Question

a hotel currently has 280 rooms the manegment company decide to build a new wing that will increase the capacity to 405 rooms by what percentage will this expand the capacity of the hotel round to nearest tenth of a percent

Answer 1

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

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

1. **Old Capacity** = 280 rooms
2. **New Capacity** = 405 rooms

First, calculate the increase in capacity:

\[
\text{Increase} = 405 - 280 = 125 \text{ rooms}
\]

Now plug the values into the percentage increase formula:

\[
\text{Percentage Increase} = \left( \frac{125}{280} \right) \times 100
\]

Calculating that:

\[
\frac{125}{280} \approx 0.44642857
\]

Now multiply by 100 to get the percentage:

\[
0.44642857 \times 100 \approx 44.642857 \%
\]

Rounding to the nearest tenth of a percent gives:

\[
\text{Percentage Increase} \approx 44.6\%
\]

Therefore, the capacity of the hotel will expand by **approximately 44.6%**.