A 9 percent salt-water solution is mixed with 4 ounces of an 18 percent salt-water solution in order to obtain a 15 percent salt-water solution. How much of the first solution should be used?
To find out how much of the 9 percent salt-water solution should be used, we can set up an equation based on the amount of salt in the mixture.
Let's assume that the amount of the 9 percent salt-water solution to be used is x ounces.
In the 9 percent solution, the amount of salt is 9% of x, which is 0.09x ounces.
In the 18 percent solution, the amount of salt is 18% of 4 ounces, which is 0.18 * 4 = 0.72 ounces.
In the final 15 percent solution, the amount of salt is the sum of the salt in both solutions: 0.09x + 0.72 ounces.
Since the result is a 15 percent solution, the amount of salt in the final mixture is 15% of the total amount, which is 0.15 times the sum of the amounts of the two solutions: 0.15(x + 4) ounces.
Setting up the equation:
0.09x + 0.72 = 0.15(x + 4)
Now, we can solve for x:
0.09x + 0.72 = 0.15x + 0.6
0.09x - 0.15x = 0.6 - 0.72
-0.06x = -0.12
x = -0.12 / -0.06
x = 2
Therefore, you should use 2 ounces of the 9 percent salt-water solution.