Benjamin had 66 more red cards than blue cards at first. He gave away an equal number of red cards and blue cards. He now had twice as many red cards as blue cards. How many blue cards did Benjamin have at first?
At the beginning he had 66 blue + whatever number of blue ones that he gives away.
Let B be the number of Blue at the beginning
So initially he has B blue and B+66 red
he gives away k of each so now he has
Blue: (B-k) and Red: B+66-k = (B-k)+66
We are told that he now has twice as many red so B-k must equal 66
So he starts out with 66 blue plus the number of blue that he gives away.
if he gives away 5 of each then he starts with 66+5 blue and 132+5 red
if he gives away 20 of each then he starts with 66+20 blue and 132+20 red