotlight: It is important for students to remember that an equation is a statement of
• Point out to students that they can easily “verify” their answer to an equation by substituting
the root for each variable in the original equation.
• Differentiate between multiple variables occurring on one side of an equation as compared
with multiple variables occurring on both sides of the equation.
• When they appear on one side, such as 3R + R = , they can simply be combined to 4R
• Use Transparency 5-4, Key Words and Phrases for Creating Equations, to help illustrate how
equations are created from written sentences. Emphasize to students that equations are
sentences that use numbers instead of words.
• Spotlight: Point out to students that the Solutions to the Examples at the end of Section I
have the key words double underlined. This should be helpful in illustrating the words used
• Collaborative Learning Activity. I use this activity before going on to Section II, Word
Problems. It provides important reinforcement for solving equations. Inevitably what
Section II Using Equations to Solve Business-Related Word Problems
• Spotlight – Classroom Activity: Have students speak with businesspeople in your area and
report to the class about how equations and formulas are used in such areas as retailing,
manufacturing, real estate, insurance and banking.
• Spotlight: Don’t always use the letter X to represent the unknown. Get students into the
• Spotlight – Classroom Activity: Have students work Try-It Exercises 12 through 16 in pairs.
This will help reduce the initial anxiety of this sometimes difficult concept.
• Collaborative Learning Activity. Have students work in groups of two’s or three’s to write
and solve five word problems. Next, have each group exchange and solve the problems of
another group. Now have them compare answers and resolve any differences.
• Spotlight: Be sure students remember, when writing a proportion, each ratio must be in the
same “order.”
• For example, if one ratio is dollars to units, the other must also be dollars to units.
• Collaborative Learning Activity: Have students break into groups of two’s or three’s to write
some business related word problems that can be solved using ratio and proportion.
Questions Students Always Ask
“Why do you do that?”
• Emphasize to students that these are algebraic principles that will make sense once
“How do I know what to do?”
• Note that the words used in a problem will clue us in as to what operation to perform.
“Why do you multiply the coefficient by both numbers inside the parentheses?”
• Many students don’t understand the distributive properties of multiplication. Draw two
“Why do you subtract a positive number from (or add a negative number to, or multiply the
inverse of a number times) the other side of the equation?”
• Remind students that, because of the equals sign, we don’t want to change the value of
“Why do I need to learn this? I’ll never use algebra in real life!”
• Students often feel frustration because they can’t see the applicability of what they’re