1. Solving Proportions 4-2 Bell work: Find two ratios that are equivalent to each given ratio. 3535 1. 45 30 3. 90 60 3232, 10 12 2. 20 24 5656, 8989 4. 24 27 16 18, 9 15 6 10, Possible answers:

2. Solving Proportions 4-2 Problem of the Day What is the better buy? A $1.29 pack of gum that has 15 pieces, Or A $1.59 pack of gum that has 20 pieces? Explain your answer.

3. Solving Proportions 4-2 Learning Target: I can tell if ratios are proportional. I can solve a proportion.

4. Solving Proportions 4-2 Vocabulary RatioProportion Cross Product

5. Solving Proportions 4-2 Tell whether the ratios are proportional. 4 10 6 15 Since the cross products are equal, the ratios are proportional. 60 = ? 60 = 60 Find cross products. 60 4 10 6 15

6. Solving Proportions 4-2 Tell whether the ratios are proportional. Since the cross products are equal, the ratios are proportional. 20 20 = 20 Find cross products. 20 2424 5 10 2424 5 10 = ?

7. Solving Proportions 4-2 A mixture of fuel for a certain small engine should be 4 parts gasoline to 1 part oil. If you combine 5 quarts of oil with 15 quarts of gasoline, will the mixture be correct? 4 parts gas 1 part oil = ? 15 quarts gas 5 quarts oil 4 5 = 201 15 = 15 20 ≠ 15 The cross products are not equal. The mixture will not be correct. Set up equal ratios. Find the cross products.

8. Solving Proportions 4-2 A mixture for a certain brand of tea should be 3 parts tea to 1 part sugar. If you combine 4 tablespoons of sugar with 12 tablespoons of tea, will the mixture be correct? 3 parts tea 1 part sugar = ? 12 T tea 4 T sugar 3 4 = 121 12 = 12 12 = 12 The cross products are equal. The mixture will be correct. Set up equal ratios. Find the cross products.

9. Solving Proportions 4-2 The ratio of boys to girls in a soccer league is 5:4. If there are 55 boys in the league, how many girls are there? 5454 boys girls = 5454 = 55 x x = 44 ‏ 5x = 220 There are 44 girls in the league.

10. Solving Proportions 4-2 The ratio of cats to dogs at a kennel is 3:2. If there are 48 dogs at the kennel, how many cats are there? 3232 Cats Dogs = 3232 = x 48 x = 72 ‏ 2x = 144 There are 72 cats at the kennel.

11. Solving Proportions 4-2 A banana slug travels 4.5 inches in 120 minutes. At this rate of speed, how long would it take the slug to travel 12 inches? 4.5 in 120 min = 12 in s One option is to use a proportion: inches/minute. 4.5s = 1440 s = 320 minutes

12. Solving Proportions 4-2 A banana slug travels 4.5 inches in 120 minutes. At this rate of speed, how long would it take the slug to travel 12 inches? 4.5s = 1440 Multiply. Divide both sides by 25. The slug will travel 12 inches in 320 min. or 5 h 20 min. Another way to do the same problem: Simplify. 4.5 s = 320

13. Solving Proportions 4-2 A cable car travels 15 miles in 80 minutes. At this rate of speed, how long would it take the cable car to travel 45 miles? x = 240 15 miles 80 min = 45 miles x 15x = 3600

14. Solving Proportions 4-2 15s = 3600 Multiply. Divide both sides by 15. The cable car will travel 15 miles in 240 min. or 4 hours. Another way to do the same problem: Simplify. 15 s = 240 A cable car travels 15 miles in 80 minutes. At this rate of speed, how long would it take the cable car to travel 45 miles?

15. Solving Proportions 4-2 Lesson Quiz Tell whether the ratios are proportional. 48 42 = ? 16 14 1. 40 15 = ? 3434 2. Solve each proportion. 3. 4. 5. An elevator travels 342 feet as it goes from the lobby of a building to the top floor. It takes 7 seconds to travel the first 133 feet. If the elevator travels at the same rate, how much longer does it take reach the top floor? yes no n = 30 n = 16 11s 45 18 n 12 = n 24 6969 =

16. Solving Proportions 4-2 Assignment: Lesson 4.2, page 164, 9-16, 26-31