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Question

Three years ago, the populations of Villages S and T were in the ratio 7 : 2. Since then, S's population has increased by 3% per year, while T's population has decreased by 3% per year. If their combined population today is 36,155, what was the population of Village T three years ago? (Round your answer to the nearest integer)

The correct answer is

7,632

Let the populations three years ago be S = 7k and T = 2k.

Today: S = 7k(1.03)3 = 7k × 1.092727 = 7.649089k; T = 2k(0.97)3 = 2k × 0.912673 = 1.825346k.

Combined: 9.474435k = 36,155 ⇒ k ≈ 3816.06.

Population of T three years ago = 2k ≈ 7632.1 ≈ 7,632.

Hence, Village T had about 7,632 people three years ago.

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