Question 393702: 1. At present, the sum of the parent's age is twice the sum of the children's ages. Five years ago, the sum of the parents' ages was 4 times the sum of the children's ages.fifteen years hence, the sum of the parent's ages will be equal to the sum of the children's ages. how many children are there?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! At present, the sum of the parent's age is twice the sum of the children's ages.
Five years ago, the sum of the parents' ages was 4 times the sum of the children's ages.
fifteen years hence, the sum of the parent's ages will be equal to the sum of the children's ages.
how many children are there?
:
Let c = sum of the childrens age at present
Let n = no. of children
Let p = sum of the parents 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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