# If y varies inversely as x and y equals 18 when x equals 5, find y when x equals 3.

## Question:

If y varies inversely as x and y equals 18 when x equals 5, find y when x equals 3.

## Inverse Variation:

Inverse variation explains the relationship between two variables that are related in the opposite direction. For such variables, an increase in one variable decreases the other variable and vice versa.

## Answer and Explanation:

If the variable {eq}y {/eq} varies inversely as the variable {eq}x {/eq}, then we can write this relationship as:

- {eq}y\propto \dfrac{1}{x} {/eq}

Removing the proportionality sign and adding a proportionality constant, we have:

- {eq}y = \dfrac{k}{x} {/eq}

If the value of *y* is 18 when the value of *x* is 5, then:

- {eq}18 = \dfrac{k}{5} {/eq}

- {eq}k = 18\times 5 = 90 {/eq}

Thus, the equation showing the relationship between the two variables is:

- {eq}y = \dfrac{90}{x} {/eq}

Using the above equation, the value of *y* when *x = 3* is equal to:

- {eq}y = \dfrac{90}{3} = \boxed{30} {/eq}

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from High School Algebra I: Help and Review

Chapter 8 / Lesson 23