Let x represent the number of pints of the first fruit juice required.
Let y represent the number of pints of the second fruit juice required.
Since the company wants to make a 90 pints mixture from pints of both drinks, it means that
x + y = 90
First drink is 20% pure fruit juice. This means that the concentration of x pints of First drink is 20/100 * x = 0.2x
Second drink is 95% pure fruit juice. This means that the concentration of y pints of Second drink is 95/100 * y = 0.95y
If the company wants to produce a mixture of 90 pints that contains 80% fruit juice, then its concentration is 80/100 * 90 = 72
Recall, concentration in first drink + concentration in second drink = concentration in mixture
Thus,
0.2x + 0.95y = 72
From the first equation, x = 90 - y
By substituting x = 90 - y into 0.2x + 0.95y = 72, we have
0.2(90 - y) + 0.95y = 72
18 - 0.2y + 0.95y = 72
- 0.2y + 0.95y = 72 - 18
0.75y = 54
y = 54/0.75
y = 72
x = 90 - y = 90 - 72
x = 18
Thus,
First fruit drink = 18 pints
Second fruit drink = 72 pints