Markov Chains & Long-Run Behavior · Hard problem

An insurance claim is modelled as an absorbing Markov chain. Each day a Filed claim either moves to Review (probability $3/5$) or stays Filed (probability $2/5$); a claim under Review is resolved (probability $7/10$, absorbing) or stays under Review (probability $3/10$). Staff time costs $\$100$ for each day a claim is Filed and $\$140$ for each day it is under Review. Starting with a newly Filed claim, what is the expected total staff-time cost until it is resolved? Express your answer as a common fraction.