It is possible to answer the question within 3 minutes. Simply factorise the cubic equation (a^{3}+b^{3}+c^{3}) and complete the square of the second degree equation for a^{2} + b^{2}. Also place the linear equation in terms of (a + b). All three equations will then be expressed in terms of linear and second degree factors. c can then be found and through substituting the equations of a and b and the value of c into the quartic equation one will arrive at 50, even though values for a and b were never found.