Question

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

If$\mathit{y}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{5}$ when $\mathit{x}\mathbf{=}\mathbf{6}$, find$\mathit{y}$ when $\mathit{x}\mathbf{=}\mathbf{-}\mathbf{16}$.

Short answer

When $x=-16,\mathit{y}\mathbf{=}\mathbf{-}\frac{\mathbf{9}}{\mathbf{16}}$.

Step-by-step solution

Step 1. Product rule for inverse variation.

If$(a_1,b_1)$ and$(a_2,b_2)$ 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.

$\begin{array}{c}{x}_1{y}_1=x_2{y}_2\\ \left(6\right)\left(1.5\right)=(-16)\left(y\right)\end{array}$

Step 3. Simplify.

Simplify the above obtained equation.

$\begin{array}{l}\frac{9}{-16}=\frac{-16y}{-16}\\ y=-\frac{9}{16}\end{array}$

Therefore, when$x=-16,y=-\frac{9}{16}$.