A foam cup with negligible mass contains liquid sweet water with a mass of m_water = 0.330 kg and a temperature of 68.0 °C. Cold ice of m_ice = 0.080 kg at an initial temperature of -20.0 °C is dropped into the sweet water. After thermal equilibrium is reached, all the ice has melted and the final temperature of the mixture (original sweet water diluted by the fresh water from the melted ice) so that the final temperature is above 0.0 °C. Find this final temperature. Take the specific heat of liquid water (and sweet water) to be c_water = 4190 J/kg⋅K, the specific heat of ice to be c_ice = 2100 J/kg⋅K, and the latent heat of fusion for water to be L_f = 3.34 × 10⁵ J/kg.