Pitt and Michigan sound like great choices for your student. My son applied to both for nursing last year. As others have said, apply to Pitt soon after the application opens on 8/1 and you should have an answer in a few weeks. For Michigan, if you are out of state, it might not meet your $80k budget unfortunately. Tuition + room and board for this year are going to be right around the $80k mark. I am expecting at least a $5k increase in cost of attendance each year plus Michigan’s junior and senior year tuition is higher than freshman and sophomore year by somewhere around $5k per year. Given all of that, we are expecting to pay around $100k by the time my son is a senior 
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