The royal fruit company produces two types of fruit drinks. the first type is
70 % pure fruit juice, and the second type is
95 % pure fruit juice. the company is attempting to produce a fruit drink that contains
85 % pure fruit juice. how many pints of each of the two existing types of drink must be used to make
160 pints of a mixture that is 85 % pure fruit juice?

Now, the percentage figures of say, 70%, 95% and so on, we'll use the decimal format of the, thus 70% is just 70/100 or 0.7 and 95% is just 95/100 or 0.95 and so on

so  

whatever "x" and "y" amounts are, we know, they must add up to 160 pints
thus  x + y = 160

now, whatever the concentrated amount of solute in the mixture, we know they must add up to 160*0.85 or 136

thus   0.7x + 0.95y = 136

thus    

solve for "x", to see how much of the 70% pure juice will be needed

what about "y"?  well, y = 160 - x