To determine if four suitcases, each measuring \(14 \frac{1}{6}\) inches tall, will fit in a trunk that is 50 inches high, we first need to calculate the total height of the four suitcases.
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Calculate the height of four suitcases:
\[ 4 \times 14 \frac{1}{6} = 4 \times \left(14 + \frac{1}{6}\right) = 4 \times 14 + 4 \times \frac{1}{6} \]
\[ = 56 + \frac{4}{6} = 56 + \frac{2}{3} \]
\[ = 56 \frac{2}{3} \text{ inches} \]
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Compare the total height with the trunk height:
- The total height of the four suitcases is \(56 \frac{2}{3}\) inches.
- The height of the trunk is 50 inches.
Since \(56 \frac{2}{3}\) inches is greater than 50 inches, you will not have enough room in the trunk.
The correct response is:
No, the height of all the suitcases is 56 \( \frac{2}{3} \) inches.