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? Write your answer in complete sentences. Show all work.

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?  Write your answer in complete sentences. Show all work.

therealone21-1 · Answer

@sammixboo @wolf1728 @Seeing.In.Pixels @.Mehek. @.Sam.

therealone21-1 · Answer

@jabez177 @linn99123 @nincompoop

mathmate · Answer

1. general way
Set up an equation, c=concentration, v=volume
 c1=0.20, c2=0.70
v1=x, v2=20-x
Since we're mixing two different concentrations, and obtain v3=20 gal. of c3=0.40 
use the equation:
c1v1+c2v2=c3v3
Put in the known numbers and solve for v1 (or x).

2. When you don't have a calculator, nor a pen/pencil and paper
Target is 40%, so put the numbers in increasing order 20,40,70
Take the ratio of the difference of adjacent numbers 40-20 : 70-40,  20:30, or 2:3
So we put the 70%:20% in the ratio of 2:3, which means 8 gal of 70%, 12 gal of 20%
and that's your answer.