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You need 10% alcohol solution. On hand, you have a 390mL of a 5% alcohol mixture. You also have 75% alcohol mixture. How much of the 75% mixture will you need to add to obtain the desired solution

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jcherry99

Remark

There is a short way of doing this problem, but I'm not sure how to do it. If you are interested, you could google for the answer to this kind of problem. In the meantime, there is one sure way of doing it.

Givens

390 mL of a 5% solution.

Enough 75% solution to satisfy the equation.

Desired result = 10%

Equation

C_75% * V + C_5% * 390 = C_10% * (390 + V)

Solution

75% * V + 5%*390 = 10% (390 + V)

75% * V + 0.05* 390 = 0.1(390 + V)

0.75 * V + 19.5 = 39  + 0.1 * V              

0.75 * V - 0.1*V + 19.6 = 39

0.65 * V  +  19.5 = 39  

0.65*V = 39 - 19.5

0.65*V = 19.5

V = 19.5 / 0.65

V = 30 mL of 75% alcohol


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