Question

Shaun needs to produce 1000 milliliters of 36% alcohol solution. At his disposal he has 20% alcohol solution and 40% alcohol solution. How much of each does he need in order to produce his desired solution?

Answer 1

The answer to your question is 200 ml of the solution 20% and 800 ml of the solution 40%.

Step-by-step explanation:

Data

Total volume = V = 1000 ml

Final concentration = F = 36%

Concentration of solution 1 = c1 = 20%

Concentration of solution 2 = c2 = 40%

Volume of solution 1 = v1 = ?

Volume of solution 2 = v2 = ?

Process

1.- Write an equation to solve this problem

FV = c1v1 + c2v2

2.- Write volume in terms of total volume

Total volume = V

v1 = x

v2 = 1000 - x

3.- Substitution

(36)(1000) = 20x + 40(1000 - x)

Solve for x

36000 = 20x + 40000 - 40x

36000 - 40000 = 20x - 40x

-4000 = -20x

x = -4000/-20

x = 200

Then v1 = 200 ml

and v2 = 1000 - v1

= 1000 - 200

= 800 ml