Four numbers are selected such that when each number is added to the average of the other three the following sums are obtained: 25, 37, 43, and 51. Determine the average of the four numbers.

Please explain how you got your answer

Let the 4 numbers be a,b,c and d.

When the first number is added to the average of the other three numbers the result is 25.

Therefore,

When the second number is added to the average of the other three numbers the result is 37.

When the third number is added to the average of the other three numbers the result is 43.

When the fourth number is added to the average of the other three numbers the result is 51.

Adding equations (1), (2), (3) and (4) we get

6a + 6b + 6c + 6d = 75 + 111 + 129 + 153

6(a + b + c + d) = 468

Divide both sides by 6

a + b + c + d = 468/6

a + b + c + d = 78

To get the average, divide both sides by 4

So, average = 19.5

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