# Suppose that y varies jointly with w and x and inversely with z and y=400 when w=10, x=25 and z=5. How do you write the equation that models the relationship?

Apr 5, 2016

$y = 8 \times \left(\frac{w \times x}{z}\right)$

#### Explanation:

As $y$ varies jointly with $w$ and $x$, this means

$y \propto \left(w \times x\right)$ .......(A)

$y$ varies inversely with $z$ and this means

$y \propto z$ ...........(B)

Combining (A) and B), we have

$y \propto \frac{w \times x}{z}$ or $y = k \times \left(\frac{w \times x}{z}\right)$ .....(C)

As when $w = 10$, $x = 25$ and $z = 5$, $y = 400$

Putting these in (C), we get $400 = k \times \left(\frac{10 \times 25}{5}\right) = 50 k$

Hence #k=400/5=80 and our model equation is

$y = 8 \times \left(\frac{w \times x}{z}\right)$