Answer:
<u>800 liters</u> of 90% saline solution and <u>1200 liters</u> of 40% saline solution should be used.
Step-by-step explanation:
Given:
At 2000 liters of 60% saline solution the attendant has to mix a 90% and a 40% saline solution.
Now, to find the number of liters of saline solution each should be used.
<u><em>Let the liters of 90% saline solution mix be </em></u>
<u><em /></u>
<u><em>And let the liters of 40% saline solution mix be</em></u> ![y.](https://tex.z-dn.net/?f=y.)
So, the total number of liters:
![x+y=2000.](https://tex.z-dn.net/?f=x%2By%3D2000.)
![y=2000-x\ \ \ ....(1)](https://tex.z-dn.net/?f=y%3D2000-x%5C%20%5C%20%5C%20....%281%29)
Now, the total percentage of saline solution:
![90\%\ of\ x+40\%\ of\ y=60\%\ of\ 2000](https://tex.z-dn.net/?f=90%5C%25%5C%20of%5C%20x%2B40%5C%25%5C%20of%5C%20y%3D60%5C%25%5C%20of%5C%202000)
![\frac{90}{100}\times x+\frac{40}{100}\times y=\frac{60}{100}\times 2000](https://tex.z-dn.net/?f=%5Cfrac%7B90%7D%7B100%7D%5Ctimes%20x%2B%5Cfrac%7B40%7D%7B100%7D%5Ctimes%20y%3D%5Cfrac%7B60%7D%7B100%7D%5Ctimes%202000)
![0.9x+0.4y=1200](https://tex.z-dn.net/?f=0.9x%2B0.4y%3D1200)
Substituting the value of
from equation (1) we get:
![0.9x+0.4(2000-x)=1200](https://tex.z-dn.net/?f=0.9x%2B0.4%282000-x%29%3D1200)
![0.9x+800-0.4x=1200](https://tex.z-dn.net/?f=0.9x%2B800-0.4x%3D1200)
![0.5x+800=1200](https://tex.z-dn.net/?f=0.5x%2B800%3D1200)
Subtracting both sides by 800 we get:
![0.5x=400](https://tex.z-dn.net/?f=0.5x%3D400)
Dividing both sides by 0.5 we get:
![x=800.](https://tex.z-dn.net/?f=x%3D800.)
<u>The liters of 90% saline solution mix = 800.</u>
Now, substituting the value of
in equation (1) to get the liters of 40% saline solution:
![y=2000-x](https://tex.z-dn.net/?f=y%3D2000-x)
![y=2000-800](https://tex.z-dn.net/?f=y%3D2000-800)
![y=1200.](https://tex.z-dn.net/?f=y%3D1200.)
<u>Thus, the liters of 40% saline solution = 1200.</u>
Therefore, 800 liters of 90% saline solution and 1200 liters of 40% saline solution should be used.