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?

Question

[___] 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.