Question 276407: How many kgs of salt must be added to 24 kg of 20% salt solution in order to increase the concentration of salt to 40%?
Found 3 solutions by mananth, ikleyn, greenestamps:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website! How many kgs of salt must be added to 24 kg of 20% salt solution in order to increase the concentration of salt to 40%?
salt 100%-------------------- 20%---------------40% strength
x------------------------------24 kgs-----------x+24 kgs
100%*x+20%*24=40%*(x+24)
1x+4.80=.4x+9.6
x-0.4x=6-4.8
0.6x=1.2
x=1.2/0.6 = 2 kgs
Answer by ikleyn(53742)  (Show Source):
You can put this solution on YOUR website! .
How many kgs of salt must be added to 24 kg of 20% salt solution in order to increase
the concentration of salt to 40%?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
When the problems are talking about salt solutions of high concentration, it is useful to remember
that water solutions of NaCl can not have concentration higher than 27%.
At 27%, the solution becomes saturated, and concentration can not go higher than this value.
This is a standard fact, which students learn from the Science course in their 6-th grade.
The second reason why I write these lines, is that the calculations in the post by @mananth
are incorrect and inaccurate and lead to wrong answer.
I came to bring a correct solution.
The balance equation for this problem is
x + 0.2*24 = 0.4*(x+24),
where 'x' is the salt mass to add.
Simplify and find 'x'
x + 4.8 = 0.4x + 9.6,
x - 0.4x = 9.6 - 4.8,
0.6x = 4.8
x = 4.8/0.6 = 8.
ANSWER. 8 kilograms of salt should be added.
Solved correctly and explained about the saturation limit.
Answer by greenestamps(13326)  (Show Source):
You can put this solution on YOUR website!
Also ignoring the fact that a 40% solt solution is not possible....
Any 2-part mixture problem like this can be solved informally (and quickly, if the numbers are "nice") using the logical fact that the ratio in which the two ingredients must be mixed is exactly determined by where the target percentage lies between the percentages of the two ingredients.
For this problem...
(1) The target percentage of 40% is "3 times as close" to 20% as it is to 100% (the difference between 20 and 40 is 20; the difference between 40 and 100 is 60; 20 is one-third of 60)
(2) That means the amount of the 20% ingredient must be 3 times the amount of the 100% ingredient
The given amount of the 20% ingredient is 24 kg, so the amount of the added 100% salt must be one-third of 24 kg, which is 8 kg.
ANSWER: 8 kg
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