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

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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) About Me  (Show Source):
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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.