Finding the Initial Temperature of Water in a Calorimeter: A Calorimetry Problem

[annedi]

please help :( I know the formula, but i don't understand the question1. Homework Statement
a 200g calorimeter, with heat capacity = 0.10 cal/g C, contains 300g of water. a 500 g aluminum shot, at 99 Celsius, was poured in the calorimeter. What would be the initial temperature of water in order that the final temperature will be as much above the room temperature as the initial temperature of water was below the room temperature

Homework Equations

(mass)(heat capacity)(change in temp) of solid= (mass)(heat capacity)(change in temp) of calorimeter + (mass)(heat capacity)(change in temp) of water

 

[ehild]

please help :( I know the formula, but i don't understand the question1. Homework Statement
a 200g calorimeter, with heat capacity = 0.10 cal/g C, contains 300g of water. a 500 g aluminum shot, at 99 Celsius, was poured in the calorimeter. What would be the initial temperature of water in order that the final temperature will be as much above the room temperature as the initial temperature of water was below the room temperature

Homework Equations

(mass)(heat capacity)(change in temp) of solid= (mass)(heat capacity)(change in temp) of calorimeter + (mass)(heat capacity)(change in temp) of water

Let be the room temperature Tr and the initial temperature of water Ti, the final temperature of water Tf. The problem says that Tf-Tr=Tr-Ti.

 

[mfb]

What is unclear?

As an example, if the room temperature is 20°C and your water and calorimeter would be at 5° C initially (15K below room temperature), then the final temperature of everything should be 35° C (15K above room temperature). This is not the solution as the energy does not match (I made up those numbers). You have to find the temperature where the numbers match.