Problem 33 - Algebra and Trigonometry

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

So, a woman who is 5 feet and 7 inches tall is recommended to weigh 135 pounds according to the HMO pamphlet.

Step 1: Interpret the Statement

According to the pamphlet, a woman should weigh 100 pounds for the first 5 feet of her height, and then an additional 5 pounds for every inch she is over 5 feet tall. This can be seen as a linear equation.

Step 2: Formulate Equation

Letting \( x \) denote the number of inches taller than 5 feet, the equation becomes \( 100 + 5x = 135 \)

Step 3: Solve the Equation

Now, solve the equation for \( x \). Subtract 100 from both sides to get \( 5x = 35 \). Then, divide both sides by 5 to yield \( x = 7 \)

Step 4: Convert to Height

As \( x \) represents height in inches over 5 feet, add the 7 inches to the 5 feet. Ensure it's understood that 1 foot equals 12 inches. Therefore, the height is \( 5 \times 12 + 7 = 67 \) inches or 5 feet 7 inches.