How can the weight loss goal for a 20-year-old male runner, currently at 11% body fat with a target of 8% body fat, be calculated?
Understand the Problem
The question provides information about a college athlete's body fat measurements and asks for the calculation of his weight loss goal based on specified formulas. Specifically, it outlines the current and target body fat percentages, as well as the athlete's height and weight.
Answer
The athlete's weight loss goal is approximately 5.65 pounds.
Answer for screen readers
The athlete's weight loss goal is approximately 5.65 pounds.
Steps to Solve
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Identify Current and Target Body Fat Percentages
The athlete currently has a body fat percentage of 11%. The target body fat percentage is set at 8%.
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Calculate Lean Body Mass
Lean Body Mass (LBM) can be calculated using the formula:
$$ \text{LBM} = \text{Weight} \times (1 - \frac{\text{Body Fat Percentage}}{100}) $$
Substituting in the current values:
$$ \text{LBM} = 160 \times (1 - \frac{11}{100}) = 160 \times 0.89 = 142.4 \text{ pounds} $$
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Calculate Target Weight for Desired Body Fat Percentage
To find the target weight with the desired body fat percentage, use the formula:
$$ \text{Target Weight} = \frac{\text{LBM}}{1 - \frac{\text{Target Body Fat Percentage}}{100}} $$
Plugging in the values:
$$ \text{Target Weight} = \frac{142.4}{1 - \frac{8}{100}} = \frac{142.4}{0.92} \approx 154.35 \text{ pounds} $$
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Calculate Weight Loss Goal
The weight loss goal can be determined by subtracting the target weight from the current weight:
$$ \text{Weight Loss Goal} = \text{Current Weight} - \text{Target Weight} = 160 - 154.35 \approx 5.65 \text{ pounds} $$
The athlete's weight loss goal is approximately 5.65 pounds.
More Information
To achieve the target body fat percentage of 8%, the athlete needs to lose around 5.65 pounds based on calculations from current and target body fat measurements. Maintaining lean body mass is key in weight loss for athletes to ensure that the weight lost comes from fat rather than muscle.
Tips
- Misunderstanding Body Fat Percentage: It's crucial to use percentages correctly in calculations. Make sure to convert percentages to decimal form (e.g., 11% to 0.11).
- Incorrect Formula Application: Ensure the formulas are applied in the right order and context. Read them carefully to avoid confusion.
- Rounding Errors: When calculating, keep track of significant digits to prevent early rounding from affecting the final value.
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