Family Age Problem

let 'x' be total age of the family excluding father . 'n' be total no. of members in family . (x+38)/n = 18 , similarly (x)/(n-1)=14 . on solving n=6 , from which 1 is father and other is mother so total child will be n=6-2 =4

Let $m$ be the mother's age, $c$ be the children's average age, and $n$ be the number of children. From the 2 given averages, the following equations can be created:

$\frac {m+nc+38}{2+n}=18$ and $\frac {x+ny}{n+1}=14$

We could get $x+ny+38=36+18n$ and $x+ny=14+14n$

If we subtract both equations, we will get $38=22+4n \Rightarrow n=4$

let,        x: be the age of the father        y:be the age of the mother       z:be the average age of the children       n: be the number of children.

General equation:    ( x + y + nz  ) / (n + 2) = 18

if x=38 :                  38 + y + nz = 18n +36 y + ( z-18 )n +2 = 0 (a)

if x is not included: ( y + nz ) / ( n +1 ) = 14 y + ( z-14 )n - 14 = 0 ( b )

by elimination: a-b

         y + ( z-18 )n +2 =0
    -  [ y + ( z-14 )n -14 = 0

           -4n + 16 = 0
                 -4n = -16

        n = 4   ( the number of children )

$\frac{s}{n}=18$

$\frac{s-38}{n-1}=14$

$n=6$

$c=n-2=6-2=4$

There are 1 father $(F)$ , 1 mother $(M)$ and $x$ children $(C)$ .

The first equation..

$\frac{F+M+xC}{2+x}=18$

$F+M+xC=36+18x$

$\boxed{M+xC=18x-2}$

The second equation..

$\frac{M+xC}{1+x}=14$

$\boxed{M+xC=14x+14}$

Then..

$18x-2=14x+14$

$4x=16$

$x=\boxed{4}$

Let the no. of family members be k. then their total age is 18k. total age of all family members without father is (18k-38). therefore the average age is (18k-38)/(k-1)=14. i.e. k=6. Therefore no. of children is 6-2=4

Let the following be used as variables/constants in this solution:

n = the number of children in the family

n + 1 = number of children with the mother

n + 2 = father included

MotherChildren = sum of ages of mother and the children

Equation 1: $\frac{MotherChildren+38}{n+2}=18$ $MotherChildren+38=18(n+2)$ $MotherChildren+38=18n+36$ Equation 2: $\frac{MotherChildren}{n+1}=14$ $MotherChildren=14(n+1)$ $MotherChildren=14n+14$ Substitute Equation 2 to Equation 1 to solve for n: $(14n+14)+38=18n+36$ $14+38-36=18n-14n$ $16=4n$ $n=\frac{16}{4}$ $n=4$ is the number of children in the family.

let the family members=x and the sum of age of mother and children=z then, 18x=38+z & 14(x-1)=z, so x=6 now remove parents, so 6-2=4 child...........

I don't know if it was a coincidence, but I just subtract (18-14) and found the answer 4.

Let X = total number of family members Let Y = Total age for all family members

Therefore: Y/X = 18 (average age), and Y = 18X 14(X-1)+38 = Y (new average age times number of family members minus father, plus father's age = total age)

Then solve simultaneous equations:

14X-14+38=18X 4X = 24, therefore X=6

Total family members = 6, then minus father and mother gives you 4.

18 = m/n, 14= m-38/n-1 18n=m, 14n-14=m-38 By solving above equations we get ,4n+14=38, 38-14=4n ,n=24/4=6

No of kids = n-2 ( mom .dad)

there is a nice solution! age of father = old average + final n x average difference, so, 38=18 + fn x 4, or, 4fn=20, fn=5 where mother included. so n of children=4!

