SOLUTION: 1. How much water must be added to 90 liters of a 20% salt solution to dilute it to a 15%salt solution? 2. How much of a 30% alcohol solution and an 18% alcohol solution must be a

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: 1. How much water must be added to 90 liters of a 20% salt solution to dilute it to a 15%salt solution? 2. How much of a 30% alcohol solution and an 18% alcohol solution must be a      Log On


   

Question 532408: 1. How much water must be added to 90 liters of a 20% salt solution to dilute it to a 15%salt solution?
2. How much of a 30% alcohol solution and an 18% alcohol solution must be added to make 20 oz of a 25% alcohol solution?
I can't figure out how to set up the equations. I got these wrong on a test and can't figure out why?
Answer by Maths68(1474) About Me  (Show Source):
You can put this solution on YOUR website!
1. How much water must be added to 90 liters of a 20% salt solution to dilute it to a 15%salt solution?
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Solution A
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Amount = x liters
Salt Concentration =%0 =0 (It is pure water so concentration of Salt will be zero)
Solution B
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Amount = 90 liters
Salt Concentration =20% = 0.2
Resultant Solution
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Amount =90+x liters
Salt Concentration =15%=0.15


[Amount Solution A * Concentration A] + [Amount Solution B * Concentration of B] = Amount of Resultant * Concentration of resultant
x*0+90*0.2=(90+x)0.15
18=13.5+0.15x
18-13.5=0.15x
4.5=0.15x
4.5/0.15=x
30=x
x=30

30 liters of pure water must be added to 90 liters of a 20% salt solution to dilute it to a 15%salt solution.




2. How much of a 30% alcohol solution and an 18% alcohol solution must be added to make 20 oz of a 25% alcohol solution?
Solution A
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Amount = x oz
Concentration =%30 =0.3
Solution B
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Amount = 20-x oz
Concentration =18% = 0.18
Resultant Solution
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Amount =20 oz
Concentration =25%=0.25


[Amount Solution A * Concentration A] + [Amount Solution B * Concentration of B] = Amount of Resultant * Concentration of resultant
x*0.3+(20-x)*0.18=20*0.25
0.3x+3.6-0.18x=5
0.12x=5-3.6
0.12x=1.4
x=1.4/0.12
x=11.66

11.66oz of a 30% alcohol solution and 8.44oz of 18% alcohol solution must be added to make 20 oz of a 25% alcohol solution.