SOLUTION: My algebra teacher gave us this problem, I don't know how to start solving it. Please help me. Marty is 1/3 as old as her mother. Five years ago she was only 1/5 of the age of her

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Question 333745: My algebra teacher gave us this problem, I don't know how to start solving it. Please help me.
Marty is 1/3 as old as her mother. Five years ago she was only 1/5 of the age of her mother. How old is Marty?
Found 2 solutions by ankor@dixie-net.com, Edwin McCravy:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Let m = mother's present age
Let d = daughter's present age (Marty)
:
Write an equation for each statement:
;
Marty is 1/3 as old as her mother.
d = 1%2F3m
or we can say
m = 3d
:
Five years ago she was only 1/5 of the age of her mother.
d - 5 = 1%2F5(m-5)
Mult both sides by 5, get rid of that fraction
5(d-5) = m - 5
5d - 25 = m - 5
5d = m - 5 + 25
5d = m + 20
Replace m with 3d
5d = 3d + 20
5d - 3d = 20
2d = 20
d = 10 yrs is Marty
:
:
check solution in the statement; m = 3(10) = 30 is mom
"Five years ago she was only 1/5 of the age of her mother.
10 - 5 = 1%2F5(30 - 5)



Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
My algebra teacher gave us this problem, I don't know how to start solving it. Please help me.

Let X = Marty's age now

Let Y = Mother's age now

Then 

Marty's age five years age = (X-5)

Mother's age five years ago = (Y-5)

1/3 of Mother's age now = 1%2F3Y

1/5 of Mother's age five years ago = 1%2F5%28Y-5%29

>>...Marty is 1/3 as old as her mother. 

Marty's age = 1/3 of Mother's age now
  
     X      =  1%2F3  %22%22%2A%22%22   Y

>>...Five years ago she (Marty) was only 1/5 of the age of her mother...<< 

Marty's age five years ago = 1/5 of Mother's age five years ago 

         (X-5)             =  1%2F5  %22%22%2A%22%22 %28Y-5%29

     
So we have these two equations 

system%28X=%281%2F3%29Y%2C%28X-5%29=%281%2F5%29%2A%28Y-5%29%29

Multiply both sides of the first equation by 3 to clear of fractions.
Multiply both sides of the first equation by 5 to clear of fractions.



Canceling clears fractions:



system%283X=Y%2Cred%285%29%28X-5%29=%28Y-5%29%29

Simplifying further:

system%283X=Y%2C5X-25=Y-5%29

Simplifying further:

system%283X=Y%2C5X=Y%2B20%29

Since the first equations tells us that Y = 3X we can replace the Y
in the second equation 

5X=Y%2B20%29

by 3X

5X=3X%2B20

2X=20

X=10

So Marty is 10 years old.  However we need to find her
Mothers age so we can check.  We use

Y = 3X

Y = 3(10)

Y = 30

So her mother is 30.

Let's check:

Marty is 1/3 as old as her mother.

Indeed 10 is 1/3 of 30

Five years ago she was only 1/5 of the age of her mother

Five years ago se was 5 and he mother was 25, and indeed
5 is 1/5 of 25.

So we know we are right.

Edwin