Problem 51 - 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

The corresponding height for a woman who weighs 135 pounds according the HMO pamphlet's recommended weight is 5 feet and 7 inches.

Step 1: Set up the Equation

Based on the description given, devise the equation: \( 100 + 5h = W \), where \( h \) represents the number of inches over 5 feet, and \( W \) represents the weight in pounds.

Step 2: Substitute the Given Values into the Equation

Replace \( W \) with 135 pounds: \( 100 + 5h = 135 \).

Step 3: Solve for h

To find \( h \), subtract 100 from both sides of the equation: \( 5h = 135 - 100 \), so \( 5h = 35 \). Now, divide both sides by 5: \( h = 35 / 5 \), so \( h = 7 \). This means the woman is 7 inches taller than 5 feet.

Step 4: Convert to Feet and Inches

To convert 7 inches into feet and inches, note that one foot is equal to 12 inches, so 7 inches is equal to \((7/12) feet = 0 foot and 7 inches\). Therefore, the woman is 5 feet and 7 inches tall.