Remember that mass * change in temperature * heat capacity is used to solve for energy.

The energy lost by the warmer water will be equal to the energy gained by the cooler water. Since we are mixing water with water the heat capacities are equal.

Using the density of 1 g/mL, we know that we have 128 g and 59.6 g of water respectively.

128*(88 - x) = 59.6 ( x - 18.5)

We can solve for x to find the final temperature.

11264 - 128x = 59.6x - 1102.6

12366.6 = 184.6x

x = 67 deg C

This makes sense because the final temperature is in between the two initial temperatures. It is also closer to the warmer temperature, because that cup contained a greater volume.

A similar problem is worked here if you would like to see another example.