Question

The average of eleven distinct positive integers is 21. If the average of the first 6 is 23 and the average of last six is 22, find the sixth integer?

Answer 1

Answer:

39

Step-by-step explanation:

let the sum of eleven integers be z

let the sum of first six integers be x

let the sum of last six integers be y

given:-

average of eleven integers= 21

sum of eleven integers ÷ eleven = 21

z/11=21

z=21×11

z=231

similarly,

average of first six integers= 23

sum of first six integers ÷ six=23

x/6=23

x=23×6

x=138

and,

average of last six integers= 22

sum of last six integers ÷ six =22

y/6=22

y=22×6

y=132

therefore,

the sixth integer = (sum of first six integers + sum of last six integers) - sum of eleven integers

the sixth integer = (x+y)-z = (138+132)-231

= 270-231 = 39

the sixth integer is 39

hope this will help