Question

How many milliliters of a 15% saline solution and how many milliliters of a 40% saline solution must be mixed to produce 10 milliliters of a 30% saline solution?

Volume of 15% solution= ____
Volume of 40% solution = ____

Answer 1

x - volume of 15% saline solution. Theres is 15% x = 0,15 x saline solution
y - volume of 40% saline solution. There is 40% y = 0,4y saline solution

You want to produce 10 mililiers so x+y= 10

And this saline has to be 30%, so you've got 30 % * 10 = 0,3 * 10 = 3 ml saline. So:
0,15x + 0,4y = 3
And you've got system of equations:

`\begin{cases} x+y=10 \\ 0,15x+0,4y=3\end{cases} \\ \begin{cases} x=10-y \\ 0,15x+0,4y=3\end{cases} \\ \hbox{Substitute value from first equation to second:} \\ 0,15(10-y)+0,4y=3 \\ 1,5-0,15y+0,4y=3 \\ 0,25y=1,5 \qquad /:0,25 \\ y=(1,5)/(0,25)=(150)/(25)=6 \\ \hbox{Then:} \\ x=10-y=10-6=4`

So answer:
Volume of 15% saline solution : 4 mililiters
Volume of 40% saline solution: 6 mililiters.