Absorption Of Heat; water and steam thermodynamics

[K29]

Homework Statement

Steam initially at 120 ^oC is passed into 0.60 kg of water initially at 20 ^o C, and the total mass of water is just brought to the boil at 100C

What is the mass of steam that has condensed? Ignore the thermal capacity of the container and heat losses.

Homework Equations

Q = cm(T2-T1) heat = specific heat * mass * change in temperature
Q = Lm heat = heat of Vaporisation or Fusion * mass
Heat of vaporisation of water is 2260 kJ/kg
Specific heat of water is 4200 J/kg.^oC
Specific heat of steam is 2100 J/kg.^oC

The Attempt at a Solution

Qgained by water being heated = Qlost by steam being cooled + Q Lost by steam being condensed

cm_w(T2-T1) = cm_stot(T2-T1) +Lm_scondensed

Unfortunately I can't seem to get rid of m_stot. It is not given and I need to either work it out or find another equation. Help!
If it helps, the final answer should be 87g

 

[Mapes]

If the problem can't be solved otherwise, why not assume that all the steam condensed?

 

[K29]

I have tried this and get
|cm_w(T2-T1)| = |cm_s(T2-T1)| +|Lm_s|
|4200 * 0.6 (100-20)| = |2100 * m_s(100-120)| + |2260m_s|
|201600|= |-42000m_s|+|2260m_s|
201600 = 42000m_s+2260m_s
201600=44260m_s
m_s=4.55 kg

As I said above the answer given in the notes is 87g = 0.087kg :(

 

[Mapes]

Check your units.