The heat lost by the 80 deg.C solution would equal the heat gained by
the colder solution, and the final temperature would be 60 deg.C. x is the
amount of colder solution added and y is the initial temp of the colder
solution.
Heat lost by 80 deg.C solution = (500 g)(1.00 cal/g C)(80 deg.C - 60 deg.C)
= 1000 cal
Heat gained by colder solution = (x)(60 - y)
By evaluating further, we will arrive at adding 100
grams of 50° Celsius water. This satisfies to the problem above.
