Solve each of the following problems using one or more conversion factors:
c. An athlete has 15% body fat by mass. What is the weight of fat, in pounds, of a 74-kg athlete?

Verified step by step guidance

1. Step 1: Understand the problem. The athlete has 15% body fat by mass, and their total mass is 74 kg. We need to calculate the weight of fat in pounds. This involves converting the percentage to mass in kilograms and then converting kilograms to pounds.
2. Step 2: Calculate the mass of fat in kilograms. Use the percentage formula: \( \text{Mass of fat (kg)} = \text{Total mass (kg)} \times \frac{\text{Percentage of fat}}{100} \). Substitute the values: \( \text{Mass of fat (kg)} = 74 \times \frac{15}{100} \).
3. Step 3: Convert the mass of fat from kilograms to pounds. Use the conversion factor: \( 1 \, \text{kg} = 2.20462 \, \text{lb} \). The formula is \( \text{Mass of fat (lb)} = \text{Mass of fat (kg)} \times 2.20462 \).
4. Step 4: Perform the unit conversion carefully, ensuring that the kilograms cancel out and the result is in pounds.
5. Step 5: Verify the calculation by checking the units and ensuring the conversion factor was applied correctly. The final result will be the weight of fat in pounds.

Key Concepts

Body Fat Percentage

Body fat percentage is a measure of the amount of fat in a person's body relative to their total body mass. It is expressed as a percentage and is crucial for understanding an individual's fitness level and health. In this context, the athlete's body fat percentage indicates that 15% of their total mass is composed of fat.

Mass to Weight Conversion

Mass and weight are related but distinct concepts; mass is the amount of matter in an object, while weight is the force exerted by gravity on that mass. To convert mass (in kilograms) to weight (in pounds), a conversion factor is used, where 1 kg is approximately equal to 2.20462 pounds. This conversion is essential for solving the problem as it requires the final answer in pounds.

Conversion Factors

Conversion factors are ratios that express how one unit of measurement relates to another. They are used to convert quantities from one unit to another, ensuring that calculations yield results in the desired units. In this problem, conversion factors will be applied to calculate the weight of fat in pounds based on the athlete's mass and body fat percentage.