10 quarts of 20 % salt solution mixed with 5 quarts of 80 % salt solution to make 15 quarts of 40 % salt solution
<em><u>Solution:</u></em>
The final mixture is 15 quarts
Let amount of 20% solution to be mixed, be x
Then, the amount of 80 % solution to be mixed is 15 - x
Thus, we can say,
"x" quarts of 20 % salt solution mixed with (15 - x) quarts of 80 % salt solution to make 15 quarts of 40 % salt solution
thus, we frame a equation as,
![x \times 20 \% + (15-x) \times 80 \% = 15 \times 40 \%](https://tex.z-dn.net/?f=x%20%5Ctimes%2020%20%5C%25%20%2B%20%2815-x%29%20%5Ctimes%2080%20%5C%25%20%3D%2015%20%5Ctimes%2040%20%5C%25)
![x \times \frac{20}{100} + (15-x) \times \frac{80}{100} = 15 \times \frac{40}{100}\\\\0.2x + 0.8(15-x) = 0.4 \times 15\\\\0.2x + 12 - 0.8x = 6\\\\0.6x = 12 - 6\\\\0.6x = 6\\\\x = 10](https://tex.z-dn.net/?f=x%20%5Ctimes%20%5Cfrac%7B20%7D%7B100%7D%20%2B%20%2815-x%29%20%5Ctimes%20%5Cfrac%7B80%7D%7B100%7D%20%3D%2015%20%5Ctimes%20%5Cfrac%7B40%7D%7B100%7D%5C%5C%5C%5C0.2x%20%2B%200.8%2815-x%29%20%3D%200.4%20%5Ctimes%2015%5C%5C%5C%5C0.2x%20%2B%2012%20-%200.8x%20%3D%206%5C%5C%5C%5C0.6x%20%3D%2012%20-%206%5C%5C%5C%5C0.6x%20%3D%206%5C%5C%5C%5Cx%20%3D%2010)
Thus 10 quarts of 20 % solution is mixed
Then, 15 - x = 15 - 10 = 5
5 quarts of 80 % salt solution is mixed