Four companies belong to a group and are listed on a stock exchange. The crossholdings of these companies are as follows:

Company A owns 20% of Company B and 10% of Company C

Company B owns 15% of Company C.

Company C owns 10% of Company A, 10% of Company B, and 5% of Company D.

Company D has no ownership in any of the other three companies.

Each company has a market cap of $50 million. You wish to adjust for cross-holding in determining the weights of these companies in a free-float market capitalization-weighted index.

a) What are the market capitalizations of each company after adjustment to reflect free float?

b) What would be the total adjusted market cap of the four companies?