Ed had 11 more marbles than Doug. Doug lost some of his marbles at the playground. Now Ed has 34 more marbles than doug. How many marbles did Doug lose?
Ed had 11 more marbles than Doug. This means that if we start with Doug's number of marbles, then add 11, we will get Ed's number of marbles. So: 

Doug's number of marbles + 11 = Ed's number of marbles

Doug lost some of his marbles at the playground. This means that Doug's current number of marbles is less than his original number of marbles. So: 

Doug's current number of marbles < Doug's original number of marbles

Now Ed has 34 more marbles than Doug. This means that if we start with Doug's current number of marbles, then add 34, we will get Ed's number of marbles. So: 

Doug's current number of marbles + 34 = Ed's number of marbles

We can solve this system of equations to find out how many marbles Doug lost: 

Doug's number of marbles + 11 = Ed's number of marbles
Doug's current number of marbles + 34 = Ed's number of marbles

Doug's number of marbles + 11 = Doug's current number of marbles + 34

11 = 34 - Doug's