State university is planning a tuition raise. the dean of admissions suggests that they increase tuition by $10\%$ each year for the next two years. the provost suggests that each year they instead increase the tuition by $30\%$ of the amount of the tuition above $\$10{,}000$.
so, for example, if the tuition now is $\$25{,}000$, the dean of admissions is suggesting a $\$2{,}500$ increase in the first year. meanwhile, the provost is suggesting a $\$4{,}500$ increase (since the current tuition is $\$15{,}000$ more than $\$10{,}000$, and $30\%$ of $\$15{,}000$ is $\$4{,}500$).
the treasurer points out that the tuition two years from now (after two annual increases) will be the same under either the dean's plan or the provost's plan. what is the tuition right now? (assume the tuition is not $0$; state university is not free! )