Question

If 4 liters of a 10% vinegar solution is mixed with x liters of a 30% vinegar solution, the result is a 25% vinegar solution. How many liters of the 30% vinegar solution were mixed? The mixture required liter(s) of the 30% solution

Answer 1

To find the amount of 30% vinegar solution needed to mix with 4 liters of a 10% solution to achieve a 25% solution, the equation 0.10 × 4 + 0.30 × x = 0.25 × (4 + x) is solved, resulting in x = 12 liters.

Step-by-step explanation:

The student's question is about mixing different concentrations of vinegar solutions to obtain a solution of a desired concentration. In the given scenario, 4 liters of a 10% vinegar solution is mixed with x liters of a 30% vinegar solution to achieve a 25% vinegar solution. To find the number of liters (x) of the 30% vinegar solution needed, we can set up an equation that represents the total amount of pure vinegar in the final mixture.

The amount of pure vinegar in the 4 liters of the 10% solution is 0.10 × 4 liters, and the amount in the x liters of the 30% solution is 0.30 × x liters. In the final solution, this amount should be equal to 25% of the total volume, which is (4 + x) liters. So the equation to solve is:

0.10 × 4 + 0.30 × x = 0.25 × (4 + x)
0.40 + 0.30x = 1 + 0.25x
0.30x - 0.25x = 1 - 0.40
0.05x = 0.60
x = 0.60 / 0.05
x = 12 liters

Hence, the student will need 12 liters of the 30% vinegar solution.