A researcher needs 60 L of 50% concentrate solution for a certain experiment, but she has only 30% solution and 70% solution. How many liters of the 30% and the 70% solutions should she mix to get what she needs?

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candidatesmaths21 candidatesmaths21 · Answer 1 · 2021-09-08T15:52:39+02:00

Answer:

30 liters of 30% solution and 30 liters of 70% of solution should be mixed by the researcher to get 60 liters of 50% solution.

Step-by-step explanation:

Let 'x' liters of 30% solution and 'y' liters of 70% solution are added together to get the required 60 liters of 50% of the solution.

According to the question, 30% solution and 70% solution are mixed and so, we get

[tex]0.3x+0.7y=0.5 \cdot 60\\\Rightarrow 0.3x+0.7y=30----(1)[/tex]

Also, sum of the final solution should be 60 liters only so, we get

[tex]x+y=60----(2)[/tex]

Solving equations (1) and (2), we get

[tex]x=30 liters\\ y=30 liters[/tex]

Hence, we can say that 30 liters of 30% solution and 30 liters of 70% of solution should be mixed by the researcher to get 60 liters of 50% solution.

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