Question 1182504
x pints of the 45% for 0.45x
110-x pints of the 95% for 104.5-0.95x
that computes the amount of "pure" fruit juice in pints

The final amount is 110 pints of 0.55 fruit juice or 60.5 pints "pure".
So, 0.45x+104.5-0.95x=60.5
-0.50x=-44
x=88 pints of 45% or 39.6 pints "pure"
110-x=22 pints of 95% or 20.9 pints "pure"

Also, 55% is 1/5th of the way between 45 and 95%
so the 45% must be weighted 4/5 and the 95% weighted 1/5 in the final result.