The-mean-of-n-number-is-20-if-the-same-numbers-together-with-30-give-a-new-mean-of-22-find-n-

Question Number 9577 by j.masanja06@gmail.com last updated on 18/Dec/16

The mean of n number is 20 . if

the same numbers together with 30

give a new mean of 22,

find n .

Answered by ridwan balatif last updated on 18/Dec/16

first condition

{\bar{x}}_{n} = 20

\frac{x_{1} + x_{2} + \dots + x_{n}}{n} = 20

x_{1} + x_{2} + \dots + x_{n} = 20 n \dots (*)

second condition

{\bar{x}}_{n + 1} = 22

\frac{(x_{1} + x_{2} + \dots + x_{n}) + 30}{n + 1} = 22

(20 n) + 30 = 22 n + 22

2 n = 8

n = 4