2. CHAPTER 7 Ratio and Proportion Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 7.1Introduction to Ratios 7.2Rates and Unit Prices 7.3Proportions 7.4Applications of Proportions 7.5Geometric Applications

3. OBJECTIVES 7.4 Applications of Proportions Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. aSolve applied problems involving proportions.

4. 7.4 Applications of Proportions a Solve applied problems involving proportions. Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Proportions have applications in such diverse fields as business, chemistry, health sciences, and home economics, as well as in many areas of daily life. Proportions are useful in making predictions.

5. EXAMPLE 7.4 Applications of Proportions a Solve applied problems involving proportions. 2Recommended Dosage. Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To control a fever, a doctor suggests that a child who weighs 28 kg be given 320 mg of a liquid pain reliever. If the dosage is proportional to the child’s weight, how much of the medication is recommended for a child who weighs 35 kg?

6. EXAMPLE 7.4 Applications of Proportions a Solve applied problems involving proportions. 2Recommended Dosage. Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 1. Familiarize. We let t = the number of milligrams of the liquid pain reliever. 2. Translate.

7. EXAMPLE 7.4 Applications of Proportions a Solve applied problems involving proportions. 2Recommended Dosage. Slide 7Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 3. Solve.

8. EXAMPLE 4. Check. We substitute into the proportion and check cross products: The cross products are the same. 5. State. The dosage for a child who weighs 35 kg is 400 mg. 7.4 Applications of Proportions a Solve applied problems involving proportions. 2Recommended Dosage. Slide 8Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

9. EXAMPLE 7.4 Applications of Proportions a Solve applied problems involving proportions. 4Waist-to-Hip Ratio. Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To reduce the risk of heart disease, it is recommended that a man’s waist-to-hip ratio be 0.9 or lower. Mac’s hip measurement is To meet the recommendation, what should his waist measurement be? Source: Mayo Clinic

10. EXAMPLE 7.4 Applications of Proportions a Solve applied problems involving proportions. 4Waist-to-Hip Ratio. Slide 10Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 1. Familiarize. We let w = waist measurement. 2. Translate.

11. EXAMPLE 7.4 Applications of Proportions a Solve applied problems involving proportions. 4Waist-to-Hip Ratio. Slide 11Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 3. Solve.

12. EXAMPLE 7.4 Applications of Proportions a Solve applied problems involving proportions. 4Waist-to-Hip Ratio. Slide 12Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 4. Check. As a check, we divide 36 by 40 and get 0.9. This is the desired ratio. 5. State. Mac’s recommended waist measurement is 36 in. or less.

13. EXAMPLE 7.4 Applications of Proportions a Solve applied problems involving proportions. 5Construction Plans. Slide 13Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Architects make blueprints of projects to be constructed. These are scale drawings in which lengths are in proportion to actual sizes. The Hennesseys are adding a rectangular deck to their house. The architectural blueprints are rendered such that in. on the drawing is actually 2.25 ft on the deck. The width of the deck on the drawing is 4.3 in. How wide is the deck in reality?

14. EXAMPLE 7.4 Applications of Proportions a Solve applied problems involving proportions. 5Construction Plans. Slide 14Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 1. Familiarize. We w = let the width of the deck. 2. Translate.

15. EXAMPLE 7.4 Applications of Proportions a Solve applied problems involving proportions. 5Construction Plans. Slide 15Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 3. Solve.

16. EXAMPLE 7.4 Applications of Proportions a Solve applied problems involving proportions. 5Construction Plans. Slide 16Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 4. Check. The cross products are the same. 5. State. The width of the deck is 12.9 ft.