Let's analyze the provided options regarding the average rainfall for the month.
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If it increased by a percentage (say x%), then the new average rainfall can be represented as: \[ r + \frac{x}{100}r = r(1 + \frac{x}{100}) \]
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If it decreased by a percentage (say y%), then the new average rainfall can be represented as: \[ r - \frac{y}{100}r = r(1 - \frac{y}{100}) \]
Let's evaluate each option:
A. The average rainfall for the month increased by 45%. An equivalent expression that represents this situation is \( r + 0.45r \).
- If the average increases by 45%, the expression would be: \[ r + 0.45r = 1.45r \] This correctly represents a 45% increase.
B. The average rainfall for the month increased by 55%. An equivalent expression that represents this situation is \( r + 0.55r \).
- If the average increases by 55%, the expression would be: \[ r + 0.55r = 1.55r \] This correctly represents a 55% increase.
C. The average rainfall for the month decreased by 45%. An equivalent expression that represents this situation is \( r - 0.45r \).
- If the average decreases by 45%, the expression would be: \[ r - 0.45r = 0.55r \] This indeed represents a 45% decrease from \( r \).
D. The average rainfall for the month decreased by 55%. An equivalent expression that represents this situation is \( r - 0.55r \).
- If the average decreases by 55%, the expression would be: \[ r - 0.55r = 0.45r \] This is correct for a 55% decrease.
Conclusion:
All statements A, B, C, and D represent valid scenarios depending on whether the average rainfall increased or decreased.
If you are looking for which statement specifically indicates a situation where the average rainfall has changed and how to express that change, you’d choose the one reflecting the correct increase or decrease percentage that's applicable based on the information given.
Without further context regarding whether the rainfall increased or decreased, all can be correct individually under different interpretations.
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