You had better do more research. I've had a little to do with aged care. The Federal Government does fund state aged care but it is the states that manage it 100%.
With regards Education the funding in part comes from the Federal. They allocate some tax revenue specifically to private schools because the states are a little short of realising that parents have a right for their share of tax being allocated to schooling where they choose to have private schooling, usually so that there children get a better education with less left wing brainwashing and better job opportunities.
