SOLUTION: I'm having trouble with this mixture problem. The back of the book says the answer is 590 but I think this is wrong, anyway I'm stumped. Any help with this would be much appreciate

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Question 1055926: I'm having trouble with this mixture problem. The back of the book says the answer is 590 but I think this is wrong, anyway I'm stumped. Any help with this would be much appreciated. Here it is.
Northern Maywood voted 60%to 40% in favor of a water project. Southern Maywood voted 90% to 10% against the project. The project passed 55% to 45%. If 5900 people voted, how many were from Southern Maywood.
Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let = number of voters in N. Maywood
Let = number of voters in S. Maywood
--------------------------------------------
(1)
(2) ( all voters in favor )
(3) ( all voters against )
--------------------------------
Note that " Southern Maywood voted 90% to 10% against the project. "
can be rewritten as: " Southern Maywood voted 10% to 90% in favor the project.
Also note that (2) and (3) are saying essentially the same thing, but can
be used as checks against eachother.
--------------------------------
(2)
Subtract (1) from (2)
(2)
(1)
--------------------------


and
(1)
(1)
(1)
590 voters were from S. Maywood
--------------------------------
check:
(3)
(3)
(3)
(3)
(3)
OK
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
I'm having trouble with this mixture problem. The back of the book says the answer is 590 but I think this is wrong, anyway I'm stumped. Any help with this would be much appreciated. Here it is.
Northern Maywood voted 60%to 40% in favor of a water project. Southern Maywood voted 90% to 10% against the project. The project passed 55% to 45%. If 5900 people voted, how many were from Southern Maywood.
Let number of voters from Southern Maywood be S

Then number of voters from Northern Maywood = 5,900 – S

Number of voters in Northern Maywood, who voted FOR the project: 60% of (5,900 – S), or .6(5,900 – S)

Number of voters in Southern Maywood who voted FOR the project: 10% of S, or .1S

Since 55% voted FOR the project, we get: .6(5,900 – S) + .1S = .55(5,900)

3,540 - .6S + .1S = 3,245

- .6S + .1S = 3,245 – 3,540

- .5S = - 295 

S, or number of voters from Southern Maywood = , or  

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