<Question>
Karla drove her vehicle 12,000 miles last year. How many gallons of gasoline would she have saved last year had she driven a fuel-efficient hybrid car averaging 48 miles per gallon rather than an SUV averaging 15 miles per gallon?
</Question>

<think>
<Plan_1>
Okay, let's see. Karla drove her vehicle 12,000 miles last year. The question is asking how many gallons of gasoline she would have saved if she had driven a hybrid car that gets 48 miles per gallon instead of her SUV which gets 15 miles per gallon. Hmm, right. So, essentially, we need to find the difference in gasoline consumption between the two cars over the 12,000 miles she drove.

First, I think the approach here is to calculate how many gallons each car would use for 12,000 miles and then subtract the more efficient car's consumption from the less efficient one. That difference should give the savings. Let me break it down step by step.

Starting with the SUV. The SUV gets 15 miles per gallon. So, for 12,000 miles, the number of gallons used would be the total miles divided by the miles per gallon. That is, 12,000 miles divided by 15 miles per gallon. Let me compute that.
12,000 divided by 15. Well, 15 times 800 is 12,000 because 15 times 100 is 1,500, so 15 times 800 is 12,000. So, the SUV would use 800 gallons.

Now, the hybrid car is 48 miles per gallon. So, using the same formula, 12,000 miles divided by 48 miles per gallon. Let me calculate that.
48 goes into 12,000 how many times? Let's see. 48 times 200 is 9,600. Subtract that from 12,000, we get 2,400. Then, 48 times 50 is 2,400. So, 200 plus 50 is 250. Therefore, the hybrid would use 250 gallons.

Then, the savings would be the difference between the two. So 800 gallons minus 250 gallons.
That's 550 gallons.

Wait, let me double-check my calculations to make sure I didn't make a mistake.

<prompt_1.1> Recheck the calculations for the gallons used by the SUV and the hybrid car. </prompt_1.1>

Alternatively, maybe set it up as unit conversions. For the SUV: 12,000 miles times (1 gallon / 15 miles) = 12,000 /15 gallons.
Same as before, 800 gallons. For the hybrid: 12,000 miles times (1 gallon /48 miles) = 12,000 /48 gallons.

<prompt_1.2> Use unit conversions to verify the calculations for the SUV and the hybrid car. </prompt_1.2>

Another way to think about it: maybe find the difference per gallon or something. But I think the straightforward approach is correct.
The key is that the savings are in gallons, so we need to find how many fewer gallons the hybrid uses compared to the SUV over the same distance.

Let me just verify with another angle. If driving 12,000 miles, the SUV uses 800 gallons, and the hybrid uses 250 gallons. So 800 - 250 = 550. So, 550 gallons saved. That seems like a lot, but considering the SUV is only 15 mpg and the hybrid is 48, which is a significant improvement, maybe it's reasonable.

Alternatively, maybe compute the miles per gallon difference, but that's not directly helpful. The savings per mile would be (1/15 - 1/48) gallons per mile. Let me compute that.

<prompt_1.3> Calculate the fuel savings per mile and verify the total savings. </prompt_1.3>
</Plan_1>

<Execution_1>
<execution_1.1>
For the SUV: 12,000 divided by 15. 15 times 100 is 1500, so 15 times 800 is 12,000. Correct. SUV uses 800 gallons.
</execution_1.1>

<execution_1.2>
Let's compute 12,000 divided by 15. 15 into 12,000. 15*800=12,000, so 800. Hybrid: 12,000 divided by 48. 48*25=1,200. So, 48*250=12,000. Yes, that's 250. So the difference is 550 gallons.
</execution_1.2>

<execution_1.3>
1/15 is approximately 0.0667 gallons per mile, and 1/48 is approximately 0.0208 gallons per mile. Subtracting those gives 0.0667 - 0.0208 ≈ 0.0459 gallons per mile. Then, multiply by 12,000 miles: 0.0459 * 12,000 ≈ 550.8 gallons. That's approximately 550.8, which rounds to about 551 gallons. Hmm, but my initial calculation was exactly 550. So, there's a slight discrepancy here. Wait, why is that?
</execution_1.3>
</Execution_1>

<Plan_2>
Based on execution_1.3:
Let me check the exact fractions. 1/15 - 1/48. To subtract these fractions, find a common denominator. 15 and 48. The least common multiple of 15 and 48. Let's see, 15 factors into 3*5, 48 is 16*3, so LCM is 3*5*16=240. So, converting both fractions to denominator 240.

<prompt_2.1> Calculate the exact fuel savings per mile using fractions and verify the total savings. </prompt_2.1>

So, the discrepancy was because I approximated 1/48 as 0.0208, which is actually exact because 1/48 is 0.0208333...., so when multiplied by 12,000, it's 12,000*0.0208333... = 250 exactly. Similarly, 1/15 is 0.066666...., so 12,000*0.066666... = 800 exactly. So, the difference is 800 - 250 = 550 exactly. So, the initial approximation was correct. So, the exact answer is 550 gallons.

Therefore, Karla would have saved 550 gallons last year by driving the hybrid instead of the SUV.

I think that's solid. Let me check once more for any possible errors. The key assumptions here are that the miles driven are the same, which they are (12,000 miles), and that the fuel efficiency numbers are accurate. There's no consideration of other factors like maintenance costs or different driving habits, which the question doesn't mention. It's strictly about fuel consumption. So, as per the given information, 550 gallons is the correct answer.
</Plan_2>

<Execution_2>
<execution_2.1>
1/15 = 16/240 and 1/48 = 5/240. So, 16/240 - 5/240 = 11/240 gallons per mile. Then, total gallons saved is 11/240 * 12,000. Let's compute that. 12,000 divided by 240 is 50. 50 times 11 is 550. So, exactly 550 gallons.
</execution_2.1>
</Execution_2>

<Final_answer>
Therefore, Karla would have saved $\boxed{550}$ gallons of gasoline last year had she driven a fuel-efficient hybrid car.
</Final_answer>
</think>