Based on the given information, Nate needs to mix blue and yellow paint in the ratio of 1:3. Since he needs a total of 8 gallons of paint, this means he needs 3 parts of yellow paint for every 1 part of blue paint.
To find the amount of yellow paint, we can set up a ratio:
Yellow paint : Blue paint = 3 : 1
Since the ratio is 3 parts yellow to 1 part blue, we can divide 8 gallons by 4 (3 parts + 1 part) to find the amount of yellow paint needed:
8 gallons / 4 = 2 gallons
Therefore, Nate needs to buy 2 gallons of yellow paint.