# SOLUTION: Dear Sir/Madam; Pls. kindly see the problem below: Question: In three years, Janice will be three times as old as her daughter. Six years ago, her age was her daughter's age squ

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 Question 331693: Dear Sir/Madam; Pls. kindly see the problem below: Question: In three years, Janice will be three times as old as her daughter. Six years ago, her age was her daughter's age squared. How old is Janice? I wrote out an Algebraic expression for this problem as follows: denoting the daughter's age by x to be able to solve for her daughter's age first, so Janice's age in three years would be: 3x+3, and her age six years ago would have been x2-6; x2-6+3x+3=0, which when simplified will look like this; x2+3x-3=0. But I do not think I am right. Could you please help. Thank you.Found 2 solutions by ankor@dixie-net.com, mananth:Answer by ankor@dixie-net.com(15639)   (Show Source): You can put this solution on YOUR website!In three years, Janice will be three times as old as her daughter. j + 3 = 3(d+3) j + 3 = 3d + 9 j = 3d + 9 - 3 j = 3d + 6 : Six years ago, her age was her daughter's age squared. j - 6 = (d-6)^2 j - 6 = d^2 - 12d + 36 Replace j with (3d+6) 3d + 6 - 6 = d^2 - 12d + 36 A quadratic equation d^2 - 12d - 3d + 36 = 0 d^2 - 15d + 36 = 0 Factors to: (d-12)(d-3) = 0 Two solutions d = 3 d = 12 yrs is the solution that makes sense here : How old is Janice? We know j = 3d + 6 j = 3(12) + 6 j = 42 yrs : Check solutions in the equation: j - 6 = (d-6)^2 42 - 6 = (12-6)^2 36 = 6^2; confirms of our solutions : Answer by mananth(12270)   (Show Source): You can put this solution on YOUR website!let daughter's age be x now. after 3 years daughter will be x+3 .. after 3 years Janice will be 3*(x+3) years .. 6 years ago daughter's age = x-6. janice ' age was (x-6)^2 .. 3x+9-9 =3x 3x= (x-6)^2 3x=x^2-12x+36 x^2-15x+36=0 x^2-12x-3x+36=0 x(x-12)-3(x-12)=0 (x-12)(x-3)=0 x=12 OR 3 After 3 years Janice will be x(x+3) plug value of x 3(12+3)=45 So now Janice will be 45-3 = 42 years ( this makes sense) .. For value x=3 3(x+3) plug value of 3 3(3+3)= 18 This was 3 years later now she will be 15