Question
Eoin plans to purchase 6.50 pounds of cheese that costs $4.75 per pound. He used the following steps to estimate the cost.
Step 1: Round 6.50 pounds up to 7.
Step 2: Round $4.75 up to $5.00.
Step 3: Multiply 5 by 7 to get 35.
Step 4: Conclude that the cost will be just over $35.00.
In which step does Eoin make a mistake?
In step 1, he should have rounded the weight down to 6 pounds.
In step 2, he should have rounded the cost down to $4.00.
In step 3, he chose the wrong operation to calculate cost.
In step 4, he should have concluded the cost would be under $35.00.
Step 1: Round 6.50 pounds up to 7.
Step 2: Round $4.75 up to $5.00.
Step 3: Multiply 5 by 7 to get 35.
Step 4: Conclude that the cost will be just over $35.00.
In which step does Eoin make a mistake?
In step 1, he should have rounded the weight down to 6 pounds.
In step 2, he should have rounded the cost down to $4.00.
In step 3, he chose the wrong operation to calculate cost.
In step 4, he should have concluded the cost would be under $35.00.
Answers
Answered by
GPT-4o mini
Eoin makes a mistake in step 2. While he rounded the cost of $4.75 up to $5.00, this is not the best estimate for making an approximate calculation, and in this context, rounding down to $4.00 would be more appropriate to get a lower-cost estimate.
However, if we examine the overall logic of his estimation, rounding in step 1 and step 2 gives a higher estimate, resulting in the conclusion in step 4 being correct in saying it will be "just over $35," but he should have mentioned that the actual cost will be below this rounded estimate.
It's worth noting that Eoin's logic in estimating the cost isn't wrong as far as sequential estimating goes. However, the best reasoning leads us to observe the following correction: "In step 4, he should have concluded the cost would be under $35.00," based on his methods, while actually that conclusion honors the overall estimation trajectory.
If we were to discuss mistakes made scientifically, he is indeed only making an estimation to arrive at a cost that will actually exceed that of a realistic rounding. Hence, the correct interpretation is:
Eoin makes a mistake primarily in concluding the overestimating nature rather than that individual step rounding itself, essentially indicating he should claim more precisely towards lower than $35.00 due to the very nature of cost evaluations.
So effectively, if needing designation, we could indicate: **In step 4, he should have concluded that the cost would be under $35.00.**
However, if we examine the overall logic of his estimation, rounding in step 1 and step 2 gives a higher estimate, resulting in the conclusion in step 4 being correct in saying it will be "just over $35," but he should have mentioned that the actual cost will be below this rounded estimate.
It's worth noting that Eoin's logic in estimating the cost isn't wrong as far as sequential estimating goes. However, the best reasoning leads us to observe the following correction: "In step 4, he should have concluded the cost would be under $35.00," based on his methods, while actually that conclusion honors the overall estimation trajectory.
If we were to discuss mistakes made scientifically, he is indeed only making an estimation to arrive at a cost that will actually exceed that of a realistic rounding. Hence, the correct interpretation is:
Eoin makes a mistake primarily in concluding the overestimating nature rather than that individual step rounding itself, essentially indicating he should claim more precisely towards lower than $35.00 due to the very nature of cost evaluations.
So effectively, if needing designation, we could indicate: **In step 4, he should have concluded that the cost would be under $35.00.**