SOLUTION: Please help me solve this word problem- ages. A woman has a daughter who is half her age and a son who is two-thirds her age. The sum of the children's ages is 12 years more than t

Question 474937: Please help me solve this word problem- ages. A woman has a daughter who is half her age and a son who is two-thirds her age. The sum of the children's ages is 12 years more than the mother's age. Find the ages of the three people.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the woman's age is x.
the daughter's age is x/2.
the son's age is 2x/3.
the sum of the childrens' ages is 12 more than the mother's age.
this means that:
x/2 + 2x/3 = x+12
solve this equation and you have the key to your answer.
multiply both sides of this equation by 6 to get:
3x + 4x = 6x + 72
combine like terms to get:
7x = 6x + 72
subtract 6x from both sides of the equation to get:
x = 72
the daughter's' age is 72/2 = 36
the son's age is 2*72/3 = 2*24 = 48
the sum of the daughter's and son's age is 36 + 48 = 84.
the sum of their ages is 12 more than the mother's age.
this means that 84 = 72 + 12 which is true, confirming the value of x = 72 is good.

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