1. © 2012 Pearson Prentice Hall. All rights reserved. CHAPTER 4 Algebra: Equations and Inequalities

2. © 2012 Pearson Prentice Hall. All rights reserved. 2 4.4 Modeling with Proportions

3. © 2012 Pearson Prentice Hall. All rights reserved. 3 Objectives 1.Solve proportions. 2.Solve problems using proportions.

4. © 2012 Pearson Prentice Hall. All rights reserved. 4 Example 2: Solving a Linear Inequality Solve and graph the solution set: Solution: We will get x by itself on the left side.

5. © 2012 Pearson Prentice Hall. All rights reserved. A ratio compares quantities by division. The ratio of a to b can be expressed as a:b or

6. © 2012 Pearson Prentice Hall. All rights reserved. In a class, there are 15 girls and 20 boys. Find the ratio of boys to girls. The ratio of boys to girls is 4 to 3 or 4:3.

7. © 2012 Pearson Prentice Hall. All rights reserved. A proportion is a statement that says two ratios are equal.

8. © 2012 Pearson Prentice Hall. All rights reserved. Cross Product Principal for Proportions The cross products ad and bc are equal.

9. © 2012 Pearson Prentice Hall. All rights reserved. Solve the proportion and check: Example 1: Solving Proportions Check:

10. © 2012 Pearson Prentice Hall. All rights reserved. Solve the proportion: Example 1: Solving Proportions

11. © 2012 Pearson Prentice Hall. All rights reserved. Solving Applied Problems Using Proportions 1.Read the problem and represent the unknown quantity by x (or any letter). 2.Set up a proportion by listing the given ratio on one side and the ratio with the unknown quantity on the other side. Each respective quantity should occupy the same corresponding position on each side of the proportion. 3.Drop units and apply the cross-products principle. 4.Solve for x and answer the question.

12. © 2012 Pearson Prentice Hall. All rights reserved. If the gas bill for an apartment with 800 square feet is $45, how much would you expect the bill to be for a 1000 square foot apartment? 1.Represent the unknown. x = gas bill for 1000 square foot apartment 2.Set up the proportion. Example

13. © 2012 Pearson Prentice Hall. All rights reserved. If the gas bill for an apartment with 800 square feet is $45, how much would you expect the bill to be for a 1000 square foot apartment? 3.Drop the units and apply the cross-products principle. 4.Solve for x and answer the question. x = 56.25Divide both sides by 800. The gas bill for the 1000 square feet apartment should be $56.25. Example-continued

14. © 2012 Pearson Prentice Hall. All rights reserved. Capture-recapture method is used to determine the wildlife population when it is impossible to count each individual animal within a population. Sampling in Nature

15. © 2012 Pearson Prentice Hall. All rights reserved. Wildlife biologists catch, tag, and then release 135 deer back into a wildlife refuge. Two weeks later they observe a sample of 140 deer, 30 of which are tagged. Assuming the ratio of tagged deer in the sample holds for all deer in the refuge, approximately how many deer are in the refuge? Example 3: Applying Proportions: Estimating Wildlife Population

16. © 2012 Pearson Prentice Hall. All rights reserved. Wildlife biologists catch, tag, and then release 135 deer back into a wildlife refuge. Two weeks later they observe a sample of 140 deer, 30 of which are tagged. Assuming the ratio of tagged deer in the sample holds for all deer in the refuge, approximately how many deer are in the refuge? Example 3: continued