Average of average

Three different numbers are given. The average of the average of two smaller numbers and the average of the two larger numbers is equal to the average of all three numbers. The average of the smallest and largest number is 2022. Determine the sum of the three given numbers.

Final Answer:

s =  6066

Step-by-step explanation:

$$\begin{gathered} (a+c)/2=2022 \\ ((a+b)/2+(b+c)/2)/2=(a+b+c)/3 \\ s=a+b+c \\ a+c=4044 \\ 3a+3b+3b+3c=4a+4b+4c \\ a+c=4044 \\ 3a+6b+3c=4a+4b+4c \\ 3\cdot 4044+6b=4\cdot 4044+4b \\ 3\cdot 4044+6\cdot b=4\cdot 4044+4\cdot b \\ 2b=4044 \\ b=\frac{4044}{2}=2022 \\ b=2022 \\ s=a+b+c \\ s=(a+c)+b \\ s=4044+b=4044+2022=6066 \end{gathered}$$

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