SOLUTION: 9)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 man

9)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? The 
percentages confused me. I didn't know how 
to set up the equation.

Let S = the total number of voters from S.M
Let N = the total number of voters from N.M

Then we can make this table:

          |  S.M. |  N.M.| Totals   
------------------------------------------
In favor  | .10S  | .60N | .55(5900)
 Against  | .90S  | .40N | .45(5900)

So the equations are
 
.10S + .60N = 55(5900)
.90S + .40N = 45(5900)

Can you solve that system?  If not post
again asking how. Be sure to clear of
fractions after multiplying out the
right sides.

S = 590, N = 5310

The desired answer is 10% of 590, or 59.

To check, fill in the chart with numbers:

          |  S.M. |  N.M.| Totals   
------------------------------------------
In favor  |   59  | 3186 | 3245
 Against  |  531  | 2124 | 2655
------------------------------------------
 Totals   |  590  | 5310 | 5900

It checks because 
55% of 5900 is 3245
45% of 5900 is 2655
10% of 590 is 59
90% of 590 is 531
60% of 5310 is 3186
40% of 5310 is 2124
and the totals come to 5900

---------------------------------------


10) An employer has a daily payroll of 
$1950 when employing some workers at 
$120 per day and others at $150 per day. 
When the number of $120 workers is 
increased by %50 and the number of $150 
workers is decreased 1/5, the new daily 
payroll is $2400. Find how many workers 
were originally employed at each rate.

Let x = number of $120 workers originally
Let y = number of $150 workers originally

Make this chart:

            | wages of the | wages of the  | Pay-
            | $120 workers | $150 workers  | roll  
---------------------------------------------------  
  Originally|    $120x     |     $150y     | $1950
After change|  $120(x+.5x) |  $150(y-1/5y) | $2400

The system of equations is

          $120x     +     $150y     = $1950
        $120(x+.5x) +  $150(y-1/5y) = $2400
       
Which simplifies to 

                120x + 150y = 1950
      120(1.5x) + 150(4/5y) = 2400

which further simplifies to

                120x + 150y = 1950
                180x + 120y = 2400

which further simplifies to

                 12x + 15y = 195
                 18x + 12y = 240

which further simplifies to

                 4x + 5y = 65
                 3x + 2y = 40

Answer x = 10, y = 5.

So there were 10 $120 workers and 5 $150 workers

To check, put numbers in the chart: 

            | wages of the | wages of the  | Pay-
            | $120 workers | $150 workers  | roll  
---------------------------------------------------  
  Originally|   $1200      |     $750      | $1950
After change|   $1800      |     $600      | $2400

It checks.

Edwin