Question

johnathan needs 70 liters of a 50% alcohol solution. he has a 30% solution and an 80% solution available. How many liters of the 30% solution and hjow many liter of the 80% solution should he mix to make the 50% solution?

Answer 1

28 l of 80%

42 l of 30%

Explanation:

Target is 70 l of 50% solution

It will contain 70*0.5= 35 l of alcohol

x l of 80% solution and y l of 30% solution mixed to get the target solution

x+y=70 is the equation for total volume, and

0.8x+0.3y= 35 is the equation for the alcohol content. Solving this:

• y= 70-x
• 0.8x+0.3*(70-x) = 35
• 0.8x+21- 0.3x= 35
• 0.5x= 35-21
• 0.5 x= 14
• x= 14/0.5
• x=28 l of 80% solution

then

• y= 70-x= 70 -28 l= 42 l of 30% solution