Since the ratio of blue to yellow paint is 1:3, and we need a total of 8 gallons of paint, we can use the ratio to find the amount of yellow paint needed.
Let's set up a proportion:
blue paint / yellow paint = 1 / 3
Let's assign a variable to represent the amount of yellow paint needed. Let's call it "y".
So, blue paint / y = 1 / 3
To find the amount of yellow paint needed, we can cross multiply:
blue paint = (y)(1)/3
Since the blue paint is labeled as 8 gallons on the illustration, we can substitute it into the equation:
8 = (y)(1)/3
Now, we can solve for y by multiplying both sides of the equation by 3:
24 = y
Therefore, Nate needs to buy 24 gallons of yellow paint.