# If z varies inversely as w, and z=3 when w=8, how do you find z when w=2?

May 8, 2016

With inverse proportions, find the value of the constant first!.
$z = 12$

#### Explanation:

Write what given as a mathematical statement:

$z \propto \frac{1}{w} \text{ }$ z is inversely proportional to w

$z = \frac{k}{w} \text{ }$ multiply by a constant to form an equation

$k = z \times w \text{ }$ find the value of the constant. $3 \times 8 = 24$

$\therefore z = \frac{24}{w} \text{ }$ This is now the equation connecting z and w.

When $w = 2 , z = \frac{24}{2} \Rightarrow z = 12$