Question
Round steak costs $6.95 per pound. Sara wants to buy 9.5 pounds of round steak which she estimates will cost $54. Which statement about Sara’s estimate is true?
Sarah rounded $6.95 and 9.5 up. $54 is enough money to buy the steak.
Sarah incorrectly multiplied 9 and 6. Her estimate should be $63.
Sarah rounded 9.5 up to 10. Her estimate of $54 is too high.
Sarah rounded $6.95 and 9.5 down. Her estimate of $54 is too low.
Sarah rounded $6.95 and 9.5 up. $54 is enough money to buy the steak.
Sarah incorrectly multiplied 9 and 6. Her estimate should be $63.
Sarah rounded 9.5 up to 10. Her estimate of $54 is too high.
Sarah rounded $6.95 and 9.5 down. Her estimate of $54 is too low.
Answers
GPT-4o mini
To determine which statement about Sara's estimate is true, let's calculate the exact cost of the round steak.
The cost per pound is $6.95, and Sara wants to buy 9.5 pounds. Therefore, the total cost can be calculated as follows:
\[
\text{Total Cost} = \text{Cost per pound} \times \text{Number of pounds} = 6.95 \times 9.5
\]
Calculating that:
\[
6.95 \times 9.5 = 66.025
\]
So, the exact cost is $66.03 (rounding to two decimal places).
Now, let's examine Sara's estimate of $54 against this exact cost:
1. **"Sara rounded $6.95 and 9.5 up. $54 is enough money to buy the steak."**
This statement is incorrect because $54 is not enough.
2. **"Sarah incorrectly multiplied 9 and 6. Her estimate should be $63."**
This statement is also incorrect as her original estimation is not based on multiplying 9 and 6.
3. **"Sarah rounded 9.5 up to 10. Her estimate of $54 is too high."**
This is incorrect because rounding 9.5 to 10 would give a higher estimation than $66.03.
4. **"Sarah rounded $6.95 and 9.5 down. Her estimate of $54 is too low."**
This statement is correct. If Sara rounded $6.95 down to $6 and 9.5 down to 9, she would estimate the cost as:
\[
6 \times 9 = 54
\]
Thus, her estimate of $54 is indeed too low compared to the actual cost of $66.03.
In conclusion, the correct statement is:
**"Sarah rounded $6.95 and 9.5 down. Her estimate of $54 is too low."**
The cost per pound is $6.95, and Sara wants to buy 9.5 pounds. Therefore, the total cost can be calculated as follows:
\[
\text{Total Cost} = \text{Cost per pound} \times \text{Number of pounds} = 6.95 \times 9.5
\]
Calculating that:
\[
6.95 \times 9.5 = 66.025
\]
So, the exact cost is $66.03 (rounding to two decimal places).
Now, let's examine Sara's estimate of $54 against this exact cost:
1. **"Sara rounded $6.95 and 9.5 up. $54 is enough money to buy the steak."**
This statement is incorrect because $54 is not enough.
2. **"Sarah incorrectly multiplied 9 and 6. Her estimate should be $63."**
This statement is also incorrect as her original estimation is not based on multiplying 9 and 6.
3. **"Sarah rounded 9.5 up to 10. Her estimate of $54 is too high."**
This is incorrect because rounding 9.5 to 10 would give a higher estimation than $66.03.
4. **"Sarah rounded $6.95 and 9.5 down. Her estimate of $54 is too low."**
This statement is correct. If Sara rounded $6.95 down to $6 and 9.5 down to 9, she would estimate the cost as:
\[
6 \times 9 = 54
\]
Thus, her estimate of $54 is indeed too low compared to the actual cost of $66.03.
In conclusion, the correct statement is:
**"Sarah rounded $6.95 and 9.5 down. Her estimate of $54 is too low."**