Perhaps I should have introduced weighted averages with GPAs, which most people are familiar with. We have w1 s1 + w2 s2 + ... + wn sn = s, where the wi weights of tests are determined in advance and the si values are scores and s is the final grade. This is different from a typical mixing problem, where the weights are not known in advance. A practical GPA problem that comes up frequently is to determine what final grade sn is required to attain a course grade of s. We want to solve for x in w1 s1 + w2 s2 + ... + wn x = s. This is a fairly straightforward calculation.