Can you help me with this word problem on heat?

Question

Mrs. Smith is having a few friends over for dinner and making iced tea, but she finds that she is out of ice. She finds that she has five aluminum bars in the freezer and decides to use them to cool down the tea. Each bar weighs 45 grams and is at 0°C. How cold will the 2 Liters of tea get when Mrs. Smith places the aluminum in the tea? Assume that the specific heat of tea is that of water. The specific heat of aluminum is 0.9025J/g°C.

Answer 1

total mass of aluminum = 5 bars x 45 g/bar = 225 g

You are trying to find final temperature (Tf) of the tea.  The tea will lose heat and the aluminum will gain heat as heat flows from warm to cold.

heat lost by tea = heat gained by aluminum

However, in order to find the final temperature of the tea, one needs to know the initial temperature of the tea.

For the aluminum, you have (225 g)(0.9025 J/g/deg)(∆T) = heat gained by the aluminum.  This will be equal to the heat lost by the tea, but without knowing the starting temperature, I don't see how you can determine the final temperature. Let's assume the initial temp of the tea is 25ºC.  Then...

(225 g)(0.9025 J/g/deg)(T_f - 0) = (2000 g)(4.184 J/g/deg)(25 - T_f)

203 Tf = 209,200 - 8368T_f

8571 T_f = 209,200

T_f = 24.4 degrees.  Not very icy iced tea.  Hopefully, the tea started at a temperature lower than 25ºC.  Also, one needs to assume that tea has a density of 1g/ml to use these calculations.