SOLUTION: The average of the first three numbers was 11. The average of the other seven numbers was 12. What was the overall average of the numbers?

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Question 692309: The average of the first three numbers was 11. The average of the other seven numbers was 12. What was the overall average of the numbers?
Found 2 solutions by vleith, htmentor:
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
How many numbers are there all together ? 3+%2B+7+=+10
How much do the numbers total? %283%2A11%29+%2B+%287%2A12%29+=+117
What is the average? 117%2F10+=+11.7

Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
The average of the first 3 numbers = S3/3 = 11 -> S3 = 33
where S3 = the sum of the first 3 numbers
The average of the other 7 numbers = S7/7 = 12 -> S7 = 84
So the overall average = (S3+S7)/10 = (33+84)/10 = 11.7