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Problem of the Week
Problem E
A Tale of Two Towns

Two towns, Centreville and Middletown, had the same population at the end \(2022.\)

The population of Centreville decreased by \(2.5\%\) from the end of \(2022\) to the end of \(2023.\) Then, the population increased by \(8.4\%\) from the end of \(2023\) to the end of \(2024.\)

The population of Middletown increased by \(r\%\), where \(r>0\), from the end of \(2022\) to the end of \(2023.\) Then, the population of Middletown increased by \((r+2)\%\) from the end of \(2023\) to the end of \(2024.\)

Surprisingly, the populations of both towns were the same again at the end of \(2024.\) Determine the value of \(r\), rounded to the nearest tenth.