Question

Of the cars in a used car lot 2/5 are the color gray and 1/3 of the gray cars are electrically powered vehicles what fraction of the cars on the lot are both gray and powered?
[___] of the cars are gray and electrically powered

Answer 1

Let's denote the total number of cars in the used car lot as \( C \).

1. **Finding the number of gray cars**:
The fraction of cars that are gray is \( \frac{2}{5} \), so the number of gray cars is:
\[
\text{Number of gray cars} = \frac{2}{5}C
\]

2. **Finding the number of gray and electrically powered cars**:
We know that \( \frac{1}{3} \) of the gray cars are electrically powered vehicles. Therefore, the number of gray and electrically powered cars is:
\[
\text{Number of gray and electrically powered cars} = \frac{1}{3} \times \text{(Number of gray cars)} = \frac{1}{3} \times \frac{2}{5}C = \frac{2}{15}C
\]

3. **Finding the fraction of all cars that are gray and electrically powered**:
The fraction of all cars that are both gray and electrically powered is:
\[
\frac{\text{Number of gray and electrically powered cars}}{C} = \frac{\frac{2}{15}C}{C} = \frac{2}{15}
\]

Thus, the fraction of cars that are gray and electrically powered is \( \frac{2}{15} \).

So, the final answer is:
\[
\frac{2}{15}
\] of the cars are gray and electrically powered.