Of the cars in a used-car lot, 3/4 are less than 4 years old. 1/4 of the cars on the lot are both less than 4 years old and also get at least 60 miles to the gallon. What fraction of the cars that are less than 4 years old also get 60 miles to the gallon?

Question

Responses
3 1/2
3/16
3
4/12

Answer 1

To find the fraction of cars that are less than 4 years old and also get at least 60 miles to the gallon, we can use the information given:

1. Let \( x \) be the total number of cars in the lot.
2. According to the problem, \( \frac{3}{4} \) of the cars are less than 4 years old. Therefore, the number of cars less than 4 years old is \( \frac{3}{4}x \).
3. We also know that \( \frac{1}{4} \) of the cars in the lot are both less than 4 years old and get at least 60 miles to the gallon. Thus, the number of cars that are both less than 4 years old and get at least 60 miles to the gallon is \( \frac{1}{4}x \).

Now, to find the fraction of cars that are less than 4 years old and also get 60 miles to the gallon, we need to divide the number of cars that meet both conditions by the number of cars that are less than 4 years old:

\[ \text{Fraction} = \frac{\text{Number of cars less than 4 years old that get 60 mpg}}{\text{Number of cars less than 4 years old}} = \frac{\frac{1}{4}x}{\frac{3}{4}x} \]

The \( x \) cancels out:

\[ \text{Fraction} = \frac{\frac{1}{4}}{\frac{3}{4}} = \frac{1}{4} \cdot \frac{4}{3} = \frac{1}{3} \]

Thus, the fraction of the cars that are less than 4 years old and also get at least 60 miles to the gallon is \(\frac{1}{3}\).

Since none of the answers provided in the responses match \(\frac{1}{3}\), let's check them one by one:

• 3 1/2: This is not a fraction form of cars and doesn’t work.
• 3/16: This is a fraction, but not the right answer.
• 3: This is not a fraction either.
• 4/12: This simplifies to \( \frac{1}{3} \).

The correct choice based on simplification is 4/12, as it is equivalent to \(\frac{1}{3}\).

Answer 2

thats not in the list choose from the list

Answer 3

Apologies for any confusion. Given the options provided:

1. 3 1/2 (which is 3.5)
2. 3/16
3. 3
4. 4/12 (which simplifies to 1/3)

Based on our calculations, the specific fraction that matches the calculation we did was \( \frac{1}{3} \), which corresponds to \( \frac{4}{12} \) when simplified.

Since 4/12 is the only fraction from the list that simplifies to \(\frac{1}{3}\), that is the correct answer from your list.

So, the answer is 4/12.

Answer 4

wrong

Answer 5

I apologize for the confusion in my previous responses. Let's re-evaluate the problem step by step to clarify.

1. Fraction of cars less than 4 years old: \( \frac{3}{4} \) of all cars.
2. Fraction of cars that are both less than 4 years old and get at least 60 miles per gallon: \( \frac{1}{4} \) of all cars.

To find the fraction of cars that are less than 4 years old and also get 60 miles to the gallon, we can use the following:

\[ \text{Number of cars less than 4 years old} = \frac{3}{4}x \]

\[ \text{Number of cars that are less than 4 years old and get 60 mpg} = \frac{1}{4}x \]

Now, to find the fraction of cars that are less than 4 years old and also get at least 60 miles to the gallon, we divide the number of cars that meet both conditions by the number of cars less than 4 years old:

\[ \text{Fraction} = \frac{\frac{1}{4}x}{\frac{3}{4}x} \]

Cancelling out \( x \) gives:

\[ \text{Fraction} = \frac{\frac{1}{4}}{\frac{3}{4}} = \frac{1}{3} \]

However, to match the response options you provided, we need to find a valid answer:

• 3 1/2: equals 3.5 (not a fraction of cars)
• 3/16: just a fraction (not logically connected)
• 3: not a fraction of cars
• 4/12: equals \(\frac{1}{3}\)

Given this understanding, I realized the options were misunderstood as I did not choose from your list before.

However, since there is no exact fraction of \(\frac{1}{3}\), it was incorrect to assign one of those options as the correct answer without first confirming the relationships correctly or noticing overlaps in presentation.

The best fit from the options 4/12 correctly simplifies—which is \(\frac{1}{3}\). So, if the prompt for deciding among these options resulted in confusion on valid choices opposed to fractions, it may have represented unique observations of different ratios not echoed in calculation at face value.

I sincerely appreciate your patience. The valid choice reflecting the fraction from recognizing conditions correctly in the list fits best from simplifications of ratios or similar.