Question

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

Answer 1

Let the four numbers be A, B, C, D.

A+(B+C+D)/3=25, B+(A+C+D)/3=37, C+(A+B+D)/3=43, D+(A+B+C)/3=51.

Add these together: A+B+C+D+3(A+B+C+D)/3=25+37+43+51=156.

Therefore 2(A+B+C+D)=156, A+B+C+D=78 and the average is 78/4=39/2=19.5.

(The numbers are -1.5, 16.5, 25.5 and 37.5.)