Question 947566: Q. How much salt should be added to 60 litres of a 20% solution of salt to increase it to a 40 % solution of salt?
Do you think you can frame the equations too? How do i convert 20% of salt to measurements (ie grams or kilograms)
i was thinking (60 + x) 40/100 = ....
Im really confused, since its a salt solution. Im in 8th grade, kindly explain in a way that is understandable to me. Thanks in advance
Found 3 solutions by Alan3354, stanbon, Theo:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! How much salt should be added to 60 litres of a 20% solution of salt to increase it to a 40 % solution of salt?
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Add s liter of 100% salt.
s + 60 = total liters
100s + 60*20 = (s + 60)*40 (total salt)
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100s + 1200 = 40s + 2400
60s = 1200
s = 20 liters
Answer by stanbon(75887)  (Show Source):
You can put this solution on YOUR website! How much salt should be added to 60 litres of a 20% solution of salt to increase it to a 40 % solution of salt?
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Equation:
salt + salt = salt
0.20*60 + 1*x = 0.40(60+x)
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Multiply thru by 100 to get:
20*60 + 100x = 40*60 + 40x
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Subtract 40x from both sides
Subtract 20*60 from both sides
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60x = 20*60
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x = 20 litres (amt. of concentrated salt solution to add)
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Cheers,
Stan H.
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Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! the question is:
How much salt should be added to 60 litres of a 20% solution of salt to increase it to a 40 % solution of salt?
20% of 60 liters is equal to 12 liters.
the solution has 12 liters of salt and 48 liters of some other substance.
we can assume they are talking about volume here, since the measurement is in liters which is a volume type measurement.
we'll let x represent the amount of salt that has to be added to the solution.
out equation will be .20 * 60 + x = .40 * (60 + x).
solve this equation for x and you will have the number of liters of salt that has to be added.
start with .20 * 60 + x = .40 * (60 + x)
simplify to get 12 + x = .40 * 60 + .40 * x
simplify further to get 12 + x = 24 + .4x
subtract 12 from both sides of this equation and subtract .4x from both sides of this equation to get .6x = 12
divide both sides of this equation by .6 to get x = 12/.6
simplify to get x = 20
you would need to add 20 liters of salt to the 20% mixture in order to get a 40% mixture.
the formula of .20 * 60 + x = .40 * (60 + x) becomes:
12 + 20 = .40 * (60 + 20) which becomes;
32 = .4 * 80 which becomes:
32 = 32
since the equation is true, the solution of x = 20 is correct.
that's easy to see because, if you add 20 to 12 you get 32, and if you add 20 to 60 you get 80 and it's clear that 32 / 80 is equal to .4 which is equal to 40%.
the weight of the salt doesn't enter the problem.
however, there are probably some conversion tables that can tell you the weight of salt by volume.
one such conversion table told me that the density of salt is 2170 grams per liter of volume of salt.
if it is dissolved in a liquid, then some other conversion factors would apply.
here's an excerpt from a google search i did on density of salt.
The molar mass of salt is 58.443 g/mol, its melting point is 801 °C (1,474 °F) and its boiling point 1,465 °C (2,669 °F). Its density is 2.17 grams per cubic centimetre and it is readily soluble in water. When dissolved in water it separates into Na+ and Cl− ions and the solubility is 359 grams per litre.
the bottom line on the problem, however, has nothing to do with the density of the salt.
20% of 60 liters is 12 liters of salt.
40% of 80 liters is 32 liters of salt.
if you start with 60 liters that is 20% salt by volume, then you need to add 20 liters of salt to get 80 liters that is 40% salt by volume.
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