Question 1180854
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The question is 
"How much pure alcohol will you need to add to obtain the desired solution?"
So we'll make that x and the goal of course is to find x.


x = amount of pure alcohol to add to the existing mix


The existing solution is 15 mL of 10% alcohol
Meaning, 15*0.10 = 1.5 mL of pure alcohol is present in this bottle. 


So x+1.5 mL of pure alcohol is the total after adding those x mL of pure alcohol. 


The total amount of solution is x+15 mL (which consists of pure alcohol plus water).


The ratio
(x+1.5)/(x+15)
represents the percentage of alcohol after we add in that x mL of pure alcohol.


Set this ratio equal to 0.95 and solve for x
(x+1.5)/(x+15) = 0.95
x+1.5 = 0.95(x+15)
x+1.5 = 0.95x+14.25
x-0.95x  = 14.25-1.5
0.05x  = 12.75
x = 12.75/0.05
x = 255


If we add 255 mL of pure alcohol to the original 1.5 mL of pure alcohol, then we have 255+1.5 = 256.5 mL of pure alcohol. 
The total amount of solution is x+15 = 255+15 = 270 mL


Note how
256.5/270 = 0.95 = 95%
showing we have a 95% alcohol mix now.


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Answers: 
You'll need to add <u>255 mL</u> of pure alcohol
This will lead to <u>270 mL</u> of 95% solution
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