Problem 51 - College Algebra Essentials

Question

An HMO pamphlet contains the following recommended weight for women: "Give yourself 100 pounds for the first 5 feet plus 5 pounds for every inch over 5 feet tall." Using this description, what height corresponds to a recommended weight of 135 pounds?

Step-by-Step Solution

Answer

The corresponding height to a weight of 135 pounds is 5 feet 7 inches.

Step 1: Understand the Given Relationship

The relationship between weight and height is given as: 100 pounds for the first 5 feet and then additional 5 pounds for every inch above 5 feet. This relationship can be expressed as an equation: \( w = 100 + 5(h - 60) \), where \( w \) is the weight in pounds and \( h \) is the height in inches.

Step 2: Substitute the Given Weight

The problem states that the woman's weight is 135 pounds. Substitute \( w = 135 \) in the equation. This results in: \( 135 = 100 + 5(h - 60) \)

Step 3: Solve the Equation

To solve for \( h \), begin by subtracting 100 from both sides of the equation, which gives \( 35 = 5(h - 60) \). Then divide both sides by 5, resulting in \( h - 60 = 7 \). Finally, add 60 to both sides to isolate \( h \), giving \( h = 67 \).

Step 4: Convert the Height to Feet and Inches

The height \( h = 67 \) inches should be converted to feet and inches for simplicity. There are 12 inches in a foot, so \( 67 \,inches = 5 \,feet \,7 \,inches \).