Question

Suppose that $y$ varies jointly with $w$ and $x$ and inversely with $z$ and $y=175$ when $w=5$, $x=20$ and $z=4$.

Write the equation that models the relationship.

Then find $y$ when $w=2$, $x=24$ and $z=6$.

Answer 1

To find the value of y:

The equation that models the relationship and find $y$ when $w=2,x=24andz=6$

If $y$ varies jointly with $w$ and $x$ and inversely with $z$ then we can write it as,

$\frac{y\times z}{w\times x}=k\text{for some constant}k$.

Now substitute the values of $x$ as $20$, $y$ as $175$, $z$ as $6$, and $w$ as $5$ in the above equation.

$\begin{array}{rcl}k& =& \frac{175\times 6}{5\times 20}\\ k& =& \frac{35\times 3}{1\times 10}\\ k& =& \frac{7\times 3}{1\times 2}\\ k& =& \frac{21}{2}\end{array}$

Therefore, the value of $k$ is $\frac{21}{2}$.

Now to find the value of $y$ when $w=2$, $x=24$ and $z=6$

$k=\frac{y\times z}{w\times x}$

Now substitute the values of $k$ as $\frac{21}{2}$, $x$ as $24$, $z$ as $6$, and $w$ as $2$ in the above equation.

$\begin{array}{rcl}\frac{21}{2}& =& \frac{y\times 6}{2\times 24}\\ \frac{2}{21}& =& \frac{2\times 24}{y\times 6}\\ \frac{1}{21}& =& \frac{2\times 4}{y\times 1}\\ y& =& 8\times 21\\ y& =& 168\end{array}$

Therefore, the value of $y=168$ when $w=2$, $x=24$ and $z=6$.