Solving Linear Equations
Use a Problem Solving Strategy
Learning Objectives
By the end of this section, you will be able to:
- Use a problem solving strategy for word problems
- Solve number word problems
- Solve percent applications
- Solve simple interest applications
Before you get started, take this readiness quiz.
Have you ever had any negative experiences in the past with word problems? When we feel we have no control, and continue repeating negative thoughts, we set up barriers to success. Realize that your negative experiences with word problems are in your past. To move forward you need to calm your fears and change your negative feelings.
Start with a fresh slate and begin to think positive thoughts. Repeating some of the following statements may be helpful to turn your thoughts positive. Thinking positive thoughts is a first step towards success.
I think I can! I think I can!
While word problems were hard in the past, I think I can try them now.
I am better prepared now—I think I will begin to understand word problems.
I am able to solve equations because I practiced many problems and I got help when I needed it—I can try that
with word problems.
It may take time, but I can begin to solve word problems.
If you take control and believe you can be successful, you will be able to master word problems.
Use a Problem Solving Strategy for Word Problems
Now that we can solve equations, we are ready to apply our new skills to word problems. We will develop a strategy we can use to solve any word problem successfully.
Normal yearly snowfall at the local ski resort is 12 inches more than twice the amount it received last season. The normal yearly snowfall is 62 inches. What was the snowfall last season at the ski resort?
| Step 1. Read the problem. | |
| Step 2. Identify what you are looking for. | What was the snowfall last season? |
| Step 3. Name what we are looking for and
choose a variable to represent it. |
Let the snowfall last season. |
| Step 4. Translate.
Restate the problem in one sentence with all the important information. |
|
| Translate into an equation. | |
| Step 5. Solve the equation. | |
| Subtract 12 from each side. | |
| Simplify. | |
| Divide each side by two. | |
| Simplify. | |
| Step 6. Check: First, is our answer reasonable?
Yes, having 25 inches of snow seems OK. The problem says the normal snowfall is twelve inches more than twice the number of last season. Twice 25 is 50 and 12 more than that is 62. |
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| Step 7. Answer the question. | The snowfall last season was 25 inches. |
Guillermo bought textbooks and notebooks at the bookstore. The number of textbooks was three more than twice the number of notebooks. He bought seven textbooks. How many notebooks did he buy?
He bought two notebooks.
Gerry worked Sudoku puzzles and crossword puzzles this week. The number of Sudoku puzzles he completed is eight more than twice the number of crossword puzzles. He completed 22 Sudoku puzzles. How many crossword puzzles did he do?