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Direct Variation and Proportion Problems

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Learn how to find equations of direct variation, solve problems with direct proportion, and understand the steps involved. Practice problems and solutions included.

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Direct Variation and Proportion Problems

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  1. Variation and Proportion Direct Proportion

  2. The formula for direct variation can be written as y=kx where k is called the constant of variation. • The steps to follow to solve a problem with direct variation: • Write the equation: y = kx • Substitute for x and y • Solve for k • Rewrite the equation with k as the constant

  3. Problem:Find an equation of direct variation where y varies directly as x. One pair of values is y = 7 when x = 35. • Write the equation: y = kx y = kx • Substitute for x and y 7 = k(35) • Solve for k 7/35 = k, or k = 1/5 • Rewrite the equation with k y = 1/5x as the constant

  4. Problem:The cost of operating a TV varies directly as the number (n) of hours it is in operation. It costs $14.00 to operate a standard size color TV continuously for 30 days. • y = cost; x = number of hours • y = kx • 14 = k(30) • 14/30 = k, or k = 7/15 • Equation: • y = 7/15x

  5. Practice Problems: Answers • y = 28 when x = 7 • Equation: y = 4x • y = 30 when x = 8 • Equation: y = 15/4x • y = 400 when x = 125 • Equation: y = 16/5x • y = 630 when x = 175 • Equation: y = 18/5x

  6. Practice Problems: Answers (Continued) • The number (b) of bolts a machine can make varies directly as the time it operates. It can make 6578 bolts in 2 hours. How many bolts can it make in 5 hours? • Set up a proportion: • 6578/2 = x/5 • x = 16445

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