SOLUTION: I get really confused when trying to set these problems up. Can you help me work this one out so I can use it for my other questions please? How many liters of a 40% alcohol soluti

Question 170410: I get really confused when trying to set these problems up. Can you help me work this one out so I can use it for my other questions please? How many liters of a 40% alcohol solution should be mixed with 40 liters of a 90% solution to get a 50% solution? Thanks for your help.
Found 2 solutions by Mathtut, Edwin McCravy:
Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!
lets call x the number of liters for the 40% solution.
40%(x)+90%(40)=50%(40+x)
:
.4x+.9(40)=.5(40+x)
:
.4x+36=20+.5x
:
.1x=16
:
liters of 40% solution
Answer by Edwin McCravy(20054) (Show Source): You can put this solution on YOUR website!
Edwin's solution with chart:
I get really confused when trying to set these problems up. Can you help me work this one out so I can use it for my other questions please? How many liters of a 40% alcohol solution should be mixed with 40 liters of a 90% solution to get a 50% solution? Thanks for your help.

Make this chart: | liters | % | pure alcohol -------------------------------------------- 1st solution | | | 2nd solution | | | ---------------|--------|-----|------------- final solution | | | Let x = liters of 1st solution and we are given that there are 40 liters of the 2nd solution, so fill in x and 40 liters. | liters | % | pure alcohol -------------------------------------------- 1st solution | x | | 2nd solution | 40 | | ---------------|--------|-----|------------- final solution | | | Add the two to get x+40 liters of final solution. | liters | % | pure alcohol -------------------------------------------- 1st solution | x | | 2nd solution | 40 | | ---------------|--------|-----|------------- final solution | x+40 | | Put in the three percentages as decimals: | liters | % | pure alcohol -------------------------------------------- 1st solution | x | .40 | 2nd solution | 40 | .90 | ---------------|--------|-----|------------- final solution | x+40 | .50 | Now get the amount of pure alcohol contained in each by multiplying by the percentage as a decimal. | liters | % | pure alcohol -------------------------------------------- 1st solution | x | .40 | .40x 2nd solution | 40 | .90 | .90(40) ---------------|--------|-----|------------- final solution | x+40 | .50 | .50(x+40) The equation comes from the last column: .40x + .90(40) = .50(x+40) Can you solve that for x? If not post again. answer: x = 160 liters Edwin

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