Final answer:
The overall change in temperature after an increase of 25% followed by a decrease of 40% results in a final temperature that is 75% of the original value, meaning the temperature decreased by 25% overall.
Step-by-step explanation:
The student's question involves a two-step percentage change scenario, which is a common problem in mathematics. To find the overall temperature change, we need to apply the percentage changes sequentially. Imagine that the initial temperature is represented by 'T'.
Firstly, the temperature is increased by 25%, so the new temperature is T + (0.25 × T) = 1.25T. Next, the temperature is decreased by 40%, which means the new temperature is 1.25T - (0.40 × 1.25T) = 0.75 × 1.25T = 0.75T. Therefore, after these two changes, the final temperature is 75% of the initial value, indicating that the temperature has actually decreased by 25% overall. This type of problem not only is useful for understanding how multiple percentage changes affect a given value, but is also essential for grasping the nonlinear nature of successive percentage changes. Such calculations are pervasive in real-world applications, from financial forecasting to understanding changes in global temperatures.