I am not just seeking the solution. Please be detailed & explanatory in how you get to the answer so that I can learn. Thank you.

Q6 (4 pts) There are two possible states of the world tomorrow: rain or sun. Asset A has a price of $1.60 and pays off $1.50 if it rains and $2.00 if it is sunny. Asset B has a price of $2.25 and pays off $2.50 if it rains and $2.00 if it is sunny. Assuming there is no arbitrage opportunity, what is the price of an asset that pays off $1.00 if it rains and nothing if it is sunny