he first solution contains 25 % acid, the second contains 35 % acid, and the third contains 55 % acid. She created 100 liters of a 45 % acid mixture, using all three solutions. The number of liters of 55 % solution used is 3 times the number of liters of 35 % solution used. How many liters of each solution was used?

Volume of first solution = 20 Liters

Volume of second solution = 20 Liters

Volume of third solution = 60 Liters

Explanation:

Let the volume second solution used = y

Let the volume of third solution used = 3y

Let the volume of first solution used = 100 - (y + 3y)

= 100 - 4y

The volume of acid in the first solution (V₁) = 25% of (100-4y)

= 25-y

The volume of acid in the second solution (V₂) = 35% of y

= 0.35y

The volume acid in the third solution (V₃) = 55% of 3y

=1.65y

The Volume of acid in Mixture (V₄) = 45% of 100

= 45

From the conservation of volume:

V₄ = V₁ + V₂ + V₃

45 = (25-y) + 0.35y + 1.65y

45 = 25 - y + 0.35y + 1.65y

45 - 25 = y

y = 20

So the volume of first solution used = 100 - 4y

= 100 - 4 (20)

= 20 Liters

So the volume of second solution used = y

= 20 Liters

So the volume of third solution used = 3y

= 3 (20)

= 60 Liters