SOLUTION: A mother is 25 years older than her daughter. Ten years ago, the daughter is 4/9 of the age of the mother was then. Find the age of each.
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Question 154824: A mother is 25 years older than her daughter. Ten years ago, the daughter is 4/9 of the age of the mother was then. Find the age of each. Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website! A mother is 25 years older than her daughter. Ten years ago, the daughter is 4/9 of the age of the mother was then. Find the age of each.
.
Let D = daughter's age
then
D+25 = Mother's age
(from:"A mother is 25 years older than her daughter.")
.
We derive our equation from:
"Ten years ago, the daughter is 4/9 of the age of the mother was then."
to get:
D-10 = (4/9)([D+25]-10)
D-10 = (4/9)(D+25-10)
D-10 = (4/9)(D+15)
9D-90 = (4)(D+15)
9D-90 = 4D+60
5D-90 = 60
5D = 150
D = 30 years (daughter's age)
.
D+25 = 30+25 = 55 years (Mothers age)
