# The number of kilograms of water in a human body varies directly as the mass of the body. An 87...

## Question:

The number of kilograms of water in a human body varies directly as the mass of the body. An 87 kg person contains 58 kg of water. How many kilograms of water are in a 72 kg person?

## Direct Proportionality

If one measure is directly proportional to another measure, this means that an increase or decrease in one measure by some number x would lead to an increase or decrease in the other measure by the same number x.

The two measures might be related by some proportionality constant to show a linear dependence as y = kx.

Given initial conditions, our idea would be to firstly identify the proportionality constant of the equation {eq}y = kx...(1) {/eq}.

Assume that y, the dependent variable, is the number of kilograms of water, while x, the independent variable, is the mass of the body. Rearranging equation (1) and given initial conditions of y = 58, x = 87, we obtain:

{eq}k = \frac{y}{x} = \frac{58}{87} {/eq}

Our equation then becomes:

{eq}y = \frac{58}{87}x {/eq}

Given x = 72, we can solve for y now:

{eq}y = \frac{58}{87}x = \frac{58}{87}\cdot 72 = 48 {/eq}.

Thus, a 72 kg person would contain 48 kg of water. 