The mean weight of Jebs pumpkin and Karls pumpkin is 120 pounds. The mean weight of Karls pumpkin and Dougs pumpkin is 140 pounds. The mean weight of Jebs pumpkin and
Dougs pumpkin is 135 pounds. Combined, how many pounds do all three pumpkins weigh?

If you write out the formulas for each of these three statements, you'll see that all you need do is add them up! For example: "The mean weight of Jeb's pumpkin and Karl's pumpkin is 120 pounds" can be written out as:

(J+K)/2 = 120

Continue with the other two statements, and see if you can take it from there.

The mean weight of Jebs pumpkin and Karls pumpkin is 120 pounds. The mean weight of Karls pumpkin and Dougs pumpkin is 140 pounds. The mean weight of Jebs pumpkin and
Dougs pumpkin is 135 pounds. Combined, how many pounds do all three pumpkins weigh?

Yep. EBaines is dead on. Think of it this way

J = weight of Jeb's pumpkin
K = weight of Karl's pumpkin
D = weight of Doub's pumpkin

\frac {J + K}{2} = 120

Generate two additional equations for the other two

Add the three equations together and simplify