Q5. - Algebra 1

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 $\mathit{x}\mathbf{=}\mathbf{4}$.

Step-by-Step Solution

Answer

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

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

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

Therefore when $x=4$ then $y=\frac{3}{2}$.