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Town Population

Date: 05/03/97 at 05:04:26
From: Elicia
Subject: Story Sums

The population of town A is 4800 more than town B. If 3100 people move 
from town B to town A, the population in town A will be 11 times that 
of town B. Find the original, total population of the two towns.

I did this:
     10 units = 4800+3100+7900
       1 unit = 7900/10 =790
     790+3100 = 3890

  Town B----3890
    3890+4800 = 8690
  Town A----8690
    8690+3890 = 12580

The total population of the two towns at first is 12580, but my 
teacher said this is wrong.

Date: 05/03/97 at 07:12:49
From: Doctor Anthony
Subject: Re: Story Sums

With this type of problem it is better to use symbols like x or y to 
represent unknown numbers.  You can then write down equations, using 
these letters, to show what happens as you follow the instructions 
given in the question.

     Let x = initial population of town B
    x+4800 = initial population of town A

Now move 3100 people from B to A:

   New population of B = x-3100
   New population of A = x+4800+3100

Now the second of these is 11 times the first, so:

        x+4800+3100 = 11(x-3100)
            x+7900  = 11x-34100

         7900+34100 = 10x

              42000 = 10x        
                  x = 4200

Initial population of B was 4200
Initial population of A was 9000

The total for both towns = 4200 + 9000 = 13200

-Doctor Anthony,  The Math Forum
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