Q5. - Algebra 1

Question

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

If  $y=3$ when $x=9$, find $x$ when $y=1$.

Step-by-Step Solution

Answer

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

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