1. 3.5 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Write Ratios and Proportions

2. 3.5 Warm-Up ANSWER 3 Solve the equation. ANSWER 30 2. (6x + 3) = 14 2 3 1. x = 25 5 6 ANSWER 95 3. – 7 = 12 g 5

3. 3.5 Warm-Up ANSWER $9.95 4. You buy three identical polyester film balloons and a birthday card. The card costs $3.95. Find the cost of each balloon if your total bill before tax was $33.80.

4. 3.5 Example 1 VOLLEYBALL A volleyball team plays 14 home matches and 10 away matches. a. Find the ratio of home matches to away matches. SOLUTION = 7 5 a. home matches away matches 14 10 = b. Find the ratio of home matches to all matches. b. home matches all matches 14 14 + 10 = = 14 24 = 7 12

5. 3.5 Guided Practice Derek and his brother decide to combine their CD collections. Derek has 44 CDs, and his brother has 52 CDs. Find the specified ratio. 1. The number of Derek ’ s CDs to the number of his brother ’ s CDs. 2. The number of Derek ’ s CDs to the number of CDs in the entire collection. 11 13 ANSWER 11 24 ANSWER

6. 3.5 Example 2 11 6 x 30 = Write original proportion. Multiply each side by 30. 330 6 = x Simplify. 55 = x Divide. 11 6 x 30 = x Solve the proportion 11 6 =.

7. 3.5 Guided Practice Solve the proportion. Check your solution. 4 7 w 35 = 3. 20 ANSWER m 12 9 2 = 4. 54 ANSWER 5 9 z 54 = 5. 30 ANSWER

8. 3.5 Example 3 ELEVATORS The elevator that takes passengers from the lobby of the John Hancock Center in Chicago to the observation level travels 150 feet in 5 seconds. The observation level is located on the 94th floor, at 1029 feet above the ground. Find the time it takes the elevator to travel from the lobby to the observation level.

9. 3.5 Example 3 SOLUTION Write a proportion involving two ratios that compare the amount of time the elevator has ascended with the distance traveled. STEP 1 x 1029 = 5 Seconds 150 feet

10. 3.5 Example 3 STEP 2 Solve the proportion. 5 150 x 1029 = Write proportion. 5 150 =1029 x Multiply each side by 1029. 5145 150 = x Simplify. 34.3 = x Use a calculator. ANSWER The elevator travels from the lobby to the observation level in 34.3 seconds.

11. 3.5 Example 3 You can use a table to check the reasonableness of your answer. CHECK The solution, 34.3 seconds, is slightly less than 35 seconds, and 1029 feet is slightly less than 1050 feet. So, the solution is reasonable.

12. 3.5 Guided Practice WHAT IF ? In Example 3, suppose the elevator travels 125 feet in 5 seconds. Find the time it will take for the elevator to travel from the lobby to the observation level. 6. ANSWER 41.16 sec When two full moons appear in the same month. The second full moon is called a blue moon. On average, 2 blue moons occur every 5 years. Find the number of blue moons that are likely to occur in the next 25 years. 7. ASTRONOMY ANSWER 10 blue moons

13. 3.5 Lesson Quiz 1. A chocolate chip cookie recipe calls for cups of flour and cup of brown sugar. Find the ratio of brown sugar to flour. 3 4 1 4 2 Solve the proportion. 2. a 7 9 21 = ANSWER 1 3 3 32 28 3. = m 14 16 ANSWER

14. 3.5 Lesson Quiz 4. A printer can print 12 color pages in 3 minutes. How many color pages can the printer print in 9 minutes? Write and solve a proportion to find the answer. ANSWER 12 3 = x 9 ; 36 color pages