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Solution to the Math Riddle Fall Newsletter 08-09
Here is an algebraic solution. Let x1 = the 1st number in our list, x2 = the 2nd number, … x5 = the 5th number x5 + x3 = 14 x4 = x2 + 1 x1 = 2x2 – 1 x2 + x3 = 10 x1 + x2 + x3 + x4 + x5 = 30 Rewrite our last equation in terms of a single variable. (x1) + (x2 + x3) + (x4) + (x5) = 30 (2x2 – 1) + (10) + (x2 + 1) + (14 – x3) = 30 (2x2 – 1) + (10) + (x2 + 1) + (14 – (10 - x2)) = 30 4x2 + 14 = 30 x2 = 4 Substitution gives us our five numbers in the following order: 7,4,6,5,8 |