a hotel has 280 rooms the mangent comany decides to build a new wing that will increase capacity to 405 rooms by what percentage will the capacity of the hotel round to the nearest tenth of aa perctage?

Answer 1

To find the percentage increase in the capacity of the hotel, we can use the following formula:

\[ \text{Percentage Increase} = \left(\frac{\text{New Capacity} - \text{Old Capacity}}{\text{Old Capacity}}\right) \times 100 \]

In this case, the old capacity is 280 rooms, and the new capacity is 405 rooms.

1. Calculate the difference in capacity: \[ \text{New Capacity} - \text{Old Capacity} = 405 - 280 = 125 \]

2. Now, plug in the values into the formula: \[ \text{Percentage Increase} = \left(\frac{125}{280}\right) \times 100 \]

3. Calculate the fraction: \[ \frac{125}{280} \approx 0.44642857 \]

4. Multiply by 100 to convert to a percentage: \[ 0.44642857 \times 100 \approx 44.642857 \]

5. Finally, round to the nearest tenth of a percentage: \[ \approx 44.6% \]

Thus, the capacity of the hotel will increase by approximately 44.6%.