Question

Find an equation of variation in which y varies jointly as x and z and inversely as the product of w and​ p, where yequalsstartfraction 7 over 28 endfraction when xequals7​, zequals4​, wequals7​, and pequals8.

Answer 1

To solve this problem you must apply the proccedure shown below:

1. You have that $y$ varies jointly as $x$ and $z$ and inversely as the product of $w$ and​ $p$. Therefore, you can write the following equation, where $k$ is the constant of proportionality:

$y=k(\frac{xz}{wp} )$

2. Now, you must solve for the constant of proportionality, as following:

$k=\frac{ywp}{xz}$

3. Susbtiute values:

$y=\frac{7}{28} \\ x=7\\ z=4\\ w=7\\ p=8$

$k=\frac{(\frac{7}{28})(7)(8))}{(7)(4)} =0.5$

4. Substitute the value of the constant of proportionality into the equation:

$y=0.5(\frac{xz}{wp})$

The answer is: $y=0.5(\frac{xz}{wp})$