Problem

10. 有七个排成一列的数, 它们的平均数是 30 , 前三个数的平均数是 28 , 后五个数的平均数是33。求第. 个数。

Answer

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Answer

\(\boxed{fourth\_number = 15}\)

Steps

Step 1 ：Find the sum of the first 7 numbers, the sum of the first 3 numbers, and the sum of the last 5 numbers: \(total\_sum = 7 \times 30 = 210\), \(first\_three\_sum = 3 \times 28 = 84\), \(last\_five\_sum = 5 \times 33 = 165\)

Step 2 ：Find the sum of the middle two numbers and then find the 4th number: \(middle\_two\_sum = total\_sum - first\_three\_sum - last\_five\_sum = 210 - 84 - 165 = 81\), \(fourth\_number = middle\_two\_sum - \frac{last\_five\_sum}{5} \times 2 = 81 - 66 = 15\)

Step 3 ：\(\boxed{fourth\_number = 15}\)

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