In what proportion should you mix 7% and 2% solutions to get 5% solutions?
To determine the proportion of 7% and 2% solutions that should be mixed to obtain a 5% solution, let's assume that we need to mix x liters of the 7% solution and y liters of the 2% solution.
Since the final solution required is 5% concentration, the total amount of solution obtained will be x + y liters.
To determine the proportion, we can write the following equation based on the concentration of the solutions:
0.07x + 0.02y = 0.05(x + y)
Simplifying the equation:
0.07x + 0.02y = 0.05x + 0.05y
0.07x - 0.05x = 0.05y - 0.02y
0.02x = 0.03y
Divide both sides by 0.03:
x = (0.03/0.02)y
Simplifying further:
x = 1.5y
This equation implies that the proportion of the 7% solution to the 2% solution must be 1.5:1.