Let X be a loss random variable with cdf
$$ F(x) = \left\{ \begin{array}{ll} 1-(θ/θ+x)^α & \textrm{for $x≥0$}\\ 0 & \textrm{for $x<0$}\\ \end{array} \right. $$
The 10th percentile is θ−k. The 90th percentile is 5θ−3k. Determine the value of α.
Answer: 2
I am stuck with the problem, I have no idea in what way α can be derived. I was trying to solve the equations F(θ−k)=0.1 and F(5θ−3k)=0.9 but I am getting nowhere with the three unknowns (θ,k,α) in those two equations. I am missing some point there.