Question

suppose that an individual has a body fat percentage of 15.7% and weighs 166 pounds. how many pounds of her weight is made up of fat? round your answer to the nearest tenth.

Explanation:

Step1: Convert percentage to decimal

To find the fat weight, we first convert the percentage \(15.7\%\) to a decimal by dividing by 100. So, \(15.7\% = \frac{15.7}{100}=0.157\).

Step2: Multiply by total weight

Then we multiply this decimal by the total weight (166 pounds) to find the fat weight. The formula is \(Fat\ weight = Total\ weight\times Fat\ percentage\ (in\ decimal)\). So, \(Fat\ weight = 166\times0.157\).
Calculating \(166\times0.157\):
\[

$$\begin{align*} 166\times0.157&=(160 + 6)\times0.157\\ &=160\times0.157+6\times0.157\\ &=25.12+0.942\\ &=26.062 \end{align*}$$

\]

Step3: Round to nearest tenth

Now we round \(26.062\) to the nearest tenth. The hundredth digit is 6, which is greater than or equal to 5, so we round up the tenth digit. So, \(26.062\approx26.1\).

Answer:

\(26.1\) pounds