To determine the reasonableness of Jonathan's solution, we can first verify the actual calculation:
Jonathan buys 8.3 pounds of potatoes at $1.90 per pound. We calculate the total cost:
\[ \text{Total Cost} = \text{Price per pound} \times \text{Number of pounds} = 1.90 \times 8.3 \]
Calculating that:
\[ 1.90 \times 8.3 = 15.77 \]
So, Jonathan's calculation is indeed correct.
Now let's evaluate the provided statements about the reasonableness:
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"Jonathan’s answer is reasonable because there are two decimal places in the factors and two in the product."
- This statement addresses the decimal places but doesn't necessarily reflect the correctness of the calculation. While it's true that the factors and product have a proper arrangement of decimal places, it doesn't confirm the accuracy.
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"Jonathan’s answer is unreasonable because there are three decimal places in the factors and two in the product."
- This statement is inaccurate because there are not three decimal places in the factors (1.90 has two, and 8.3 has one).
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"Jonathan’s answer is reasonable because 2 times 8 is 16, and 16 is close to 15.77."
- This statement is valid as an estimation. Since \( 1.90 \) is close to \( 2 \) and \( 8.3 \) is close to \( 8 \), multiplying these gives \( 16 \), which is indeed close to \( 15.77 \).
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"Jonathan’s answer is unreasonable because 1 times 8 is 8, and 8 is not very close to 15.77."
- This statement incorrectly uses a simplified version of the multiplication that does not reflect the actual values being rounded.
Based on the evaluation, the most accurate and reasonable description of Jonathan's solution is:
"Jonathan’s answer is reasonable because 2 times 8 is 16, and 16 is close to 15.77."
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