document.write( "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. \n" ); document.write( "
Algebra.Com's Answer #325685 by Theo(13342)\"\" \"About 
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the woman's age is x.
\n" ); document.write( "the daughter's age is x/2.
\n" ); document.write( "the son's age is 2x/3.
\n" ); document.write( "the sum of the childrens' ages is 12 more than the mother's age.
\n" ); document.write( "this means that:
\n" ); document.write( "x/2 + 2x/3 = x+12
\n" ); document.write( "solve this equation and you have the key to your answer.
\n" ); document.write( "multiply both sides of this equation by 6 to get:
\n" ); document.write( "3x + 4x = 6x + 72
\n" ); document.write( "combine like terms to get:
\n" ); document.write( "7x = 6x + 72
\n" ); document.write( "subtract 6x from both sides of the equation to get:
\n" ); document.write( "x = 72
\n" ); document.write( "the daughter's' age is 72/2 = 36
\n" ); document.write( "the son's age is 2*72/3 = 2*24 = 48
\n" ); document.write( "the sum of the daughter's and son's age is 36 + 48 = 84.
\n" ); document.write( "the sum of their ages is 12 more than the mother's age.
\n" ); document.write( "this means that 84 = 72 + 12 which is true, confirming the value of x = 72 is good.
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