2. SOLUTION Write a ratio EXAMPLE 1 VOLLEYBALL A volleyball team plays 14 home matches and 10 away matches. a. Find the ratio of home matches to away matches. = 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 = 14 12

3. SOLUTION EXAMPLE 1 Derek and his brother to combine their CD Collections. Derek has 44 CDs, and his brother has 52 CDs. Find the specified ratio. 1. Find the ratio of Derek ’ s CD to his brother ’ s CDs. = 11 13 1. Derek ’ s CD Brother ’ s CD 44 52 = 2. Find the ratio of Derek ’ s CD to entire collection. 2. Derek ’ s CD entire collection 44 44 + 52 = = 44 96 = 11 24 GUIDED PRACTICE for Example 1

4. Solve a proportion 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 =.

5. EXAMPLE 2 w 35 4 7 = Write original proportion. Multiply each side by 35. 140 7 = w Simplify. w = 20 Divide. w 35 4 7 = Solve the proportion. Check your solution. GUIDED PRACTICE for Example 2 4 7 w 35 =. 3.3.

6. EXAMPLE 2 9 2 m 12 = Write original proportion. Multiply each side by 12. 108 2 = m Simplify. 54 = m Divide. 9 2 m 12 = Solve the proportion. Check your solution. GUIDED PRACTICE for Example 2 m 12 9 2 =. 4.4.

7. EXAMPLE 2 z 54 5 9 = Write original proportion. Multiply each side by 54. 270 9 = z Simplify. z = 30 Divide. z 54 5 9 = Solve the proportion. Check your solution. GUIDED PRACTICE for Example 2 5 9 z 54 = 5.

8. Solve a multi-step problem 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. Solve a multi-step problem EXAMPLE 3 SOLUTION STEP 2 Solve the proportion. 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. Solve a multi-step problem EXAMPLE 3 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. Solve a multi-step problem 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. GUIDED PRACTICE for Example 3 WHAT IF ? In Example 3, suppose the elevator travels 125 feet in 5 seconds. Find the time it will take for elevator to travel from the lobby to the observation level. 6.

13. EXAMPLE 3 SOLUTION STEP 2 Solve the proportion. Write a proportion involving two ratios that compare the amount of time the elevator has ascended with the distance traveled. STEP 1 GUIDED PRACTICE for Example 3 5 Seconds x = 125 feet 1029

14. EXAMPLE 3 5 125 x 1029 = Write proportion. 5 125 =1029 x Multiply each side by 1029. 5145 125 = x Simplify. 41.16 = x Divide. ANSWER The elevator travels from the lobby to the observation level in 41.16 seconds. GUIDED PRACTICE for Example 3

15. GUIDED PRACTICE for Example 3 When two full moons appear in the same month. The seconds 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

16. EXAMPLE 3 SOLUTION STEP 2 Solve the proportion. Write a proportion involving two ratios that compare number of blue moons appear every year. STEP 1 GUIDED PRACTICE for Example 3 x 25 = 2 number 5 year

17. EXAMPLE 3 2 5 x 25 = Write proportion. 2 5 = 25 x Multiply each side by 25. 50 5 = x Simplify. 10 = x Divide. ANSWER 10 Blue moons are likely to occur in the next 25 years. GUIDED PRACTICE for Example 3