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 $2.5\mathrm{\%}$ from the end of $2022$ to the end of $2023.$ Then, the population increased by $8.4\mathrm{\%}$ from the end of $2023$ to the end of $2024.$

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