Chapter 1.11, Problem 3E

To determine

To fill: The relation of the quantity $z$ to the quantities $x$ and $y$ if the quantities $x,y$ and z are related by $z=3\frac{x}{y}$.

Answer to Problem 3E

The quantity $z$ is directly proportional to the quantity $x$ and inversely proportional to the quantity $y$.

Explanation of Solution

If the quantities $x,y$ and $z$ are related by an equation,

$z=k\frac{x}{y}$ (1)

For some constant $k\ne 0$, we say that $z$ varies directly as $x$, or $z$ is inversely proportional to $y$. The constant $k$ is called the constant of proportionality.

The given equation is,

$z=3\frac{x}{y}$ (2)

Compare the equation (2) with equation (1) to infer that z is directly proportional to x and z is inversely proportional to y.

Therefore, the quantity $z$ is directly proportional to the quantity $x$ and inversely proportional to the quantity $y$.