What is the value of all 112 proof state quarters?

There aren't 112 proof state quarters. There are only 50 proof state quarters, (along with 6 in the DC/US territories). Unless you are meaning you had both the clad (copper-nickel, common) proofs and the silver proof sets. But just about every clad US proof state quarter is worth about $1 or so, silver proof quarters go for about $7-8 or about fifty cents or a dollar above melt value individually.