# If z varies inversely as w, and z=10 when w=0.7, how do you find z when w=20?

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Jun 25, 2016

When $w = 20 , z = 0.35$

#### Explanation:

As per data provided :
$z = 10 ,$ when $w = 0.7$

As $z$ is inversely proportional to $w :$

color(blue)(z prop 1/w

Introducing constant $k :$

$z = k \times \frac{1}{w}$

$z = \frac{k}{w}$

$k = z \times w$

$k = 10 \times 0.7$

color(blue)( k = 7

Now, we are required to find $z$ , when $w = 20.$

$z = \frac{k}{w}$

Substituting values for $k$ and $w :$

$z = \frac{7}{20}$

$z = 0.35$

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