Question

how many gallons of 35 % alcohol solution and 50 % alcohol solution must be mixed to get 12 gallons of 40 % alcohol solution?

Answer 1

• 8 gallons of 35%
• 4 gallons of 50%

Explanation:

You want the quantities of 35% alcohol and 50% alcohol that must be mixed to get 12 gallons of 40% alcohol solution.

Setup

Let x represent the quantity of 50% alcohol in the mix. Then (12 -x) is the quantity of 35% alcohol solution. The total amount of alcohol in the final solution is ...

0.50x +0.35(12 -x) = 0.40(12)

Solve

0.15x = 0.05(12) . . . . . . . subtract 0.35(12)

x = 4 . . . . . . . . . . . . divide by 0.15

12 -x = 8 . . . . . quantity of 35% solution

8 gallons of 35% solution must be mixed with 4 gallons of 50% solution to make a 40% solution of alcohol.