SOLUTION: The product of the present ages of a mother and her daughter is 432. Four years ago the mother was exactly four times as old as the daughter .what are their present ages?

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Question 1158138: The product of the present ages of a mother and her daughter is 432. Four years ago the mother was exactly four times as old as the daughter .what are their present ages?
Found 3 solutions by ikleyn, mananth, MathTherapy:
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.

Let x be the present age of the daughter.

Then  the present age of the mother is 4*(x-4)+4 = 4x - 12.


From the condition, you have this equation

    x*(4x-12) = 432.


Cancel the factor 4 in both sides

    x*(x-3) = 108.


You can solve this quadratic equation.


An alternative way is to decompose MENTALLY the number 108 into the product of two factors with the difference 3 between them 
    
    108 = 9*12,

so the answer is the greater of these two factors x= 12.


ANSWER.  The daughter is 12 years old.  The mother is 4x - 12 = 4*12-12 = 36 years old.


CHECK.  12*36 = 432.   ! Correct !

Solved.


Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!

The product of the present ages of a mother and her daughter is 432.
let age of a mother be x years
and that of her daughter be y years
x*y =432
x=432/y
Four years ago the mother was x-4 years
daughter was y-4 years .
Mother was exactly four times as old as the daughter
(x-4) =4(y-4)
substitute x
(432/y -4) = 4y-16
(432-4y)/y = 4y-16
432-4y = 4y^2-16y
Rearrange
4y^2-12y-432=0
Solve
4(y+9)(y-12)=0
y=-9 OR 12
Age cannot be negative
so daughter is 12 years
432/12 is mother's age






what are their present ages?
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

The product of the present ages of a mother and her daughter is 432. Four years ago the mother was exactly four times as old as the daughter .what are their present ages?
Let mother's and daughter's ages be M and D, respectively

Then we get: MD = 432 ------ eq (i)

Also, M - 4 = 4(D - 4)____M - 4 = 4D - 16_____M = 4D - 12 ----- eq (ii)

D(4D - 12) = 432 ------ Substituting 4D - 12 for M in eq (i)



(D - 12)(D + 9) = 0

Daughter's age, or        OR      D = - 9 (ignore) 

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