To answer this question, we can use the given information from the image.
We know that Nate needs a total of 8 gallons of paint and he wants to combine blue and yellow paint in a ratio of 1:3.
Looking at the image, we can see that the rectangle labeled as Blue represents the blue paint, and the set of three adjacent rectangles labeled as Yellow represents the yellow paint.
The bracket on the right side encompasses both sets and points to the number 8, indicating that the combined area of both the blue and yellow rectangles is equal to 8.
Since the ratio of blue to yellow paint is 1:3, this means that for every 1 gallon of blue paint, Nate will need 3 gallons of yellow paint.
To find out how much yellow paint Nate needs to buy, we can set up a proportion. Let's let x represent the amount of yellow paint in gallons.
1 gallon blue paint / 3 gallons yellow paint = 8 gallons blue paint / x gallons yellow paint
Cross-multiplying, we get:
1 * x = 3 * 8
x = 24
Therefore, Nate needs to buy 24 gallons of yellow paint.