Congress enacted a statute appropriating money to the states on condition that the states use the money to support "public performances of classical ballet open to the public." The statute provided that the money was not to be used to support any other type of dance, and that tickets to any performance paid for with these funds were to be distributed to the public on a first come, first served basis. A state that accepted a grant of $500,000 under the federal statute gave half of the grant to a state-sponsored ballet company. The company had been started 20 years earlier as part of a state effort to bring culture to poor, inner-city areas. By state law enacted when the company was formed, no less than 35% of the tickets to each performance of the ballet company must be distributed to the inner-city school systems to be given to minority school children. Is the state's method of distributing tickets to the state ballet company's performances constitutional?

The question does not mention what the remaining 65% are used for.  If they are used to support "public performances of classical ballet open to the public," then we cannot conclude that the state's method of distributing tickets to the state ballet company's performances is unconstitutional.

Let us assume that the 65% left from the $500,000 special-purpose grant was used as per statute, then the state's method is constitutional, because the other 35% is still used for purpose, but only to encourage the participation of the vulnerable persons in the state.

If however, the 65%, amounting to $325,000 was used for another purpose, perhaps, to support any other type of dance other than "public performances of classical ballet open to the public," then the state would have obviously breached the law.

Explanation:

The evidence does not point to a conclusive unconstitutional act on the part of the state.  Surely, more information is required in order to arrive at a better judgement.