Answer:
Julie weighs 35 lbs, Ted weighs 70 lbs, Mike weighs 105 lbs.
Step-by-step explanation:
Let the weight of Julie be 
Given:
Ted weighs twice as much as Julie
Weight of Ted = 
Mike weighs three times as much as Julie.
Weight of Mike = 
Together, Ted, Mike, and Julie weigh 210 lbs.

Solving above we get;

Hence Julie weight is 35 lbs.
Weight of Ted = 
Hence Ted weight is 70 lbs.
Weight of Mike = 
Hence Mike weight is 105 lbs.