Problem 106 - Introductory Algebra for College Students

Question

A woman'sheight, \(h\), is related to the length of her femur, \(f\) (the bone from the knee to the hip socket), by the formula \(f=0.432 h-10.44 .\) Both \(h\) and \(f\) are measured in inches. A partial skeleton is found of a woman in which the femur is 16 inches long. Police find the skeleton in an area where a woman slightly over 5 feet tall has been missing for over a year. Can the partial skeleton be that of the missing woman? Explain.

Step-by-Step Solution

Answer

Yes, the partial skeleton could possibly be that of the missing woman, as the calculated height based on the femur length is approximately 61.28 inches, which is slightly over 5 feet, the height of the missing woman.

Step 1: Convert feet to inches

First, the given height 5 feet needs to be converted to inches because the formula uses inches. 1 foot = 12 inches, therefore 5 feet = 5 x 12 = 60 inches. The height of the woman is now 60 inches.

Step 2: Substitute the given femur length into the equation

The given equation is \(f=0.432h - 10.44\). Substitute the given femur length f = 16 inches into the equation. Therefore the equation becomes \(16 = 0.432h - 10.44\)

Step 3: Solve the equation for h

To solve for h, first add 10.44 to both sides of the equation to get rid of the negative number, giving a new equation \(26.44 = 0.432h\). Then, divide each side of the equation by 0.432 to solve for h. This gives the calculated height as \( h = 26.44 / 0.432 = 61.28 inches approximately\)

Step 4: Compare the calculated height with the given height

To solve the problem, compare the calculated height with that of the missing woman (60 inches). In this case, the calculated height (61.28 inches) is slightly over 5 feet (or 60 inches), indicating that the skeleton can be that of the missing woman. Although there is a difference of around 1.28 inches, it is a negligible difference in height especially considering that the height of a person can vary due to various factors such as posture, time of the day, etc. Therefore, based on the analysis it can be concluded that the partial skeleton could possibly be that of the missing woman.