here are my thoughts...
10[a/(a+b) + 2b/(a+b)] = c just factored out the 10
(a+2b) / (a+b) = c/10 divided both sides by 10... and added numerators b/c they have same denominator
think of it kind of like a ratio... (a + 2b) = c and (a+b) = 10
what are all the possibilities where a+b = 10 and a<b
plug these into a + 2b to find the value of c.. it is 18.
There may be an easier way with out plugging in, but this seems to work.
agree good job
IE IMBA 2010