To find the balanced reaction, you have to predict the products and write the equation first.
This will be a single replacement reaction because aluminum is an element and copper nitrate is a compound.
The reaction will be:
Al + Cu(NO3)2 -> Cu + Al(NO3)3
Now, we can balance it:
2 Al + 3 Cu(NO3)2 -> 3 Cu + 2 Al(NO3)3
Q = mc(θ₂-θ₁)
47 calories = 10 g *c*(50.4 - 25)
47cal = 10*c* 25.4
47 /(10*25.4) = c
0.185 = c
Specific heat of iron = 0.185 cal/g°C