A female client weighs 180 pounds. You measure her body fat and determine it is 26%. What is the goal weight if body fat is reduced to 22%?

To determine the goal weight of the female client when aiming to reduce her body fat percentage from 26% to 22%, we first need to calculate her current lean body mass and then the weight she should be at to achieve the target body fat percentage.

Her current weight is 180 pounds, with a body fat percentage of 26%. To find her fat mass, we multiply her weight by her body fat percentage:

Current fat mass = 180 pounds x 0.26 = 46.8 pounds.

Next, we calculate her lean body mass by subtracting her fat mass from her total weight:

Lean body mass = 180 pounds - 46.8 pounds = 133.2 pounds.

Now, to find out the goal weight at 22% body fat with the same lean body mass, we need to set up an equation. Let the goal weight be represented as 'X.' At 22% body fat, lean body mass remains constant, so:

Lean body mass = 0.78 * X, because 100% - 22% = 78% of the goal weight will be lean mass.

Setting the equation:

133.2 pounds = 0.78 * X.

To isolate X, divide