1. Section 7.1 Ratio, Proportion and Variation Geometry

2. Learning Objectives  Write ratios in fraction form.  Solve proportions.  Solve real-world problems using proportions.  Solve real-world problems using direct variation.  Solve real-world problems using inverse variation.

3. Ratios A ratio is a comparison of two quantities using division. For two nonzero numbers, a and b, the ratio of a to b is written as a:b (read a to b) or ab.

4. EXAMPLE 1 Writing Ratios According to the Sporting Goods Manufacturers’ Association, 95.1 million Americans participate in recreational swimming, 56.2 million Americans participate in recreational biking, 52.6 million Americans participate in bowling, and 44.5 million Americans participate in freshwater fishing. Find each: (a) The ratio of recreational swimmers to recreational bikers (b) The ratio of people who fish to people who bowl

5. Proportions A proportion is a statement of equality of two ratios. Two ratios form a proportion if the cross products of their numerators and denominators are equal. For example, the ratio of 4:7 and 8:14 can be written as a proportion as shown.

6. EXAMPLE 3 Deciding if a Proportion is True Decide if each proportion is true or false.

7. EXAMPLE 4 Solving a Proportion Solve the proportion for x.

8. EXAMPLE 5 Solving a Proportion Solve the proportion:

9. EXAMPLE 6 Applying Proportion to Fuel Consumption While on a spring break trip, a group of friends burns 12 gallons of gas in the first 228 miles, then stops to refuel. If they have 380 miles yet to drive, and the SUV has a 21-gallon tank, can they make it without refueling again?

10. EXAMPLE 7 Applying Proportion to Wildlife Population As part of a research project, a biology class plans to estimate the number of fish living in a lake thought to be polluted. They catch a sample of 35 fish, tag them, and release them back into the lake. A week later, they catch 80 fish and find that 5 of them are tagged. About how many fish live in the lake?