How many pints of a 7% cleaning solution must be mixed with 9 pints of a 15% cleaning solution to give a 13% solution?
.07x + .15(9) = .13(x+9)
To determine how many pints of a 7% cleaning solution must be mixed with 9 pints of a 15% cleaning solution to give a 13% solution, we can use a basic formula based on the principle of mixing solutions.
Let's assume we need x pints of a 7% cleaning solution to be mixed with 9 pints of a 15% cleaning solution to obtain a 13% solution.
To solve the problem, we can set up an equation based on the amounts of the cleaning solution and their respective concentrations.
The equation can be established by multiplying the volume of each solution by its concentration and then adding the products to get the total amount of cleaning solution and its concentration.
For the 7% solution, the equation would be 0.07x, and for the 15% solution, the equation would be 0.15(9) since there are 9 pints of the 15% solution.
The equation to solve the problem would be:
0.07x + 0.15(9) = 0.13(x + 9)
Simplifying the equation, we get:
0.07x + 1.35 = 0.13x + 1.17
Now, we can solve for x by isolating the variable:
0.07x - 0.13x = 1.17 - 1.35
-0.06x = -0.18
Dividing both sides of the equation by -0.06, we find:
x = (-0.18) / (-0.06)
x = 3
Therefore, you would need to mix 3 pints of the 7% cleaning solution with 9 pints of the 15% cleaning solution to obtain a 13% cleaning solution.