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. Identify the given information: The athlete has 15% body fat by mass and weighs 74 kg.
2. Convert the athlete's total body weight from kilograms to pounds using the conversion factor: 1 kg = 2.20462 pounds.
3. Calculate the total body weight in pounds by multiplying the weight in kilograms by the conversion factor.
4. Determine the weight of the body fat by calculating 15% of the total body weight in pounds.
5. Use the formula: Weight of fat (pounds) = Total body weight (pounds) * 0.15 to find the weight of fat.

Key Concepts

Percentage by Mass

Percentage by mass is a way to express the concentration of a component in a mixture. It is calculated by dividing the mass of the component by the total mass of the mixture and multiplying by 100. In this case, the athlete's body fat percentage indicates that 15% of their total mass is fat.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one unit to another unit. In this problem, the athlete's mass is given in kilograms, but the desired output is in pounds. Understanding how to convert between these units is essential for accurately calculating the weight of fat.

Mass Calculation

Mass calculation involves determining the mass of a specific component based on the total mass and its percentage. To find the weight of fat in this scenario, you multiply the total mass of the athlete by the percentage of body fat (expressed as a decimal). This calculation provides the mass of fat in kilograms, which can then be converted to pounds.