SOLUTION: Ahmed's family consists of ahmed, his wife and some children. The average age of all family is 22 years.if ahmed age is 46 years old, and the average age of his wife and children i

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Question 989434: Ahmed's family consists of ahmed, his wife and some children. The average age of all family is 22 years.if ahmed age is 46 years old, and the average age of his wife and children is 18 then how many children there in the family

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Ahmed's family consists of ahmed, his wife and some children.
The average age of all family is 22 years.
if ahmed age is 46 years old, and the average age of his wife and children is 18 then how many children there in the family
:
let n = the number of children in the family
let a = the average of the children's ages
let w = his wife's age
:
"The average age of all family is 22 years. Amed is 46."
%28w+%2B+na+%2B+46%29%2F%28%28n%2B2%29%29 = 22
multiply both sides by (n+2)
w + na + 46 = 22(n+2)
w + na + 46 = 22n + 44
w + na = 22n + 44 - 46
w + na = 22n - 2
:
"the average age of his wife and children is 18"
%28w+%2B+na%29%2F%28n%2B1%29 = 18
From the 1st simplified equation we can replace (w+na) with (22n-2)
%2822n-2%29%2F%28n%2B1%29 = 18
22n - 2 = 18(n+1)
22n - 2 = 18n + 18
22n - 18n = 18 + 2
4n = 20
n = 20/4
n = 5 children in the family