# 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.

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}