There is a 12 pound bag on the left plate of a scale. There is a 4 pound bag on the right plate.

There is a 12 pound bag on the left plate of a scale. There is a 4 pound bag on the right plate. Ken has to balance the scale by adding 7 pound bags to the left plate and 9 pound bags to the right plate. Suppose that he must add the same number of bags to each side. How many bags must he add to each side in order to balance the scale?