~72% of the initial water would freeze as ice.

Phase #1, water cooling and boiling:

    mc dT = λv dm

    dT = λv/(mc) dm | ∫

    Tƒ - T₀ = λv/c ∫ (dm/m) 
        = λv/c (ln mƒ' - ln m₀) =
        = λv/c ln (mƒ'/m₀)

    ln (mƒ'/m₀) = c/λv (Tƒ - T₀)

    mƒ'/ m₀ = exp[c/λv (Tƒ - T₀)]

    mƒ'/m₀ = exp[ 4192J/(kg K) * 1/(2257 * 10^3J/kg) * (-100K)] =
        = exp[ -4192/2257 * 10^-3 * 10^2 ] = 
        = exp[ -4192/2257 * 10^-1 ] ≈
        ≈ 83%.

Phase #2, water freezing, remaining water still boiling:

    mƒ = mƒ' - mv

    |Qced| = Qabs

    mƒ λc = mv λv

    mƒ = λv/λc mv

    mƒ = λv/λc (mƒ' - mƒ) = λv/λc mƒ' - λv/λc mƒ

    mƒ (1 + λv/λc) = λv/λc mƒ'

    mƒ = λc/(λc + λv) * λv/λc mƒ' =
        = λv/(λc + λv) mƒ'

    mƒ/m₀ = 2257kJ/kg * 1/(2257kJ/kg + 335kJ/kg) * 0.83 ≈
        ≈ 2257/2592 * 0.83 ≈
        ≈ 72%