# 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

Algebra ->  Customizable Word Problem Solvers  -> Age -> 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      Log On

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 Click here to see ALL problems on Age Word Problems 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(3556)   (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.