Answer:
13.3 L of 5% salt solution and 11.7 L of 20% salt solution
Step-by-step explanation:
Let
x L = amount of 5% solution
y L = amount of 20% solution.
1. A chemistry teachers needs 25 liters of salt solution, then
![x+y=25](https://tex.z-dn.net/?f=x%2By%3D25)
2. A chemistry teachers needs 25 liters of a 12% salt solution, so there are
liters of salt.
Amount of salt in 5% solution
liters
Amount of salt in 20% solution
liters,
thus
![0.05x+0.2y=3](https://tex.z-dn.net/?f=0.05x%2B0.2y%3D3)
3. Solve the system of two equations:
![\left\{\begin{array}{l}x+y=25\\ \\0.05x+0.2y=3\end{array}\right.](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bl%7Dx%2By%3D25%5C%5C%20%5C%5C0.05x%2B0.2y%3D3%5Cend%7Barray%7D%5Cright.)
From the first equation,
![x=25-y](https://tex.z-dn.net/?f=x%3D25-y)
Substitute it into the second equation:
![0.05(25-y)+0.2y=3\\ \\1.25-0.05y+0.2y=3\\ \\0.2y-0.05y=3-1.25\\ \\0.15y=1.75\\ \\15y=175\\ \\y\approx 11.7\ L\\ \\x=25-11.7=13.3\ L](https://tex.z-dn.net/?f=0.05%2825-y%29%2B0.2y%3D3%5C%5C%20%5C%5C1.25-0.05y%2B0.2y%3D3%5C%5C%20%5C%5C0.2y-0.05y%3D3-1.25%5C%5C%20%5C%5C0.15y%3D1.75%5C%5C%20%5C%5C15y%3D175%5C%5C%20%5C%5Cy%5Capprox%2011.7%5C%20L%5C%5C%20%5C%5Cx%3D25-11.7%3D13.3%5C%20L)