Objective: Modeling variation.

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Direct Variation and Proportion

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Objective: Modeling variation. Warm up Solve the inequality. a. b. c.

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Solving variation problems: Write an equation that models the given English statement. Substitute the given pair of values into the equation in step 1 and solve for k, the constant of variation. Substitute the value of k into the equation in step 1. Use the equation form step 3 to answer the problem’s questions.

Example 1 The volume of blood B, in a person’s varies directly as body weight, W. A person who weighs 160 pounds has approximately 5 quartz of blood. Estimate the number of quarts of blood in a person who weighs 200 pounds.

Multiple Choice Example 2 The distance from San Francisco to Los Angeles is 420 miles. The time that it takes to drive to San Francisco to Los Angeles depends on the rate. Choose the best answer. Time is directly proportional to rate. Time is inversely proportional to rate.

Example 3 The length of a violin string varies inversely as the frequency of its vibrations. A violin string 8 inches long vibrates at a frequency of 640 cycles per second. What is the frequency of a 10-inch string?

Example 4 The number of minutes needed to solve an exercise set of variation problems varies directly as the number of problems and inversely as the number of people working to solve the problems. It takes 4 people 32 minutes to solve 16 problems. How many minutes will it take 8 people to solve 24 problems?