The Robertson's find that have used 1/2 gallon of paint to cover 480 square feet of wall. They used 3/4 gallon of paint to cover 720 square feet of wall. Write an equation to find the number of gallons of paint they will need (G), in order to cover S square feet of wall.
Thanks in advance for any help. I really need to see HOW to equation is worked out, so if you can help set up the equation, I don't mind if you don't give me the answer.
look at it as 2 ordered pairs
(1/2 , 480) and (3/4 , 720)
and find the linear equation
slope = (720-480)/(3/4 - 1/2)
= 240/(1/4) = 960
S = 960g + b , (using y = mx + b )
for (1/2, 480)
480 = 960(1/2) + b
480 = 480 + b
b = 0
S = 960G
(tells me 1 gallon covers 960 square feet)
Thank you so much!! When you set it up as a slope intercept equation, it is much easier to solve. I get it now :)
To set up the equation, we can use the idea of a proportion. We know that the amount of paint used is directly proportional to the area of the wall covered.
We are given two scenarios:
Scenario 1: Using 1/2 gallon of paint to cover 480 square feet of wall.
Scenario 2: Using 3/4 gallon of paint to cover 720 square feet of wall.
Let's represent the amount of paint used in scenario 1 as P1 (1/2 gallon) and the area covered in scenario 1 as S1 (480 square feet).
Similarly, let's represent the amount of paint used in scenario 2 as P2 (3/4 gallon) and the area covered in scenario 2 as S2 (720 square feet).
Now, we can set up the proportion:
P1 / S1 = P2 / S2
In this case, we want to find the amount of paint needed (G) to cover a given area S. So, we can rewrite the equation as:
G / S = P2 / S2
Now, we can use this equation to find the number of gallons of paint needed (G) to cover any given area S by substituting the known values of P2 and S2 into the equation.