Calculating New Weight After Body Fat Reduction

This problem involves understanding how changes in body composition, specifically body fat percentage, affect total body weight while assuming lean body mass remains constant. We need to calculate the initial lean body mass and then use the new fat percentage to find the new total weight.

Understanding Body Composition

Body weight is generally composed of two main components:

• Body Fat: This includes essential and storage fat.
• Lean Body Mass (LBM): This includes muscles, bones, organs, and water.

In scenarios like this, where a person loses weight by reducing body fat, it is typically assumed that the lean body mass remains constant unless stated otherwise. The reduction in total weight comes from the loss of fat.

Step-by-Step Calculation

Step 1: Calculate the Initial Fat Weight

The man initially weighs 150 lbs and has 30% body fat.

Initial Fat Weight = Initial Total Weight $\times$ Initial Fat Percentage

Initial Fat Weight = $150 \text{ lbs} \times 30\%$

Initial Fat Weight = $150 \text{ lbs} \times \frac{30}{100}$

Initial Fat Weight = $150 \text{ lbs} \times 0.30$

Initial Fat Weight = $45 \text{ lbs}$

Step 2: Calculate the Initial Lean Body Mass (LBM)

The lean body mass is the total weight minus the fat weight.

Initial Lean Body Mass = Initial Total Weight - Initial Fat Weight

Initial Lean Body Mass = $150 \text{ lbs} - 45 \text{ lbs}$

Initial Lean Body Mass = $105 \text{ lbs}$

Step 3: Determine the Percentage of Lean Body Mass in the New Scenario

The man reduces his body fat to 25%. This means that in the new state, the lean body mass will constitute the remaining percentage of the total weight.

New Lean Body Mass Percentage = $100\%$ - New Fat Percentage

New Lean Body Mass Percentage = $100\%$ - $25\%$

New Lean Body Mass Percentage = $75\%$

Step 4: Calculate the New Total Weight

We know the Lean Body Mass remains constant at 105 lbs, and this LBM now represents 75% of the New Total Weight.

New Lean Body Mass = New Total Weight $\times$ New Lean Body Mass Percentage

$105 \text{ lbs} = \text{New Total Weight} \times 75\%$

$105 \text{ lbs} = \text{New Total Weight} \times \frac{75}{100}$

$105 \text{ lbs} = \text{New Total Weight} \times 0.75$

To find the New Total Weight, we rearrange the equation:

New Total Weight = $\frac{105 \text{ lbs}}{0.75}$

New Total Weight = $140 \text{ lbs}$

So, if the man reduces his body fat percentage to 25% while maintaining his lean body mass, his new weight will be 140 lbs.

Summary Table

Using the New State values:

Lean Body Mass + Body Fat = Total Weight

$105 \text{ lbs} + W_{new} \times 0.25 = W_{new}$

$105 \text{ lbs} = W_{new} - 0.25 W_{new}$

$105 \text{ lbs} = W_{new} (1 - 0.25)$

$105 \text{ lbs} = W_{new} \times 0.75$

$W_{new} = \frac{105 \text{ lbs}}{0.75}$

$W_{new} = 140 \text{ lbs}$

Both methods yield the same result.

Conclusion

Based on the calculations, if a man weighing 150 lbs with 30% body fat reduces his fat percentage to 25% while keeping his lean body mass constant, his new weight will be 140 lbs.

The final answer is $\boxed{140 lbs}$.

Revision Table: Weight and Body Fat Calculation

Additional Information: Body Composition and Health

Body composition is an important health indicator, often considered more relevant than just total body weight. It provides insight into the proportion of fat mass versus lean body mass.

• Why is LBM important? Lean body mass, particularly muscle mass, is metabolically active, meaning it burns calories even at rest. Maintaining or increasing LBM is beneficial for metabolism, strength, and overall health.
• Healthy Body Fat Ranges: These vary depending on age, sex, and activity level. Generally, healthy ranges are lower for men than for women. Achieving a lower body fat percentage often involves a combination of diet and exercise aimed at reducing fat mass while preserving or building muscle mass.
• Weight Loss vs. Fat Loss: It's crucial to understand the difference. Simple weight loss can include loss of water or muscle. Healthy weight loss primarily focuses on losing fat mass while preserving muscle, which is reflected in a reduction in body fat percentage.
• Methods to Measure Body Fat: There are various methods, ranging from simple skinfold calipers to more advanced techniques like DXA scans, bioelectrical impedance analysis (BIA), and hydrostatic weighing.

This problem highlights a common scenario where fat loss leads to a change in total weight and body composition percentage, assuming the non-fat component remains stable.