From 1990 to 2000, the population of city A rose from 12,000 to 28,000 and the population of city B rose from 18,000 to 24,000. If the population of the two cities increased at a constant rate, in what year was the population of both cities the same?
Correct answer: A. 1996
- A. 1996
- B. 1997
- C. 1994
- D. 1999
Explanation
To find the year when the populations of the two cities are equal, first calculate the annual increase in population for each city.For City A, the population increased from 12,000 to 28,000 over 10 years, which is an increase of 16,000. Therefore, the annual increase is 16,000 / 10 = 1,600 people per year.For City B, the population increased from 18,000 to 24,000 over 10 years, which is an increase of 6,000. Therefore, the annual increase is 6,000 / 10 = 600 people per year.The population of City A after x years from 1990 is given by 1,600x + 12,000, and for City B, it is 600x + 18,000. Set these two expressions equal:1,600x + 12,000 = 600x + 18,000Solving for x gives 1,000x = 6,000, hence x = 6.Adding 6 years to 1990 gives 1996 as the year when the populations are equal. Therefore, the correct answer is Option A, 1996. The other options are incorrect because they do not satisfy the condition where both populations are equal.
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