Carol has three policies covering the exact same property. Policy A has a limit of $$50,000,$ Policy B has a limit of $$30,000,$ and Policy $C$ has a limit of $$20,000.$ If Carol has a loss of $$85,000,$ how much will each policy pay if:

a$.$ the three policies have pro$-$rata other insurance clauses?

b$.$ the three policies have contribution by equal shares other insurance clauses?

You own a home with an actual cash value of $$150,000$ that is insured for $$100,000$ with Ted Insurance Company. You have recently done some comparison shopping and decide to buy a policy that insures your home for $$110,000$ from Alice Insurance Company for the same premium as your policy from Ted. Before you have a chance to cancel the coverage with Ted, you suffer a $$40,000$ loss to your house. Both policies have $80\%$ coinsurance clauses and pro$-$rata other insurance clauses. How much are you entitled to collect from each insurance company?