Calorimetry: adding ice to water

[e46lover]

Homework Statement

A 53.5 g ice cube, initially at 0°C, is dropped into a Styrofoam cup containing 369 g of water, initially at 21.4°C. What is the final temperature of the water, if no heat is transferred to the Styrofoam or the surroundings?

Homework Equations

Lf*m + Mc Delta T = MC Delta T this is the equation am using but can't seem to get a reasonable answer.

The Attempt at a Solution

This seems like a simple problem but I just can not seem to get the correct answer on webassign. Thanks for anyone who helps.

 

[Stonebridge]

You are on the right track there with the equation.
On the left is the heat required to melt the ice, plus the heat required to heat the water formed from zero to T degrees. [T is final temperature]
On the right is the heat lost by the warm water cooling from 21.4 degrees to T.

If you set up that equation you can solve for T

 

[Borek]

Note: trick is to correctly write both delta T on the left and delta T on the right.