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 80% pure fruit juice. how many pints of each of the two existing types of drink must be used to make 70 pints of a mixture that is 80% pure fruit juice?

Let x pints be the required amount of 70% pure juice.
Let y pints be the required amount of 95% pure juice.
x + y = 70 pints
Therefore we can write:
y = 70 - x (1)
Amount of pure juice in x pints = 0.7x.
Amount of pure juice in y pints = 0.95y = 0.95(70 - x).
Amount of pure juice in 70 pints = 0.8 x 70 = 56 pints.
Equating the amounts of pure juice, we get:
0.7x + 0.95(70 - x) = 56 (2).
The solution to equation (2) is x = 42. Therefore y = 70 - 42 = 28.
The answer is: 42 pints of 70% pure fruit juice and 28 pints of 95% pure fruit juice are required.