The United Way board determines St. Jude needs $100,000 this year in funding. Designated contributions specifically naming St. Jude come in at $20,000.
St. Jude receives $100,000 ($20,000 in designated funds, $80,000 in undesignated funds) from the United Way, not $120,000. The $20,000 in designated funding simply frees up $20,000 to give to another not so worthy charity.
Give your $100 directly to St Jude.
If you give it through the United Way St Jude will get $85.
St Jude will also incur expenses (typically 3%) for all the paperwork the UW makes them submit to justify their need.