X = total age n = number of childern 1) X/2+n=18 --> X=36+18n 2) X-38/1+n=14 than subtitude them (36+18n)-38=14+14n -->4n=16 -->n=4

Let no of children be x .F denote father's age M denotes mother's age C denotes Children's age.F+M+xC/x+2=18- eqn (1) according to the first statement.M+xC/x+1=14 is the new avg eqn. substitute M+xC=14(x+1) in eqn 1.and also F= 38 solving for x we get x=4. So 4 Children

let ages of children=x,age of mother =y and total members are n then (x+y+38)/n=18 and (x+y)/n-1=14 we will get n=6 so 4 children are there in the family

let total age be "S" n tot family members be "X". then S/X = 18, and (S-38)/ (X-1)=14, solving which you get X=6. so children = 4 (6-dad-mom)

All 6 member 4children+father+mother=6 18*6=108,then Substract father then family members=5& age is 108-38=70..... Then the average age is 70/5=14

y=total age of all family members minus father. n=total number of family members minus father so, average age of family minus father is: y/n = 14, similarly y = 14n and average age of all family members plus father is: (y+38)/(n+1) = 18 By substitution: (14n+38)/(n+1) = 18 n=5 (this is not the answer) so, the number of children is 5 minus the mother = 4

Let the total age of the family = x
Total no of family members (including mother and father) = n
Total no of children = n-2
Given x/n = 18, age of father = 38 years
Excluding father's age, we have (x-38)/(n-1) = 14 implies x = 14n + 24
Putting the value of x in equation x/n = 18 we get
14n + 24 = 18n implies n = 6
Therefore Total no of children = n-2 = 4

There are two equations like 38+y/2+x=18 and y/1+x=14,here x is number of children and y is total age of the children and their mother. solving these equations we can get x=4

Let x be the number of children.

Thus, (38 + 14(X + 1))/(x+2) = 18

x = 4

Hey yo...

as for this, let y = total ages of the family, x = number of childeren,

for average 18( the whole family members),

y / ( x + 2 ) = 18

y = 18( x + 2)

y = 18x + 36

for average 14( father is not included),

y - 38 / ( x + 1 ) = 14

y = 14( x + 1) + 38

y = 14x + 52

by comparison,

18x + 36 = 14x + 52

4x = 16

x = 4

thanks...

The average age of including the father's age = $\frac { x+38 }{ n+1 }$ = 18

where x is the total age of all the family members except father's age and n is the number of family members except father.

And, the average age excluding father is = $\frac {x}{n}$ = 14

=> x = 14n

Thus, $\frac {14n+38}{n+1}$ = 18

i.e. 14n + 38 = 18 (n + 1)

i.e. 14n + 38 = 18n + 18

i.e. 4n = 20

=> n = 5

So the number of family members except father and including mother is, 5.

Thus, the number of children in the family is 4.

18 = (38+x)/n+2. 14=(x)/n+1.

Solve by exec lauding x n will be 4. Number of children 4. First average is by 4 +2 including father and mother. Second average by n+1 mother only.

let us take the total family members as n 38+age of mother+age of all childerns/n=18 so 38+age of mother+age of childerns=18n but age of mother+age of childerns=14(n-1) (excluding father) so 38+14(n-1)=18n n=6 6-2=4(father and mother) no of childrens=4

let the total age of the members of that family is : A
And the number of children is : x If there is only one wife of that family then according to the problem A/(x+2) = 18 [here 2 with x is for father & mother]
And for second average : (A-38)/(x+1) = 14 [subtracts father age ] Now solving the equations x = 4 So there are 4 children in that family.

Let S be the total sum of all ages (including that of mother, father and children) and the total number of family members be n. we have, S/n = 18, => S= 18n. (equation 1)

Also, as per given, ( S-38)/ (n-1) = 14; when the father is excluded. From here we have 14n-14 = S-38 (equation 2)

From equations 1 and 2, we have, 4n = 24 => n=6. But, n is the total number of family members and the family comprises the mother, the father and the children only. So, number of children = n-2=4

Ans: 4

let x be the total age of the mother and the children and n be the total number of children.....

(38+x)/(2+n)=18
38+x = 36+18n
x=18n-2 -------> eq.1

x/(1+n) = 14
x = 14+14n -------> eq.2

Substitute eq.1 -----> eq.2
18n - 2 = 14 + 14n
4n = 16
n = 4