Question
3.) Over the summer Kathleen sold 1,092 jars of jam at outdoor markets. She made a $12 profit on each one. She wants to use the profits to buy a piano for $11,500. She said, "Since 1,000 × 12 = 12,000, and 1,092 is greater than 1,000, I know my profits add up to more than $12,000. So, I can buy the piano." Explain whether Kathleen's conclusion is lodgical
Answers
GPT-4o mini
Kathleen's conclusion is not logical because she has made an error in her reasoning about the actual profits.
First, let's break down the profits she made:
- She sold 1,092 jars of jam at a profit of $12 each.
- To calculate her total profit, we can multiply the number of jars sold by the profit per jar:
\[
1,092 \text{ jars} \times 12 \text{ dollars/jar} = 13,104 \text{ dollars}
\]
Kathleen's calculation of \(1,000 \times 12 = 12,000\) is accurate, but her conclusion that she can afford the piano based solely on the fact that 1,092 is greater than 1,000 is misleading.
The important factor is that her total profit of $13,104 is indeed greater than $11,500, which means she can buy the piano. However, while her reasoning leading to the conclusion that she can afford the piano seems to stem from comparing the number of jars to 1,000, it doesn't directly support or clarify her ability to purchase it.
In conclusion, while she can afford the piano based on her profits, the logic she used to arrive at that conclusion is flawed because it doesn't directly relate the total profit to the cost of the piano. The correct reasoning should focus on the actual total profit calculated rather than a comparison to 1,000 jars.
First, let's break down the profits she made:
- She sold 1,092 jars of jam at a profit of $12 each.
- To calculate her total profit, we can multiply the number of jars sold by the profit per jar:
\[
1,092 \text{ jars} \times 12 \text{ dollars/jar} = 13,104 \text{ dollars}
\]
Kathleen's calculation of \(1,000 \times 12 = 12,000\) is accurate, but her conclusion that she can afford the piano based solely on the fact that 1,092 is greater than 1,000 is misleading.
The important factor is that her total profit of $13,104 is indeed greater than $11,500, which means she can buy the piano. However, while her reasoning leading to the conclusion that she can afford the piano seems to stem from comparing the number of jars to 1,000, it doesn't directly support or clarify her ability to purchase it.
In conclusion, while she can afford the piano based on her profits, the logic she used to arrive at that conclusion is flawed because it doesn't directly relate the total profit to the cost of the piano. The correct reasoning should focus on the actual total profit calculated rather than a comparison to 1,000 jars.