how much liquid containing 6% boric acid should be mixed with 2 quarts of a liquid that is 15% boric acid in order to obtain a solution that is 12% boric acid?
5 quarts
.06x + .15*2 = .12(x+2)
To solve this problem, we can set up an equation based on the amount of boric acid in each solution.
Let's assume x represents the amount of liquid containing 6% boric acid needed to be mixed.
The total amount of boric acid in the 6% solution will be 6% of x.
The total amount of boric acid in the 15% solution will be 15% of 2 quarts (which is 0.15 * 2 = 0.3 quarts).
The total amount of boric acid in the final 12% solution will be 12% of (x + 2).
Now, we can set up the equation:
0.06x + 0.3 = 0.12(x + 2)
Simplifying the equation:
0.06x + 0.3 = 0.12x + 0.24
Subtracting 0.06x from both sides:
0.3 - 0.24 = 0.12x - 0.06x
0.06 = 0.06x
Dividing both sides by 0.06:
x = 1
Therefore, you would need 1 quart of the liquid containing 6% boric acid to mix with 2 quarts of the liquid containing 15% boric acid in order to obtain a solution that is 12% boric acid.
To solve this problem, we need to use the concept of concentrations and the formula for mixing solutions.
Let's start by defining the variables:
Let "x" be the amount (in quarts) of the 6% boric acid liquid to be mixed.
Now, let's calculate the amount of boric acid (in quarts) in each solution:
For the 6% boric acid liquid, the amount of boric acid is 0.06x.
For the 15% boric acid liquid, the amount of boric acid is 0.15(2), which simplifies to 0.3.
Next, let's set up the equation based on the idea that the total amount of boric acid in the final solution should be the sum of the amounts in each individual liquid. In other words:
0.06x + 0.3 = 0.12(x + 2)
Now, let's solve for "x":
0.06x + 0.3 = 0.12x + 0.24
0.06x - 0.12x = 0.24 - 0.3
-0.06x = -0.06
x = -0.06 / -0.06
x = 1
So, to obtain a solution that is 12% boric acid, you need to mix 1 quart of the 6% boric acid liquid with 2 quarts of the 15% boric acid liquid.