Math, asked by jainhardik1440, 1 year ago

The average of 15 numbers is 11. If the average of the first 8 numbers be 8.5 and average of the last 8 numbers be 10.5, then the middle number is

Answers

Answered by MotiSani
0
let the 15 numbers be X1,X2............X15
As provided in the question
Average of 15 numbers =
11 = (X1+X2.........X8+........X15)/15

(X1+X2+........X15)= 165
Also it is provided that the average of first eight numbers is 8.5
Similarly,
X1+X2+.........+X8=8.5×8=68
X1+X2....+X7= 68-X8 ......... -(1)

Also it is provided that the average of last eight numbers is 10.5
Formulating the equation for it
X8+X9......X15= 10.5×8=84
X9+........+X15= 84- X8 ..............(2)


Now putting the value from (1) and (2) into the equation for average of 15 numbers
68-X8 +X8 + 84-X8 = 165
X8= 68+84-165
X8= -17
Therefore on solving the equation we get the value of the middle number is -17. We use the substitution method to find the value of X8.
On calculating through the equatios we find that
Hence X8= -17.


Similar questions