how much liquid containing 6% boric acid should be mixed with quarts of liqud that is 15% boric acid in order to obtain a solution that is 12% boric acid?

something is missing? How many quarts of 15percent? As it is written, there are a infinite number of solutions.

2 quarts of liquid

To find the amount of liquid containing 6% boric acid that needs to be mixed with a certain amount of liquid containing 15% boric acid to obtain a solution that is 12% boric acid, we need to use a mathematical approach known as the method of mixtures.

Let's denote the amount of liquid containing 6% boric acid that we need to find as "x" quarts.

Now, let's break down the information we have:

1. The concentration of the liquid containing 6% boric acid is 6%.
2. We want the final solution to have a concentration of 12% boric acid.
3. The concentration of the liquid containing 15% boric acid is 15%.
4. We know the amount of liquid containing 15% boric acid is "quarts" (a value not provided, so we will keep it general for now).

To solve the problem, we use the equation:

(total amount of boric acid in the 6% solution + total amount of boric acid in the 15% solution) / (total amount of solution) = desired concentration

Expressing this equation mathematically:

(0.06 * x + 0.15 * quarts) / (x + quarts) = 0.12

Now we can solve this equation to find the value of "x" (the amount of liquid containing 6% boric acid).

First, we can multiply both sides of the equation by (x + quarts) to eliminate the denominator:

0.06 * x + 0.15 * quarts = 0.12 * (x + quarts)

Expanding further:

0.06 * x + 0.15 * quarts = 0.12 * x + 0.12 * quarts

Next, we can simplify the equation:

0.15 * quarts - 0.12 * quarts = 0.12 * x - 0.06 * x

0.03 * quarts = 0.06 * x

Dividing both sides of the equation by 0.06:

quarts / 2 = x

Therefore, the amount of liquid containing 6% boric acid that should be mixed with "quarts" of liquid containing 15% boric acid to obtain a solution that is 12% boric acid is half the amount of the liquid containing 15% boric acid.

In summary, to find the amount of liquid containing 6% boric acid, divide the amount of liquid containing 15% boric acid by 2.