In what proportion should you combine a 2:5 soaking solution and distilled water to create a 300 ml of a 1:20 solution?
To find the proportion in which the soaking solution and distilled water should be combined, we need to understand the ratio of concentration.
First, let's break down the given ratio of the soaking solution, which is 2:5. This means that for every 2 units of soaking solution, there are 5 units of distilled water.
Next, we need to understand the ratio of the desired solution, which is 1:20. This indicates that for every 1 unit of soaking solution, there are 20 units of distilled water.
Now, we can set up a proportion to find the correct combination. Let's denote x as the amount of soaking solution, and y as the amount of distilled water.
For the soaking solution, we have:
x / (x + y) = 2 / 5
For the distilled water, we have:
y / (x + y) = 5 / 5
To create a 1:20 solution, we want the ratio of soaking solution to distilled water to be 1:20. Therefore, we can set up another proportion:
x / y = 1 / 20
Now we have a system of equations. To solve for x and y, we can use the method of substitution.
From the first equation, we can solve for y in terms of x:
y = 5/2 * x
Now we substitute the value of y in the second equation:
x / (5/2 * x) = 1 / 20
Simplifying the equation:
2x / 5x = 1 / 20
Cross-multiplying:
2x * 20 = 5x * 1
40x = 5x
Simplifying:
40 = 5
This equation is not possible, so there is no valid solution for this specific combination of ratios.
In conclusion, there is no proportion in which the 2:5 soaking solution and distilled water can be combined to create a 300 ml 1:20 solution.