[Community College] Thermodynamics

[igotrhythm]

I'm getting absolutely stonewalled by problems involving more than two components. Take this rather vanilla three-component problem:

A coffee cup calorimeter contains 480.0g of water at 25.00 C. To it are added: 380.0g of water at 53.5C and 525.0g water at 65.5C. Calculate the expected final temperature of the mixture.

Specific heat of water = 4.184 J/g*C

Gyah. I have no clue where to start, except maybe by treating it as two consecutive 2-component problems (add one sample, let it equalize, then add the other sample).