To create a 10 ml solution of 30% saline, Ramona needs to mix certain amounts of the 50% saline solution and the 25% saline solution. We can use the concept of alligation to determine the correct proportions.
First, we denote:
- x: the amount of 50% saline solution needed (in ml)
- y: the amount of 25% saline solution needed (in ml)
Since the total volume of the solution must be 10 ml, we have:
x + y = 10
Next, we need the final concentration to be 30% saline. The equation for the salt concentration will be:
0.50x + 0.25y = 0.30(10)
Which simplifies to:
0.50x + 0.25y = 3
Now we have a system of two equations:
- x + y = 10
- 0.50x + 0.25y = 3
We can solve these equations step by step. From the first equation, we can express y in terms of x:
y = 10 – x
Substituting y into the second equation gives us:
0.50x + 0.25(10 – x) = 3
Expanding this, we find:
0.50x + 2.5 – 0.25x = 3
Combine like terms:
0.25x + 2.5 = 3
Now, isolate x:
0.25x = 3 – 2.5
0.25x = 0.5
x = 0.5 / 0.25
x = 2
Now substitute x back into the first equation to solve for y:
y = 10 – 2
y = 8
Thus, Ramona needs to mix:
- 2 ml of the 50% saline solution
- 8 ml of the 25% saline solution
By mixing 2 ml of the 50% saline solution and 8 ml of the 25% saline solution, she will successfully create 10 ml of a 30% saline solution.