Jonathan pays $1.90 per pound for potatoes. He buys 8.3 pounds of potatoes. He determines that he will pay $15.77, before tax, for the potatoes. Which best describes the reasonableness of Jonathan’s solution?

Jonathan’s answer is reasonable because there are two decimal places in the factors and two in the product.
Jonathan’s answer is unreasonable because there are three decimal places in the factors and two in the product.
Jonathan’s answer is reasonable because 2 times 8 is 16, and 16 is close to 15.77.
Jonathan’s answer is unreasonable because 1 times 8 is 8, and 8 is not very close to 15.77.

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
25 days ago

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:

1. **"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.

2. **"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).

3. **"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 \( 15.77 \).

4. **"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."**