Final answer:
To decrease his body fat to 17% while maintaining the same lean body mass, the student's target weight would be approximately 185 lbs. This is calculated by first determining the lean body mass by subtracting the current fat mass from the total weight, and then dividing by the remainder after subtracting the desired body fat percentage expressed as a decimal.
Step-by-step explanation:
The student wishes to find out his target body weight if he wants to decrease his body fat percentage to 17%, while maintaining the same lean body mass. To calculate this, we first find out his current fat mass by multiplying his weight with his current body fat percentage. With a weight of 202 lbs and 24% body fat, his fat mass is 48.48 lbs. We then subtract this fat mass from the total body weight to get his lean body mass, which is 153.52 lbs. To find the target weight at 17% body fat, we divide the lean body mass by 1 minus the desired body fat percentage (expressed as a decimal), which gives us the target weight that includes both the lean body mass and the desired fat mass.
Current fat mass = total body weight × current body fat percentage
202 lbs × 24% (0.24) = 48.48 lbs
Current lean body mass = total body weight - current fat mass
202 lbs - 48.48 lbs = 153.52 lbs
Target total body weight = lean body mass ÷ (1 - desired body fat percentage)
153.52 lbs ÷ (1 - 17% (0.17)) = 153.52 lbs ÷ 0.83 ≈ 185 lbs
Therefore, the student's target body weight to decrease his body fat to 17% while preserving lean body mass is approximately 185 lbs.