Let's solve this problem step-by-step to find the area of the new kitchen.
1. Understand the problem:
- The current width of the kitchen is \( w = 16 \) feet.
- The new width will be increased by 2 feet, resulting in \( w + 2 \).
2. Calculate the new width:
- New width = \( w + 2 \)
- Substitute \( w = 16 \):
[tex]\[
\text{New width} = 16 + 2 = 18 \text{ feet}
\][/tex]
3. Calculate the new length:
- The new length will be \( 2w - 5 \).
- Substitute \( w = 16 \):
[tex]\[
\text{New length} = 2 \cdot 16 - 5 = 32 - 5 = 27 \text{ feet}
\][/tex]
4. Calculate the new area:
- The new area is given by the product of the new length and the new width.
[tex]\[
\text{New area} = \text{New length} \times \text{New width} = 27 \text{ feet} \times 18 \text{ feet}
\][/tex]
5. Perform the multiplication:
[tex]\[
\text{New area} = 27 \times 18 = 486 \text{ square feet}
\][/tex]
Thus, the area of the new kitchen is [tex]\( 486 \)[/tex] square feet.
