SOLUTION: average of ? 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 Note-In very long process

Algebra ->  Average -> SOLUTION: average of ? 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 Note-In very long process       Log On


   



Question 1130966: average of ? 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
Note-In very long process

Answer by ikleyn(52876) About Me  (Show Source):
You can put this solution on YOUR website!
.

            As presented,  the post/(the problem) makes no sense,
            but the sense returns back if to edit the condition in this way

    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.

            replacing the  " ? "  mark by the number  9.
            Also,  it helps very much if to replace the word  "figures"  by the word  "numbers".
            Now the solution is as follows.


Solution

Let the 9 numbers are a%5B1%5D, a%5B2%5D, a%5B3%5D, a%5B4%5D, a%5B5%5D, a%5B6%5D, a%5B7%5D, a%5B8%5D  and  a%5B9%5D.


Then from the condition 

    P = a%5B1%5D + a%5B2%5D + a%5B3%5D + a%5B4%5D + a%5B5%5D = 5*163   and

    Q = a%5B5%5D + a%5B6%5D + a%5B7%5D + a%5B8%5D + a%5B9%5D = 5*430,



while

    R = a%5B1%5D + a%5B2%5D + a%5B3%5D + a%5B4%5D + a%5B5%5D + a%5B6%5D + a%5B7%5D + a%5B8%5D + a%5B9%5D = 9*301.



Next, it is clear that  


    P + Q - R = a%5B5%5D = 5*163 + 5*430 - 9*301,


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


Answer.  At given conditions,   a%5B5%5D = 256.

Solved.