For European options, all expiring on the same date, you are given:

• P(K) is a put option with strike price K, and C(K) is a call option with strike price K.

• A portfolio consisting of a long P(55) and a short P(50) has value 4.20

• A portfolio consisting of a long P(65) and a short P(55) has value 4.80

• A portfolio consisting of a long C(50) and a short C(55) has value 2.30

  Determine the value of a portfolio consisting of buying C(55) and selling C(65). Add portfolios together and use put-call parity.