Question 1149316: You need a 90% alcohol solution. On hand, you have a 30 mL of a 55% alcohol mixture. How much pure alcohol will you need to add to obtain the desired solution?
Found 4 solutions by Boreal, greenestamps, josgarithmetic, ikleyn:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! 30 ml of 55% is 16.5 ml of pure alcohol.
add x ml of pure alcohol
the solution now has (30+x) ml of 90% alcohol, which is 16.5ml+ x ml pure alcohol
Those two are equal 27ml+.9x ml=16.5ml +x ml
10.5 ml=0.1 x
x=105 ml ANSWER
total solution is .9 (135)=121.5 ml pure alcohol
this is 105 ml pure added +16.5 there to begin with.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
Here is a simple non-algebraic method for solving "mixture" problems like this.
You are starting with 55% alcohol and adding pure (100%) alcohol, stopping when you get to 90% alcohol.
(1) 90% is 7/9 of the way from 55 to 100. (55 to 90 is 35; 55 to 100 is 45; 35/45 = 7/9.)
(2) That means 7/9 of the mixture has to be what is being added.
So 7/9 of the mixture is the 100% alcohol and 2/9 is the 30 mL you started with.
(3) 2/9 = 30 mL --> 1/9 = 15 mL --> 7/9 = 105 mL
ANSWER: Add 105 mL of pure alcohol.
Answer by josgarithmetic(39618)  (Show Source):
Answer by ikleyn(52790)  (Show Source):
You can put this solution on YOUR website! .
When I see such posts from @josgarithmetic, I become really sad and angry.
The educational value of such posts is 0 (zero, ZERO).
Moreover, posting such a nonsense, he actually blocks the posts from other tutors (from me, for example),
from which the reader / (the visitor) could learn something useful.
It is why I say that real contribution of @josgarithmetic is, actually, NEGATIVE at this forum.
Dear visitors, you will continue to get such GIBBERISH from him until YOU APPLAUD him.
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