Ed had 2 more marbles than Doug. Doug lost some of his marbles at the playground. Now Ed has 19 more marbles than doug. How many marbles did Doug lose?
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Ed had 2 more marbles than Doug. So we can write this as:

Ed: 2 + x
Doug: x

Doug lost some of his marbles at the playground. Now we don't know how many marbles Doug lost, but we know that after he lost them, Ed had 19 more marbles than Doug. So we can write this as:

Ed: 2 + x + 19
Doug: x - y

We don't know what x and y are, but we know that x is 2 more than y. So we can write this as:

Ed: 2 + x + 19
Doug: x - (x-2)

Now we can solve for x. 

2 + x + 19 = x - (x-2)

2 + x + 19 = x - x + 2

2 + x + 19 = 2

x = -16

Doug lost 16 marbles at the playground.