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?

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  • 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     
    1
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