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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.
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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(20879)
(
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):
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(69061)
(
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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