Question 1130966
.


            As presented,  the post/(the problem) makes no sense,

            but the sense returns back if to edit the condition in this way


<pre>
    Average of 9 figures is 301; average of first five figures is 163, and average of last 5 figures is 430. Find the value of the fifth figure.
</pre>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;replacing the &nbsp;" ? " &nbsp;mark by the number &nbsp;9.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Also, &nbsp;it helps very much if to replace the word &nbsp;"figures" &nbsp;by the word &nbsp;"numbers".

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Now the solution is as follows.



<U>Solution</U>


<pre>
Let the 9 numbers are {{{a[1]}}}, {{{a[2]}}}, {{{a[3]}}}, {{{a[4]}}}, {{{a[5]}}}, {{{a[6]}}}, {{{a[7]}}}, {{{a[8]}}}  and  {{{a[9]}}}.


Then from the condition 

    P = {{{a[1]}}} + {{{a[2]}}} + {{{a[3]}}} + {{{a[4]}}} + {{{a[5]}}} = 5*163   and

    Q = {{{a[5]}}} + {{{a[6]}}} + {{{a[7]}}} + {{{a[8]}}} + {{{a[9]}}} = 5*430,



while

    R = {{{a[1]}}} + {{{a[2]}}} + {{{a[3]}}} + {{{a[4]}}} + {{{a[5]}}} + {{{a[6]}}} + {{{a[7]}}} + {{{a[8]}}} + {{{a[9]}}} = 9*301.



Next, it is clear that  


    P + Q - R = {{{a[5]}}} = 5*163 + 5*430 - 9*301,


and the last expression in the right side is equal to  256.


<U>Answer</U>.  At given conditions,   {{{a[5]}}} = 256.
</pre>

Solved.