Question

The boys mixed 10 gallons of the 20% pure lemon juice mix and 10 gallons of the 70% pure lemon juice mix, because they wanted 20 gallons of lemonade at a 40% lemon juice mixture. They thought that because 40% was almost halfway between 20% and 70%, they should just mix equal parts of both, but the lemonade turned out too tart. How much of each should they have used to get a final mixture of 20 gallons at 40% lemon juice?

Answer 1

You have to prepare 20 gallons of 40% mixture using 20% and 70% mixtures.
Therefore lemon in final mixture =40% of 20 gallons =8 gallons.
Suppose x gallons were taken from 20% mixture.
Lemon contribution by this =20% of x gallons.
=x/5 gallons.
Again, now the mixture has to be of 20 gallons, we have to take (20-x) gallons of 70% mixture.
Lemon contribution by this =70% of (20-x)
=14-(7x/10) gallons.
But, these both added should be equal to final amount of lemon.
Therefore x/5 +14-(7x/10) =8
=> (2-7)x/10 = -6
=> x = 6×10/5
=> x = 12 gallons.
Thus, 20% mixture =12 gallons and
70% mixture =8 gallons
[Answer]
Hope this helps. For any clarifications please comment. Thanks!