Question

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

If$\mathit{y}\mathbf{=}\mathbf{3}$ when $\mathit{x}\mathbf{=}\mathbf{2}$, find$\mathit{y}$ when $\mathit{x}\mathbf{=}\mathbf{4}$.

Short answer

When$x=4$then $\mathit{y}\mathbf{=}\frac{\mathbf{3}}{\mathbf{2}}$.

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 y when x=4 and if y=3 when x=2.

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$x_1=2,y_1=3$and$x_2=4$in $x_1{y}_1=x_2{y}_2$.

localid="1650904035932" $\begin{array}{l}2\left(3\right)=4\left(y_2\right)\\ 6=4y_2\\ y_2=\frac{6}{4}\\ y_2=\frac{3}{2}\end{array}$

Therefore when localid="1650904026878" $x=4$then localid="1650904022237" $y=\frac{3}{2}$.