If x varies inversely as v, and x = 21 when v = 9, find x when v = 27.

Question:

If x varies inversely as v, and x = 21 when v = 9, find x when v = 27.

Inverse Variation:

Inverse variation explains the relationship between two variables that vary in the opposite direction. For such variables, their ratio is equal to a constant, known as the constant of variation.

Answer and Explanation:


If{eq}x {/eq} varies inversely as {eq}v {/eq}, then:

  • {eq}x\propto \dfrac{1}{v} {/eq}

Adding a proportionality constant to remove the proportionality sign:

  • {eq}x = \dfrac{k}{v} {/eq}

If {eq}x = 21 {/eq} when {eq}v = 9 {/eq}, then:

  • {eq}21 = \dfrac{k}{9} {/eq}

Solving for k:

  • {eq}k = 21\times 9 = 189 {/eq}

Therefore:

  • {eq}x = \dfrac{189}{v} {/eq}

Using the above equation, the value of {eq}x {/eq} when {eq}v = 27 {/eq} is:

  • {eq}x = \dfrac{189}{27} {/eq}
  • {eq}\boxed{\color{blue}{x = 7}} {/eq}

Learn more about this topic:

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Inverse Variation: Definition, Equation & Examples

from High School Algebra I: Help and Review

Chapter 8 / Lesson 23
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