Question

The average of 9 numbers is 8.What tenth number must be added to make the average 9?

Answer 1

Average of 9 numbers = 8

Sum of the 9 numbers = 8 x 9 = 72

Average of 10 numbers = 9

Sum of the 10 numbers = 9 x 10 = 90

Tenth number = 90 - 72 = 18

Answer: The tenth number is 18

Answer 2

since the average of the 9 numbers is 8 then:

(x1 + x2 + x3 + ...x9)/9 = 8

which means x1 + x2 + x3 + ...x9= 9*8 =72

lets add x10 , the average will be 9 :

(x1+x2+x3+.....x9+x10)/10=9

which means (x1+x2+x3+.....x9+x10)=90

then x10 = 90-(x1+x2+x3+....x9) , we previously prooved that (x1+x2+x3+....x9)=72

x10=90-72=18