[Jekel0000]

23) A 192-g piece of copper is heated to 100.0 °C in a boiling water bath and then dropped into a beaker containing 750 mL of water (density = 1.00 g/cm³) at 4.0 °C. What is the final temperature of the copper and water after they come to thermal equilibrium? (The specific heat of copper is 0.385 J/g•K). the specific heat of water is 4.184 J/g·K

the answer in the book is 6.22°C I believe it is because at the end of the equation they divided
96/42 then added 4 getting 6.22°C. I think it is wrong...

[Jekel0000]

In this problem q_metal is the amount of heat energy of a Metal
q_metal units are in Joules(kinetic energy) not calories(heat energy) and is equal to

q_metal =
(mass of the Metal)·(specific heat of the metal)·(Final Temperature - Initial Temperature)

specific heat is measured in Joule/grams·(change in temperature)
Temperature is Kelvin or Celsius
mass = weight/gravity....

[Borek]

6.2°C is the correct answer.

Solution you attached is probably the most convoluted thing I have seen in the last few years. You should plug expressions for q_metal and q_water into

[tex]q_{metal} = -q_{water}[/tex]

and solve directly for T_final.

[Jekel0000]

Could you show me?

[Borek]

Yes. But I won't. Try to follow what you were told, that's the best way of learning.