Question

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%**.