Chapter 10.6, Problem 53E

To determine

The value of Y when $X=8$ and $Z=3$ .

Explanation of Solution

Given information:

Y varies jointly as X and Z.

When $X=5$ and $Z=2$ ,then $Y=16$

Calculations:

Since Y varies jointly as X and Z.

Therefore,

  $\begin{array}{l}Y\propto X\\ Y\propto Z\\ or,\\ Y\propto XZ\\ Y=kXZ\end{array}$

Now, when $X=5$ and $Z=2$ ,then $Y=16$ . Putting the values in the above equation, we get,

  $\begin{array}{l}Y=kXZ\\ 16=k\times 5\times 2\\ 16=10k\\ k=\frac{16}{10}=1.6\end{array}$

Now, when $X=8$ and $Z=3$ ,then

  $\begin{array}{l}Y=kXZ\\ Y=1.6\times 8\times 3\\ Y=38.4\end{array}$