Problem 55 - College Algebra

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

According to the HMO pamphlet's rule, the height that corresponds to a recommended weight of 135 pounds is 5 feet 7 inches.

Step 1: Understand the problem

The problem gives us the formula for calculating weight based on height. We need to find the height for a given weight of 135 pounds. First, let's understand the formula. The rule is that for the first 5 feet of height, the weight is 100 pounds, and after that, for each inch over 5 feet, the weight increases by 5 pounds.

Step 2: Set up the equation

Since the given weight is 135 pounds, we can set this equal to the formula derived from the rule: 100 pounds (for the first 5 feet) plus 5 pounds (for each inch over 5 feet). The height over 5 feet is unknown, we'll designate this as \( x \). So the equation looks like this: \( 100 + 5x = 135 \).

Step 3: Solve for x

To find \( x \), which represents the number of inches over 5 feet, we need to isolate \( x \) in the equation. First, subtract 100 from both sides of the equation to get \( 5x = 35 \). Then, divide both sides by 5 to solve for \( x \), which gives \( x = 7 \).

Step 4: Interpret the result

The result \( x = 7 \) means that the height exceeding 5 feet is 7 inches. So the height corresponding to a weight of 135 pounds is 5 feet 7 inches.