To determine the total amount of paint [tex]\( P \)[/tex] needed to paint the walls of the room twice, let's break down the problem step by step.
1. Understand the Coverage:
One gallon of paint covers 220 square feet.
2. Identify the Area:
The total wall area of the room is [tex]\( w \)[/tex] square feet.
3. Double the Area for Two Coats:
Since we need to paint the room twice, we need to consider twice the total wall area:
[tex]\[
\text{Total area to be painted} = 2 \times w
\][/tex]
4. Calculate Total Area:
Let's denote the total area to be painted as [tex]\( A \)[/tex]:
[tex]\[
A = 2w
\][/tex]
5. Convert Area to Amount of Paint Needed:
Given that one gallon of paint covers 220 square feet, the amount of paint required [tex]\( P \)[/tex] in gallons is calculated by dividing the total area by the coverage per gallon:
[tex]\[
P = \frac{A}{220}
\][/tex]
6. Substitute the Expression for Total Area:
Substitute [tex]\( A = 2w \)[/tex] into the equation:
[tex]\[
P = \frac{2w}{220}
\][/tex]
7. Simplify the Equation:
Simplify the fraction:
[tex]\[
P = \frac{2w}{220} = \frac{w}{110}
\][/tex]
Therefore, the equation that represents the total amount of paint [tex]\( P \)[/tex], in gallons, needed to paint the walls of the room twice is:
[tex]\[
P = \frac{w}{110}
\][/tex]
Thus, the correct answer is (A) [tex]\( P = \frac{w}{110} \)[/tex].
