When dealing with questions that include LOTS of variables, it often helps to make your variables as simple as possible (e.g., make 'groups' of them the same number, etc.).
Here, we're asked for the average monthly rain fall for the year 1984 in region Y. From this prompt, we would need to have information on ALL 12 months (the actual numbers, ratio data or equivalent) to answer this question.
Fact 1: In region Y the total rainfall for the first 6 months of 1984 was twice the total rainfall for the last 6 months of 1984.
This tells us NOTHING about the amount of rain that fell in any of the months. However, we can organize the information in a simple example:
First 6 months of the year: 2X rain per month
Last 6 months of the year: X rain per month
Fact 1 is INSUFFICIENT
Fact 2: In region Y the average monthly rainfall for the first 6 months of 1984 was 2.31 inches more than the average monthly rainfall for the last 6 months of 1984.
Again, this tells us NOTHING about the actual amount of rain that fell in any of the months. We can organize the information though....
First 6 months of the year: (Y + 2.31) inches per month
Last 6 months of the year: Y inches per month
Fact 2 is INSUFFICIENT
Combined, we know:
The average amount of rain that fell in the LAST 6 months = X = Y.
The average amount of rain that fell in the FIRST 6 months is 2X = X + 2.31
We can now solve for X.
X = 2.31, so we CAN answer the question.
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