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2.6 Write Ratios and Proportions • You will find ratios and write and solve proportions. • Essential Question: How do you find ratios and write and solve proportions? EXAMPLE Warm-Up1Exercises 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 home matches 7 14 a. = 10 = 5 away matches b. home matches all matches = 14 14 7 14 + 10 = 24 = 12 EXAMPLE 1Exercises Warm-Up GUIDED PRACTICE for Example 1 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. ANSWER 11 13 2. The number of Derek’s CDs to the number of CDs in the entire collection. ANSWER 11 24 EXAMPLE Warm-Up2Exercises Solve a proportion Solve the proportion 11 = x . 30 6 30 11 x 6 = 30 Write original proportion. x 11 6 = 30 30 Multiply each side by 30. 330 x = 6 55 = x Simplify. Divide. EXAMPLE 2Exercises Warm-Up GUIDED PRACTICE for Example 2 Solve the proportion. Check your solution. 3. 4 w = 7 35 ANSWER 20 EXAMPLE 2Exercises Warm-Up GUIDED PRACTICE for Example 2 Solve the proportion. Check your solution. m 9 4. 2 = 12 ANSWER 54 EXAMPLE 2Exercises Warm-Up GUIDED PRACTICE for Example 2 Solve the proportion. Check your solution. 5 z 5. 54 = 9 ANSWER 30 EXAMPLE Warm-Up3Exercises Solve a multi-step problem 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. EXAMPLE Warm-Up3Exercises 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. 5 150 x = 1029 STEP 2 Solve the proportion. Seconds feet EXAMPLE Warm-Up3Exercises Solve a multi-step problem 5 x = 150 1029 x 5 1029 = 1029 1029 150 5145 150 = x 34.3 = x Write proportion. Multiply each side by 1029. Simplify. Use a calculator. ANSWER The elevator travels from the lobby to the observation level in 34.3 seconds. EXAMPLE Warm-Up3Exercises 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. Warm-Up Exercises GUIDED PRACTICE 6. 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. ANSWER 41.16 sec Warm-Up Exercises GUIDED PRACTICE for Example 3 ASTRONOMY 7. 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. ANSWER 10 blue moons Daily Homework Quiz Warm-Up Exercises 1. 1 A chocolate chip cookie recipe calls for 2 4 3 cups of flour and cup of brown sugar. Find 4 the ratio of brown sugar to flour. ANSWER 1 3 Solve the proportion. 2. a 9 = 7 21 ANSWER 3 Daily Homework Quiz Warm-Up Exercises Solve the proportion. 3. m 32 = 28 14 ANSWER 4. 16 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 x 3 = 9 ; 36 color pages • You will find ratios and write and solve proportions. • Essential Question: How do you find ratios and write and solve proportions? • Ratios compare two quantities. • A proportion states that two ratios are equivalent. When writing a proportion, put like quantities in the same location in each ratio, such as nuts = nuts ounces ounces A ratio is an expression that relates one quantity to another by division, while a proportion is an equation of two ratios. Solve proportions with unknown numbers in the same way as you solve equations, by isolating the variable.