One gallon of paint will cover 220 square feet of a surface. A room has a total wall area of [tex]w[/tex] square feet. Which equation represents the total amount of paint [tex]P[/tex], in gallons, needed to paint the walls of the room twice?

A. [tex]P = \frac{w}{110}[/tex]
B. [tex]P = 440w[/tex]
C. [tex]P = \frac{w}{220}[/tex]
D. [tex]P = 220w[/tex]



Answer :

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].