unanswered question

the sum of ages of parents is twice sum of children's age.5 years ago ,the sum of parent's age is 4 times sum of children's age.in 15 years sum of parent's age will be equal to sum of children's age.so how many children are there in the family?

Your Answer

Let c = sum of the children’s age at present
Let n = no. of children
Let p = sum of the parent’s age at present
:
"At present, the sum of the parent's age is twice the sum of the children's ages."
p = 2c
:
" Five years ago, the sum of the parents' ages was 4 times the sum of the children's ages.
p-10 = 4(c-5n); (we have to subtract 5 yrs for each person)
p-10 = 4c - 20n
Replace p with 2c
2c - 10 = 4c - 20n
2c - 4c + 20n = 10
-2c + 20n = 10
:
"fifteen years hence, the sum of the parent's ages will be equal to the sum of the children's ages."
p + 30 = c + 15n; (we have to add 15 yrs for each person)
Replace p with 2c
2c + 30 = c + 15n
2c - c - 15n = -30
c - 15n = -30
Multiply the above equation by 2, add to the previous equation
2c - 30n = -60
-2c +20n = 10
-----------------adding eliminates c, find n
-10n = -50
n = +5 children
:
:
Check this by finding c, using c - 15n = -30
c - 15(5) = - 30
c = -30 + 75
c = 45 is the sum of the childrens age
then
p = 2(45)
p = 90 is sum of the parents age
:
Check solution in the statement:
" Five years ago, the sum of the parents' ages was 4 times the sum of the children's ages.
90 - 10 = 4(45-5(5))
80 = 4(45-25)
80 = 4(20)
:
We can say that there are 5 children 

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