Using Residuals to Solve Ratios/Proportions

[galinagranskay]

Can you please explain how to solve proportions/ratios using residuals. This was one of the shortcuts in the Manhattan GMAT , book on Word Translations in the Advanced Comb/Prob/Stats chapter.
The problem was that there is ...
Boys have an average of 86% on a test.
Girls have an average of 80% on the same test.
Class average is 82%. What's the ratio of boys to girls?

I understand that residuals must add up to zero. But how is that information relevant to proportions?

[tim]

if the average is to be 82, then each girl (representing 80%) has a residual of -2 and each boy (representing 86%) has a residual of +6. Now you just need to figure out a number of girls and boys that will make the residual 0. 3 girls at -2 and 1 boy at +6 will do the trick, which gives us a ratio of 1 boy to 3 girls..