mixing liters to get a percent solution

Question

How many liters of a 30% alcohol solution must be mixed with 80 liters of a 90% solution to get a 80% solution?

Answer 1

Hi Becky,

Let X be the amount of 30% alcohol solution

80 L of 90% solution to be mix with the above to obtain (X+80)L of 80% solution

Mix the 30% and 90% solutions = to get 80% solution

(30%)(X) + (90%)(80L)= (80%)(X+80)

0.30X + 0.90*80 = 0.8(X + 80)

0.30X + 72 = 0.8X + 64

              8 = 0.5X

           8/0.5 = X or X = 16 L

You will need 16 liters of 30% alcohol solution to mix an 80 liter 90% alcohol solution to get a 96 liters 80% alcohol solution.