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?

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Answer 1 · 2016-04-05T16:33:11

$y = 8 \times (\frac{w \times x}{z})$ $y=8xx((wxx x)/z)$

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

$y \propto (w \times x)$ $yprop(wxx x)$ .......(A)

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

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

Combining (A) and B), we have

$y \propto \frac{w \times x}{z}$ $yprop(wxx x)/z$ or $y = k \times (\frac{w \times x}{z})$ $y=kxx((wxx x)/z)$ .....(C)

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

Putting these in (C), we get $400 = k \times (\frac{10 \times 25}{5}) = 50 k$ $400=kxx((10xx25)/5)=50k$

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

$y = 8 \times (\frac{w \times x}{z})$ $y=8xx((wxx x)/z)$