First, we need to determine the area of the rectangular cake and the area of each square piece of cake.
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Calculate the area of the rectangular cake:
- Length = 22 1/2 inches = \( 22.5 \) inches
- Width = 15 inches
- Area of the rectangular cake = Length × Width = \( 22.5 \times 15 \)
\[ 22.5 \times 15 = 337.5 \text{ square inches} \]
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Calculate the area of each square piece:
- Side length = 2 1/2 inches = \( 2.5 \) inches
- Area of each square piece = Side length × Side length = \( 2.5 \times 2.5 \)
\[ 2.5 \times 2.5 = 6.25 \text{ square inches} \]
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Determine how many square pieces can fit into the rectangular cake:
- Number of square pieces = Area of the rectangular cake / Area of one square piece
\[ \text{Number of square pieces} = \frac{337.5}{6.25} \]
To perform this division:
\[ \frac{337.5}{6.25} = 54 \]
Therefore, the total number of whole square pieces of cake that can be cut from the cake is 54.
Thus, the answer is B. 54.
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