Question
Of the cars in a used-car lot, 2/5 are the color gray. 13/ of the gray cars are electrically powered vehicles. What fraction of the cars on the lot are both gray and electrically powered? Leave your answer in simplified fraction form.
Answers
GPT-4o mini
Let the total number of cars on the lot be represented as \( x \).
Given that \( \frac{2}{5} \) of the cars are gray, the number of gray cars is:
\[
\frac{2}{5}x
\]
Next, it is stated that \( \frac{1}{3} \) of the gray cars are electrically powered. Therefore, the number of electrically powered gray cars is:
\[
\frac{1}{3} \times \frac{2}{5}x = \frac{2}{15}x
\]
To find the fraction of the total number of cars on the lot that are both gray and electrically powered, we take the number of electrically powered gray cars, \( \frac{2}{15}x \), and divide it by the total number of cars \( x \):
\[
\frac{\frac{2}{15}x}{x} = \frac{2}{15}
\]
Thus, the fraction of the cars on the lot that are both gray and electrically powered is:
\[
\boxed{\frac{2}{15}}
\]
Given that \( \frac{2}{5} \) of the cars are gray, the number of gray cars is:
\[
\frac{2}{5}x
\]
Next, it is stated that \( \frac{1}{3} \) of the gray cars are electrically powered. Therefore, the number of electrically powered gray cars is:
\[
\frac{1}{3} \times \frac{2}{5}x = \frac{2}{15}x
\]
To find the fraction of the total number of cars on the lot that are both gray and electrically powered, we take the number of electrically powered gray cars, \( \frac{2}{15}x \), and divide it by the total number of cars \( x \):
\[
\frac{\frac{2}{15}x}{x} = \frac{2}{15}
\]
Thus, the fraction of the cars on the lot that are both gray and electrically powered is:
\[
\boxed{\frac{2}{15}}
\]