1. Section 2.5 Problem Solving

2. Objectives Apply the steps of a problem-solving strategy Solve consecutive integer problems Solve geometry problems

3. Objective 1: Apply the Steps of a Problem- Solving Strategy Strategy for Problem Solving:  1. Analyze the problem by reading it carefully to understand the given facts. What information is given? What are you asked to find? What vocabulary is given? Often, a diagram or table will help you visualize the facts of the problem.  2.Assign a variable to represent an unknown value in the problem. This means, in most cases, to let x = what you are asked to find. If there are other unknown values, represent each of them using an algebraic expression that involves the variable.  3. Form an equation by translating the words of the problem into mathematical symbols.  4. Solve the equation formed in step 3.  5.State the conclusion clearly. Be sure to include the units (such as feet, seconds, or pounds) in your answer.  6. Check the result using the original wording of the problem, not the equation that was formed in step 3.

4. EXAMPLE 1 The first part of California’s magnificent 17-Mile Drive begins at the Pacific Grove entrance and continues to Seal Rock. It is 1 mile longer than the second part of the drive, which extends from Seal Rock to the Lone Cypress. The final part of the tour winds through the Monterey Peninsula, eventually returning to the entrance. This part of the drive is 1 mile longer than four times the length of the second part. How long is each part of 17-Mile Drive? California Coastline

5. EXAMPLE 4 The year George Washington was chosen president and the year the Bill of Rights went into effect are consecutive odd integers whose sum is 3,580. Find the years. U.S. History

6. EXAMPLE 4 U.S. History Solve State George Washington was chosen president in the year 1789. The Bill of Rights went into effect in 1789 + 2 = 1791. Check 1789 and 1791 are consecutive odd integers whose sum is 1789 + 1791 = 3,580. The answers check.

7. Crime Scenes. Police used 400 feet of yellow tape to fence off a rectangular- shaped lot for an investigation. Fifty less feet of tape was used for each width as for each length. Find the dimensions of the lot. EXAMPLE 5 Crime Scenes Objective 3: Solve Geometry Problems