Changing Words into Math | Setting Up and Solving Equations | Lesson Summary

Setting up and Solving Equations
http://www.homeschoolmath.net/teaching/teach-solve-word-problems.php
CA GR7 AF 1.1 &4.1

Your first step in setting up and solving equations should be to put the facts (your clues) down on paper. We will show you how to do it by example. Here's the problem:

The larger of two numbers is seven less than eight times the smaller. Their total is 29. What are the two numbers?

Step 1: Figure out what you are trying to find? (What are your unknowns?)

You are trying to find two numbers. You can call the smaller one x. Then, the other one becomes 8x - 7.

Step 2: What other facts do you have? (Put them on paper)

The total of the two numbers is 29. So you can write: 29 = total

Step 3: What equation can you write? (How are your clues related)

x + 8x - 7 = 29

Step 4: Solve your equation:

x + 8x - 7 = 29
9x - 7 = 29
9x = 36
x = 4 (your smaller number), and
 8x - 7 = 25 (your larger number)

Here's another problem, a little different from above:

Mike's salary is three times Pete's salary. Together they earn $2400. Find the salary of each.

Step 1: Figure out what you are trying to find? (What are the unknowns?)

You are looking for Pete's and Mike's salaries. You can call Pete's salary x. Then, Mike's salary becomes 3x.

Step 2: What other facts do you have? (Put them on paper)

Total of the salaries is $2400. So you can write: $2400 = total

Step 3: What equation can you write? (How are your clues related?)

x + 3x = $2400

Step 4: Solve your equation:

x + 3x = $2400
4x = $2400
x = $600 (Pete's salary), and
 3x = $1800 (Mike's salary)

Let's try another numbers problem:

Separate 80 into two parts, so that the second part is 20 less than four times the first part.

Step 1: Figure out what you are trying to find? (What are your unknowns?)

You are looking for two numbers. You can call the first one x.
Then, the second number becomes 4x - 20

Step 2: What other facts do you have?  (Put them on paper)

Total of the two numbers is 80.

Step 3: What equation can you write? (How are your clues related?) 

x + 4x - 20 = 80

Step 4: Solve your equation:

x + 4x - 20 = 80
5x = 100
x = 20 (the first number), and
 4x - 20 = 60 (the second number)

Now, let's stop and take Practice Exercise 12 - 2, Practice Exercise 12-2-a

For additional instructional material and practice exercises on this subject, go to:
www.mathgoodies.com/lessons/vol7/expressions.html.  

Also, for more exercises go to: www.algebrahelp.com/lessons/equationbasics/pgw.htm for their Equation Basics Worksheet and read the instructions and do the exercises that follow.  After answering a question click on the question number for a step by step solution to the problem.

Lesson Summary

In this lesson you have learned how to change 'word' expressions into mathematical expressions with math symbols; and how to set up and solve word problems, using algebra. You have learned to:
  1. Identify the unknowns (and represent them with literal numbers).
     
  2. Put the remaining facts (clues) on paper.
     
  3. Write your equation, and
     
  4. Solve your equation for the unknowns.

The ability to write and solve equations will prove valuable to you throughout your life.

Tutoring Video services are provided by www.PersonalProfessors.com  at an additional cost.

Next Page: Lesson 12 Problems