Question

what mass of water at 10.0 degrees C is needed to cool 500.0ml of tea from 25.0 degrees C to 18.3 degrees C? Density and specific heat of the tea are the same as water.

Answer 1

This is done the same way as adding cool water to warm water. The only difference is that you solve for mass cool water rather than Tfinal.

Answer 2

(? x 4.184 x 6.7) = (500 x 4.184 x 8.3)
28.03x = 17363.6
x= 6.19 x 10(2)g

is this correct?

Answer 3

I don't think so.
It appears to me that you've reversed the delta T values.
[? x 4.184 x (8.3)] = 500 x 4.184 x 6.7
mass 10 C H2O needed approximately 400 g if I didn't punch the wrong keys.