SOLUTION: Town A and Town B were located close to each other, and recently merged into one city. Town A had a population with 12% African Americans. Town B had a population with 8% African A

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Question 1157597: Town A and Town B were located close to each other, and recently merged into one city. Town A had a population with 12% African Americans. Town B had a population with 8% African Americans. After the merge, the new city has a total of 4000 residents, with 9.4% African Americans. How many residents did Town A and Town B used to have?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52784)   (Show Source): You can put this solution on YOUR website!
.

       a +      b = 4000          (1)

    0.12a + 0.08b = 0.094*4000    (2)


From equation (1), express a = 4000 - b  ans substitute it into equation (2), replacing "a" there


    0.12*(4000-b) + 0.08b = 0.094*4000.


Now  b =  = 2600.


ANSWER.  Population B is 2600 residents; population A is the rest 4000-2600 = 1400 residents.

Solved.


Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


Here is a non-algebraic method for solving this type of "mixture" problem.

The difference between 8% and 9.4% is 1.4%; the difference between 12% and 9.4% is 2.6%.
That means the ratio of the populations of the two towns before the merger was 1.4:2.6, or 14:26.
With a combined population of 40,000, and a ratio of 14:26, the populations of the two towns were 14,000 and 26,000.
And since 9.4% is closer to 8% than to 12%, town B had the larger population.

ANSWERS:
Town A: 14,000
Town B: 26,000

CHECK:
.12(14,000) + .08(26,000) = 1680+2080 = 3760
.094(40,000) = 3760
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