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?

Question

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.

Answer 1

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."