Question

Use the following information. When a person walks, the pressure P on each boot sole varies inversely with the area A of the sole. Denise is walking through deep snow, wearing boots that have a sole area of 29 square inches each. The boot-sole pressure is 4 pounds per square inch when she stands on one foot. The constant of variation is Denise’s weight in pounds. What is her weight?

Short answer

Denise weights 116 pounds.

Step-by-step solution

Understand the Components of the Problem

Here, we're working with an inverse variation problem. This means that one quantity increases as the other one decreases. The formula needed for an inverse variant is \(k = P \cdot A\), where \(k\) is a constant, \(P\) is the pressure of the boot's sole, and \(A\) is the area of the boot's sole. The weight of Denise acts as the constant of variation in this particular situation.

Input the Given Values

We are given that the pressure \(P\) on Denise's boot when she stands on one foot is 4 pounds per square inch and that the area \(A\) of the boot's sole is 29 square inches. These values are to be substituted into the formula: \(k = P \cdot A\) which transforms into \(k = 4 \cdot 29\).

Calculate Denise's Weight

The calculation from the previous step will give us the value of \(k\), which is the constant of variation and represents Denise's weight in this scenario. Therefore, Denise's weight is \(k = 4 \cdot 29 = 116\) pounds.