Question

a chemistry teacher needs to mix a 20% salt solution with a 80% salt solution to make 15 qt of a 40% salt solution. how many quarts of each solution should the teacher mix to get the desired result?​

Answer 1

10 quarts of 20 % salt solution mixed with 5 quarts of 80 % salt solution to make 15 quarts of 40 % salt solution

Solution:

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,

$x \times 20 \% + (15-x) \times 80 \% = 15 \times 40 \%$

$x \times \frac{20}{100} + (15-x) \times \frac{80}{100} = 15 \times \frac{40}{100}\\\\0.2x + 0.8(15-x) = 0.4 \times 15\\\\0.2x + 12 - 0.8x = 6\\\\0.6x = 12 - 6\\\\0.6x = 6\\\\x = 10$

Thus 10 quarts of 20 % solution is mixed

Then, 15 - x = 15 - 10 = 5

5 quarts of 80 % salt solution is mixed