Question 1200677: How much water must be evaporated from 180 L of 72% brine solution in order to increase the solution’s concentration by 8%?
A. 12 L
B. 16 L
C. 18 L
D. 20 L
Found 5 solutions by Alan3354, josgarithmetic, ikleyn, math_tutor2020, greenestamps:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! How much water must be evaporated from 180 L of 72% brine solution in order to increase the solution’s concentration by 8%?
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180 L of 72% brine solution --> 180*0.72 = 129.6 L of salt and 50.4 L of water.
For 129.6 L to be 80%, the water is 20% = 32.4 L
50.4 - 32.4 = 18 L of water to evaporate.
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PS Most, maybe all, salts can't have a concentration that high.
Answer by josgarithmetic(39617)  (Show Source):
Answer by ikleyn(52786)  (Show Source):
You can put this solution on YOUR website! .
Brine solution becomes saturated at about of 27% concentration,
and after that DOES NOT dissolve salt, anymore.
The extra salt goes to sediment.
Read and learn about it from this Wikipedia article
https://en.wikipedia.org/wiki/Brine
Those who studied Science in middle school in their 6th - 7th grade, usually know about it.
At least, they SHOULD know.
So, the person who composed this problem, clearly has huge void omissions in his (or her) middle school education.
Which does not prevent him (or her) from composing incorrect problems and littering the Internet.
Answer by math_tutor2020(3817) (Show Source):
You can put this solution on YOUR website!
x = amount of water to evaporate
amount is in liters
72% of 180 = 0.72*180 = 129.6 = amount of pure salt.
This amount stays the same no matter how much water evaporates (since salt isn't carried into the air by the water particles).
A = 129.6 = amount of salt left after evaporation
B = 180-x = amount of solution left after evaporation
A/B = concentration of salt after evaporation
A/B = (129.6)/(180-x)
A/B = 0.80
(129.6)/(180-x) = 0.80
129.6 = (180-x)0.80
129.6 = 0.80(180-x)
129.6 = 0.80(180)+0.80(-x)
129.6 = 144-0.80x
129.6+0.80x = 144
0.80x = 144-129.6
0.80x = 14.4
x = (14.4)/(0.80)
x = 18
Check:
(129.6)/(180-x) = 0.80
(129.6)/(180-18) = 0.80
(129.6)/(162) = 0.80
0.80 = 0.80
The answer is confirmed.
Answer:
18 liters of water must evaporate.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
We can ignore the fact that a salt concentration of 72% is not possible and treat the problem as a mathematical exercise.
A couple of the other tutors have done that and shown algebraic solution methods. Here is a different method.
The increase of 8% in the concentration makes the new concentration 80%. So 72% of the original 180 L is equal to 80% of the new total volume.
Let x be the new volume; then
So the amount of water that must be evaporated is 180-162 = 18 L.
ANSWER: 18 L
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