Question

Assume that$\mathit{y}$ varies inversely as $\mathit{x}$.

If$\mathit{y}\mathbf{=}\mathbf{6}$ when $\mathit{x}\mathbf{=}\mathbf{3}$, find$\mathit{x}$ when $\mathit{y}\mathbf{=}\mathbf{5}$.

Short answer

When$y=5$ then $\mathit{x}\mathbf{=}\frac{\mathbf{18}}{\mathbf{5}}$.

Step-by-step solution

Step 1. Define an inverse variation equation.

The inverse variation equation of two variables $x$ and$y$ is given by

$xy=k$

Where,$k$ is called the constant of variation.

Step 2. Define the product rule for inverse variation.

If$(x_1,y_1)$ and$(x_2,y_2)$ are solutions of an inverse variation, then the equation$x_1{y}_1=x_2{y}_2$ is called the product rule for inverse variation.

Step 3. Calculate x when y=5 and if y=6 when x=3.

Assume that $y$varies inversely as $x$.

Then the product rule for inverse variation is given by

$x_1{y}_1=x_2{y}_2$

Substitute $x_1=3,y_1=6$and $y_2=5$in $x_1{y}_1=x_2{y}_2$.

$\begin{array}{l}3\left(6\right)=x_2\left(5\right)\\ 18=5x_2\\ x_2=\frac{18}{5}\end{array}$

Therefore when $y=5$then $x=\frac{18}{5}$.