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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
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Word Problems

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