Question 856361
This will give only ratios between the 150 proof and the 80 proof:


{{{150v+80u=100}}} and {{{u+v=1}}}; and just solve the system for u and v.  Your description did not include an expected amount of mixture.  The two equations just given assume the mixture amount is 1.
You might want some help on how the system works.  See this lesson:


<a href="http://www.algebra.com/tutors/Mixtures%3A-All-in-Symbols.lesson?content_action=show_dev">Two-Part Mixture for Known Concentration Result - both parts unknown</a>