In what proportion should you mix 7% and 1% solutions to get 4% solution
Let's assume we want to mix x liters of the 7% solution and y liters of the 1% solution to get a total of z liters of the 4% solution.
The amount of pure solution in the 7% solution is 7/100 * x liters.
The amount of pure solution in the 1% solution is 1/100 * y liters.
To get a total of z liters of the 4% solution, the amount of pure solution in the 4% solution would be 4/100 * z liters.
Since the amount of pure solution in the 7% and 1% solutions should equal the amount of pure solution in the 4% solution, we can create the equation:
7/100 * x + 1/100 * y = 4/100 * z
We also know that x + y = z, since the total volume of the mixture is equal to the sum of the volume of the 7% and 1% solutions.
To solve this, we can substitute x + y into the equation:
7/100 * x + 1/100 * y = 4/100 * (x + y)
Multiplying through by 100 to eliminate the denominators:
7x + y = 4x + 4y
Simplifying the equation:
7x - 4x = 4y - y
3x = 3y
Divide both sides by 3:
x = y
This means that the proportion of the 7% and 1% solutions should be equal, or in other words, they should be mixed in a 1:1 ratio.