Solve using linear equation

Question

The Royal Fruit Company produces two types of fruit drinks. The first type is 80% pure fruit juice, and the second type is 100% pure fruit juice. The company is attempting to produce a fruit drink that contains 95% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 220 pints of a mixture that is 95% pure fruit juice?

First fruit drink:

Second fruit drink:

Answer 1

Here's a way to "logic" it out. If you mix 1 pint of the 100% and 1 pint of the 80%, you get 2 pints of 90%. If you mix those 2 pints of 90% with 2 pints of 100%, you get 4 pints of what you want: 95%. You will do this process 220/4 or 55 times. Each time you'll use 1 80% pint and 3 100% pints so you'll end up using (1x55) or 55 pints of the 80% and (3x55) or 165 pints of the 100%.

Answer 2

f represents the amount of the first drink (80%)

220 - f represents the amount of the second drink (100%)

0.80f + 1,00(220 - f) = 0.95(220)

Can you solve for f and answer?