Question 1080685
 1.) The average of 7 numbers is 5.
 If the average of first six of these numbers is 4, the seventh number is?
let n = the 7th number
{{{((6(4)+n))/7}}} = 5
24 + n = 7 * 5
n = 35 - 24
n = 11 is the 7th number
; 
 2.) Three years ago the average age of a family of 5 member was 27 years.
let A =  average of the 5 people now
then 3 yrs ago
{{{((5A - 5(3)))/5}}} = 27
{{{((5A - 15))/5}}} = 27
Cancel the 5 and you have:
 A - 3 = 27
 A = 30 yrs is their present average age
:
"On the addition of a child to the family, the present average age of the family is still 27 years."
let c = the age of the additional child
{{{((5(30) + c))/6}}} = 27
multiply both sides by 6
150 + c = 162
c = 162 -150
c = 12 yrs is the present age of the child.