Calculating Final Temperature of Two Solids in Thermal Contact

[Any Help]

Homework Statement

55. Solid A, with mass M, is at its melting point TA. It is placed in thermal contact with solid B, with heat capacity CB and initially at temperature TB (TB > TA). The combination is thermally isolated. A has latent heat of fusion L and when it has melted has heat capacity CA. If A completely melts the final temperature of both A and B is:
A. (CATA + CBTB − ML)/(CA + CB)
B. (CATA − CBTB + ML)/(CA + CB)
C. (CATA − CBTB − ML)/(CA + CB)
D. (CATA + CBTB + ML)/(CA − CB)
E. (CATA + CBTB + ML)/(CA − CB)
correct answer is A ?

Homework Equations

Q=mL+mCdeltaT

The Attempt at a Solution

in A Q1=ML+MCATfinal-MCATA
in B Q=mCBTfinal-mCBTB
-Q1=Q
-ML-MCATfinal+MCATA=mCBTfinal-mCBTB
-ML+MCATA+mCNTB=MCATf+mCBTf
Tf=(MCATA+mCBTB-ML)/(MCA+mCB)
how they get rid of the m in the above equation?

 

[Simon Bridge]

Q=mL=mCdeltaT
... this is not strictly correct because mL is not usually going to be equal to mCdeltaT.

how they get rid of the m in the above equation?
... you need to explain the reasoning (physics) behind your maths, but basically, in one of the steps, the "m" terms cancel out.
Try dividing the problem into two stages. Take the algebra carefully, step by step, and explain each step you do.

 

[Any Help]

Q=mL=mCdeltaT

sorry it is a keyboard mistake I mean Q=mL+mCdeltaT

 

[Simon Bridge]

sorry it is a keyboard mistake I mean Q=mL+mCdeltaT

Um OK. So what is your reasoning?

Note: you should probably get the concepts down from the other question before tackling this one.