Roman mixes 12 liters of 8% acid solution with a 20% acid solution, which results in a 16% acid solution. Find the number of liters of 20% acid solution in the new mixture. show your work

.08*12 + .20*x = .16 (12+x)

To solve this problem, we can use the concept of the concentration of the acid solution.

Let's assume that Roman mixed x liters of the 20% acid solution.

The amount of acid from the 8% solution is given by 8% of 12 liters, which is 0.08 * 12 = 0.96 liters of acid.

The amount of acid from the 20% solution is given by 20% of x liters, which is 0.2x liters of acid.

In the new mixture, the total amount of acid is given by the sum of the acids from the two solutions, which is 0.96 + 0.2x liters of acid.

Since the total volume of the new mixture is 12 + x liters, the concentration of the acid in the new mixture can be expressed as 16%.

We can write the equation as (0.96 + 0.2x) / (12 + x) = 16%.

To solve this equation, we can start by multiplying both sides by (12 + x) to get rid of the denominator:

0.96 + 0.2x = 0.16(12 + x).

Simplifying this equation, we have:

0.96 + 0.2x = 1.92 + 0.16x.

Now, let's isolate the term with x on one side:

0.2x - 0.16x = 1.92 - 0.96.

Simplifying further:

0.04x = 0.96.

Dividing both sides by 0.04:

x = 0.96 / 0.04 = 24.

Therefore, the number of liters of the 20% acid solution in the new mixture is 24 liters.

To summarize the steps:
1. Set up the equation using the amount of acid from each solution and their concentrations.
2. Simplify the equation.
3. Isolate the term with x on one side.
4. Solve for x.
5. Interpret the solution, which gives the number of liters of the 20% acid solution in the new mixture.