To answer this question, let's analyze the information provided in the image.
We can see that the blue rectangle represents 1 part of the mixture, and the three yellow rectangles represent 3 parts of the mixture. The total number of parts in the mixture is 4 (1 + 3).
We are given in the question that Nate needs 8 gallons of paint. Since the total number of parts in the mixture is 4, we can set up a proportion to determine how much yellow paint Nate needs to buy.
Proportion: (Amount of yellow paint) / (Total number of parts) = (Amount of paint needed) / (Total number of parts in the mixture)
From the image, we can see that the total number of parts is 4, and the amount of paint needed is 8 gallons.
Substituting the values into the proportion, we have:
(Amount of yellow paint) / 4 = 8 / 4
Simplifying the right side of the equation, we get:
(Amount of yellow paint) / 4 = 2
To solve for the amount of yellow paint, we can multiply both sides of the equation by 4:
(Amount of yellow paint) = 2 * 4
Therefore, the amount of yellow paint that Nate needs to buy is:
(Amount of yellow paint) = 8 gallons.
So the correct answer is 8 gallons.