SOLUTION

2. 14 14 10 14 + 10 a. = = 14 7 14 24 12 5 home matches home matches b. = = = all matches away matches EXAMPLE 1 Write a ratio VOLLEYBALL A volleyball team plays 14 home matches and 10 away matches. a.Find the ratio of home matches to away matches. b.Find the ratio of home matches to all matches. SOLUTION

3. 44 44 1. = = 44 + 52 52 44 11 11 96 24 13 Derek’s CD Derek’s CD = 2. = = entire collection Brother’s CD EXAMPLE 1 for Example 1 GUIDED PRACTICE 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. 2.Find the ratio of Derek’s CD to entire collection. SOLUTION

4. 330 . x 11 x x Solve the proportion = = 30 30 30 6 6 x = 11 11 6 6 30 30 = EXAMPLE 2 Solve a proportion Write original proportion. Multiply each side by 30. Simplify. 55= x Divide.

5. . = 140 4 w 4 4 = 35 7 7 7 7 3. w w 35 35 w = 35 35 = EXAMPLE 2 for Example 2 GUIDED PRACTICE Solve the proportion. Check your solution. Write original proportion. Multiply each side by 35. Simplify. w= 20 Divide.

6. . = 108 m 9 m m = 2 12 12 12 2 4. 9 9 2 2 m = 12 12 = EXAMPLE 2 for Example 2 GUIDED PRACTICE Solve the proportion. Check your solution. Write original proportion. Multiply each side by 12. Simplify. 54= m Divide.

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

8. The elevator that takes passengers from the lobby of the John Hancock Center in Chicago to the observation level travels150feet 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. EXAMPLE 3 Solve a multi-step problem ELEVATORS

9. 5 Seconds x = 150 1029 feet STEP 2 Solve the proportion. EXAMPLE 3 Solve a multi-step problem SOLUTION STEP 1 Write a proportion involving two ratios that compare the amount of time the elevator has ascended with the distance traveled.

10. 1029 = 1029 5 150 ANSWER The elevator travels from the lobby to the observation level in 34.3 seconds. x x 5 5145 = x = 1029 1029 150 150 EXAMPLE 3 Solve a multi-step problem Write proportion. Multiply each side by1029. Simplify. 34.3 =x Use a calculator.

11. EXAMPLE 3 Solve a multi-step problem CHECK You can use a table to check the reasonableness of your answer 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. 6. 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. GUIDED PRACTICE for Example 3

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

14. 1029 = 1029 5 125 ANSWER The elevator travels from the lobby to the observation level in 41.16 seconds. x x 5 5145 = x = 1029 1029 125 125 EXAMPLE 3 for Example 3 GUIDED PRACTICE Write proportion. Multiply each side by1029. Simplify. 41.16 =x Divide.

15. 7. 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. GUIDED PRACTICE for Example 3 Astronomy

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

17. 2 x = 25 5 25 = 25 2 5 50 x = 5 ANSWER 10 Blue moons are likely to occur in the next 25 years. x 25 EXAMPLE 3 for Example 3 GUIDED PRACTICE Write proportion. Multiply each side by25. Simplify. 10 =x Divide.