a 9 percent salt water solution is mixed with 4 oz. of an 18 percent salt water solution in order to obtain a 15 percent salt water solution. how much of the first should be used?
solve
.09x + .18(4) = .15(x+4)
Cheater.
To solve this problem, we need to use the concept of a salt-water solution's concentration and the amount of solution. Let's break down the steps:
1. Assign variables: Let's say we need x ounces of the 9% salt water solution.
2. Express the amount of salt in each solution: In the 9% salt water solution, 9% of the x ounces is actual salt. So, 0.09x ounces of salt will be in this solution. In the 18% salt water solution, 18% of the 4 ounces is actual salt. Therefore, 0.18 * 4 = 0.72 ounces of salt will be in this solution.
3. Express the amount of salt in the final 15% solution: We know that the total amount of salt in the final solution is the sum of the salt in the 9% solution and the salt in the 18% solution. So, 0.09x + 0.72 ounces = 0.15 * (x + 4) ounces.
4. Solve the equation: We can now solve the equation to find the value of x.
0.09x + 0.72 = 0.15x + 0.6
Rearrange the equation:
0.09x - 0.15x = 0.6 - 0.72
-0.06x = -0.12
Divide both sides by -0.06:
x = -0.12 / -0.06
x = 2
So, to obtain a 15% salt water solution, you should use 2 ounces of the 9% salt water solution.