Coupled systems and heat of reaction

Today we worked through a coupled systems problem in which a warm block of lead transferred energy to a cooler block of silver. In working through the algebra, I made an error somewhere and came up with the wrong answer, so let's try to correct it here. The set-up was OK, so we got to the following equation:
(0.128 ^J/_g.degC)(17.89g)(T_final-42.73degC) = -(0.235 ^J/_g.degC)(23.13g)(T_final-15.42degC)
This is set up correctly, now we have to work through the algebra:
(T_final-42.73degC) = -^{{(0.235 J/g.degC)(23.13g)}}/_{{(0.128 J/g.degC)(17.89g)}}(T_final-15.42degC)
Turning the great big ugly fraction into a number, we get:
(T_final-42.73degC) = -(2.3737)(T_final-15.42degC)
Distributing the -2.3737:
(T_final-42.73degC) = -(2.3737T_final)+(2.3737)(15.42degC)
Moving the T_final terms to one side and the numerical terms to the other:
T_final + 2.3737T_final = (2.3737)(15.42degC) + 42.73degC
Factoring out T_final and solving:
T_final = ^{{(2.3737)(15.42degC) + 42.73degC}}/_{{1 + 2.3737}} = 23.5degC

There is a new Mastering Chemistry posted, due Tuesday. Have a great weekend.