Question

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

Ifrole="math" localid="1648108402222" $y=3$ when role="math" localid="1648108411399" $x=9$, find$x$ when $y=1$.

Short answer

When $y=1$, $x=27$.

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.

$\begin{array}{c}{x}_1{y}_1=x_2{y}_2\\ \left(9\right)\left(3\right)=x\left(1\right)\end{array}$

Step 3. Simplify.

Simplify the above obtained equation.

$x=27$

Therefore, when $y=1$, $x=27$.