How did US-UK defeat the Donitz's "Wolfpack" tactics of U-boats during WWII?

I read books on this subject including John Keegan's book, but it's still not clear. Using Soner, Huff-Duff and other anti-submarines weapons, you can beat one submarine. But as U-boats form "wolfpack", usually 5-12 U-boats, even if you want to pursue to destroy one U-boat, other U-boat will counterattack you. It seems to me that it requires tremendous numbers of destroyers (probaly 30-40), to effectively destroy all the U-boats. But I don't think US had that many destroyers to guards the merchant ships. How possibly can you defeat "wolfpack"??