Questions: A crew is made up of 8 men; the rest are women. 66 2/3% of the crew are men. How many people are in the crew?

Solution Steps

To find the total number of people in the crew, we can use the given percentage of men in the crew. We know that 66⅔% of the crew are men, and there are 8 men. We can set up a proportion to find the total number of people in the crew.

We know that \(66 \frac{2}{3} \% = \frac{200}{3} \%\) of the crew are men. The number of men in the crew is given as \(8\).

Let \(x\) be the total number of people in the crew. According to the percentage, we can express the number of men as: \[ \frac{200}{3} \% \text{ of } x = 8 \] This can be rewritten as: \[ \frac{200}{3} \cdot \frac{x}{100} = 8 \]

To isolate \(x\), we multiply both sides by \(100\) and then by \(\frac{3}{200}\): \[ x = 8 \cdot \frac{100 \cdot 3}{200} \] Calculating this gives: \[ x = 8 \cdot \frac{300}{200} = 8 \cdot 1.5 = 12 \]

Final Answer