The amount of paint p needed to paint walls of a room varies directly as the area A of the wall of 2gallons of paint are needed to paint a wall with an area of 100sq. meters?
2/100 * A = p
To solve this problem, we need to use the concept of direct variation. Direct variation means that two quantities are directly proportional to each other. In this case, the amount of paint needed (p) is directly proportional to the area of the wall (A).
We can set up a proportion to solve for the amount of paint needed:
p / A = k
where k is the constant of proportionality. Using the given information, we can substitute the values into the equation:
2 / 100 = k
Simplifying the equation, we get:
1 / 50 = k
Now we can use this value of k to find out how many gallons of paint are needed to paint a wall with a different area.
For example, if we want to find out how many gallons of paint are needed to paint a wall with an area of 150 square meters, we can substitute the value of the area into the equation:
p / 150 = k
Simplifying the equation, we get:
p = (1/50) * 150
p = 3 gallons
Therefore, 3 gallons of paint would be needed to paint a wall with an area of 150 square meters, based on the direct variation relationship given in the problem.