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# how many liters is 70% alcohol solution must be added to 50 L of 40% alcohol solution to produce a 50% alcohol solution

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how many liters is 70% alcohol solution must be added to 50 L of 40% alcohol solution to produce a 50% alcohol solution

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Mathematics
1 year
2021-09-03T15:02:33+00:00
2021-09-03T15:02:33+00:00 1 Answers
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Answer:50%

Step-by-step explanation:

This question is solved by C1V1 + C2V2 ÷ V1 + V2 = final concentration

Let x = volume of 70% solution

let’s express the concentrations as decimals, so 70% = 0.7, 50% = 0.5, and 40% = 0.4

then 0.7X + 50L.4 ÷ X + 50L = 0.5

this equation becomes 0.5(X + 50) = 0.7X + 20

which yields 0.5X + 25 = 0.7X +20

combining, we get 5 = 0.2X, and 25 = X

when we mix the two volumes, we get 50L x 40% + 25L x 70%,

which yields 20L of 100% alcohol, and 17.5L of 100% alcohol, for a total of 37.5L of alcohol in 75L of solution

which is a final concentration of 50%