Q4. - Algebra 1

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 $\mathit{y}\mathbf{=}\mathbf{5}$.

Step-by-Step Solution

Answer

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

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 $x=\frac{18}{5}$.