Question

Mara needs to mix some 30% acid solution and some 70% alcohol solution to end up with 20 liters of 54% solution. How many liters of the 70% solution will she need? Type in your numerical answer only; do not type any words or letters with your answer.

Answer 1

Answer:

12 liters

Step-by-step explanation:

Let the solution with 30% acid solution be x litres

And the solution of with 70% alcohol to be y liters

X = Volume of 30% solution in liters

Y = Volume of 70% solution in liters

For acid solution,

30/100 × x = 0.3x

For alcohol solution,

70/100 × y = 0.7y

Since we need 54% of the combination of the 2 solutions: 54/100 = 0.54

The combination of the 2 solutions must give us 54 solutions combination and that is:

0.3x + 0.7y = 0.54(x+y)___ equation 2

X+y = 20_____ equation 1

solve the system of equations and we have:

From equation 2,  x +y = 20

Therefore x = 20 -y

Replace the above in equation 2

0.3(20 - y) + 0.7y = 0.54(20)

6 - 0.3y + 0.7y = 10.8

Collect like terms

0.4y = 4.8

Y = 12 liters and that means 12 liters of 70% alcohol solution