Question

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

If$y=2$ when $x=0.5$, find$y$ when $x=3$.

Short answer

When $x=3$, $y=\frac{1}{3}$.

Step-by-step solution

Step 1. Product rule for inverse variation.

If$\left(a_1,b_1\right)$ and$\left(a_2,b_2\right)$ are solutions of an inverse variation, then the products$a_1{b}_1$ and$a_2{b}_2$ are equal.

Step 2. Apply product rule.

Apply product rule for inverse variation.

$\begin{array}{c}{x}_1{y}_1=x_2{y}_2\\ \left(0.5\right)\left(2\right)=3\left(y\right)\end{array}$

Step 3. Simplify.

Simplify the above obtained equation.

$\begin{array}{c}\frac{1}{3}=\frac{3y}{3}\\ y=\frac{1}{3}\end{array}$

Therefore, when width="36">x=3, $y=\frac{1}{3}$.