SOLUTION: A lady is three times as old as her daughter. 8 years ago the product of their ages was 112. find their present ages.

Question 298112: A lady is three times as old as her daughter. 8 years ago the product of their ages was 112. find their present ages.
Found 2 solutions by solver91311, stanbon:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Let represent the daughter's age now.

Then represents the mother's age now, represents the mother's age 8 years ago, and represents the daughter's age 8 years ago. The product of their ages 8 years ago is then:

and this is equal to 112, so:

which is to say

The quadratic factors to:

So

or

You can safely exclude the negative root since that would mean that the mother would have been -4 15 months before her daughter was born. The other answer is the correct value for the daughter's age now.

Check:

Daughter is

Mom is

Eight years ago daughter was and mom was .

John

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A lady is three times as old as her daughter.
8 years ago the product of their ages was 112.
find their present ages.
---------------------------------
Equations:
L = 3D
(L-8)(D-8) = 112
------------------------------
Substitute for "L" and solve for "D":
(3D-8)(D-8) = 112
3D^2 -32D + 64 = 112
---
Rearrange:
3D^2 -32D - 48 = 0
Factor:
(3D+4)(D-12) = 0
D = 12 (daughter's age)
----
Since L = 3D, L = 36 (the lady's age)
===========================================
Cheers,
Stan H.
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