1. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Hawkes Learning Systems: Introductory Algebra Section 3.1b: Applications of Linear Equations: Addition and Subtraction

2. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Objective o Solve applications involving linear equations of the form x + b = c.

3. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Procedure for Solving Applications Many applications (or word problems) can be solved by proceeding as follows: Procedure for Solving Applications 1.Read the problem carefully. 2.Let a variable represent the unknown quantity. 3.Set up an equation representing the known relationships. 4.Solve the equation. 5.Check to see that the solution makes sense.

4. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Procedure for Solving Applications Note You may find that many of the applications in this section can be solved by applying simple logic rather than algebraic equations. However, you will be better off in the long run if you use these simple problems to practice and learn the algebraic techniques you will need to solve the trickier problems that you will soon run into.

5. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Procedure for Solving Applications Note (cont.) Reasoning is a fundamental part of all of mathematics. However, keep in mind that the algebraic techniques you are learning are important, also involve reasoning, and will prove very useful in solving more complicated problems in later sections and in later courses.

6. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Example 1: Solving x + b = c A T-shirt costs a total of $7.95, including $0.40 sales tax. What was the actual price of the T-shirt? Solution: First, note the key words: A T-shirt costs a total of $7.95, including $0.40 sales tax. What was the actual price of the T-shirt? Here, we let x = the actual price of the T-shirt. Thus, we have the equation given on the following slide. Continued on the next slide…

7. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Example 1: Solving x + b = c (cont.) price of the T-shirt sales tax total cost Continued on the next slide…

8. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Example 1: Solving x + b = c (cont.) Use the Addition Principle of Equality. Simplify. The price of the T-shirt was $7.55. Check: Substitute x = 7.55. True statement.

9. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Example 2: Solving x + b = c The original price of a calculator was reduced by $12.95. The sale price was $77.10. What was the original price? Solution: First, note the key words: The original price of a calculator was reduced by $12.95. The sale price was $77.10. What was the original price? Here, we let x = the original price of the calculator. Thus, we have the equation given on the following slide.

10. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Example 2: Solving x + b = c (cont.) original price reduction sale price Continued on the next slide…

11. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Example 2: Solving x + b = c (cont.) Use the Addition Principle of Equality. Simplify. The original price of the calculator was $90.05. Check: Substitute x = 90.05. True statement.

12. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Example 3: Solving x + b = c The sum of the measures of all angles in a triangle is 180⁰. If the measures of two of the angles are 66⁰ and 25⁰, what is the measure of the third angle? Solution: First, note the key words: The sum of the measures of all angles in a triangle is 180⁰. If the measures of two of the angles are 66⁰ and 25⁰, what is the measure of the third angle? Here, we let x = the measure of the third angle. Thus, we have the equation given on the following slide.

13. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Example 3: Solving x + b = c (cont.) first angle second angle third angle Continued on the next slide… total of the angles

14. HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2011 Hawkes Learning Systems. All rights reserved. Example 3: Solving x + b = c (cont.) Use the Addition Principle of Equality. Simplify. The measure of the third angle is 89⁰. Check: Substitute x = 89. True statement. Simplify.