Question 1140737: How would you solve this word problem?
You need 570 mL of a 85% alcohol solution. On hand, you have a 95% alcohol mixture. How much of the 95% alcohol mixture and pure water will you need to obtain the desired solution?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617)   (Show Source):
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
I don't know why the other tutor called the solution an estimate. The method is valid, and the answer is exact.
Since you asked how I would solve the problem, I will show you a method that, if you understand it, will get you to the answer to any mixture problem like this much faster, and with much less effort, than the traditional algebraic method shown by the other tutor.
Here it is, in its entirety:
(1) You are starting with 95% alcohol and you are adding 0% alcohol; you want to stop when you get 85% alcohol.
(2) 85% is 10/95 = 2/19 of the way from 95% to 0%. (Picture the numbers 95, 85, and 0 on a number line. The difference between the 95 and 0 is 95; the difference between 95 and 85 is 10. So the distance from 95 to 85 is 10/95 = 2/19 of the distance from 95 to 0.)
(3) That "2/19 of the way" from 95 to 0 means 2/19 of the mixture must be the added 0% alcohol.
2/19 of 570 mL is 2*30 = 60 mL.
ANSWER: You need 60 mL of pure water and 570-60 = 510 mL of the 95% alcohol.
All the words of explanation make it sound like a long and complicated process; but here is all you need to do to solve the problem:
95-0 = 95; 95-85 = 10; 10/95 = 2/19
2/19 of 570 = 60; 570-60 = 510
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