Algebra · Inequalities · Ratios · Mediant
Aca, Branka, Vera and Goran were each given the same kind of task by their mathematics teacher: divide one positive real number by another. Aca computed \(a_1 : a_2\), Branka computed \(b_1 : b_2\), Vera computed \(v_1 : v_2\), and Goran computed \(g_1 : g_2\). On the board the teacher computed
It turned out that none of the four quotients the students obtained was greater than the quotient the teacher obtained. (All eight numbers are positive, and every division was carried out correctly.)
Can the quotients obtained by Branka and Goran be different?
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Serbian Regional Competition 2014, high school grade I, category A, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source