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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 = ____

Verified Answer :

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

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

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