The number of gallons needed of paint needed to cover a wall varies directly with the area of the wall. The Robertsons find that they have used 1/2 gallon of pain to cover 540 square feet of wall. Which of the follow equations shows the number of gallons of paint they will need , G, to cover s square feet of wall.
A: G=s/540
B: G=270s
C: G=s/1080
D: G=s/1350
I don't get this problem.
If 1/2 gallon covers 540 square feet, then 1 gallon will cover 1080 square feet.
Thank You
You're welcome.
To solve this problem, we need to understand the concept of direct variation. In this case, we are given that the amount of paint needed is directly proportional to the area of the wall. This means that as the area of the wall increases, the amount of paint needed also increases proportionally.
To find the equation that represents this relationship, we can use the given information. The Robertsons used 1/2 gallon of paint to cover 540 square feet of wall. This gives us a ratio of 1/2 gallon to 540 square feet.
Now, if we let G represent the number of gallons of paint needed and s represent the area of the wall, the equation that represents this relationship can be written as:
G = ks
Here, k is the constant of variation. To find its value, we can use the ratio we obtained earlier:
1/2 gallon / 540 square feet = k
Simplifying this equation, we get:
k = 1/1080
Now we can substitute the value of k into the equation:
G = (1/1080)s
To match the available options, we can simplify the equation further:
G = s/1080
Therefore, the correct equation is option C: G = s/1080.