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=\frac{1,5}{0,25}=\frac{150}{25}=6 \\ \hbox{Then:} \\ x=10-y=10-6=4](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D%20x%2By%3D10%20%5C%5C%200%2C15x%2B0%2C4y%3D3%5Cend%7Bcases%7D%20%5C%5C%20%5Cbegin%7Bcases%7D%20x%3D10-y%20%5C%5C%200%2C15x%2B0%2C4y%3D3%5Cend%7Bcases%7D%20%5C%5C%20%5Chbox%7BSubstitute%20value%20from%20first%20equation%20to%20second%3A%7D%20%5C%5C%200%2C15%2810-y%29%2B0%2C4y%3D3%20%5C%5C%201%2C5-0%2C15y%2B0%2C4y%3D3%20%5C%5C%200%2C25y%3D1%2C5%20%5Cqquad%20%2F%3A0%2C25%20%5C%5C%20y%3D%5Cfrac%7B1%2C5%7D%7B0%2C25%7D%3D%5Cfrac%7B150%7D%7B25%7D%3D6%20%5C%5C%20%5Chbox%7BThen%3A%7D%20%5C%5C%20x%3D10-y%3D10-6%3D4)
So answer:
Volume of 15% saline solution : 4 mililiters
Volume of 40% saline solution: 6 mililiters.