SOLUTION: Gwenn is one fourth as old as her mother. Six years ago, she was one tenth as old as her mother. Find the age of her mother.

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Question 991832: Gwenn is one fourth as old as her mother. Six years ago, she was one tenth as
old as her mother. Find the age of her mother.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Gwenn one fourth as old as her mother.
 
G%22%22=%22%22expr%281%2F4%29M

Clear the fraction by multiplying both sides by 4

4G%22%22=%22%22M

Six years ago, she was one tenth as old as her mother. 
Six years ago she was G-6 and her mother was M-6

...she was one tenth as old as her mother. 
G-6%22%22=%22%22expr%281%2F10%29%28M-6%29

Clear the fraction by multiplying both sides by 10

10G-60%22%22=%22%22M-6

10G-M%22%22=%22%2254

10%28G-6%29%22%22=%22%22M-6%29

10G-60%22%22=%22%22M-6

10G-M%22%22=%22%2254

So you have this system of equations:

system%284G=M%2C10G-M=54%29

Solve that by substitution and you get that 
Gwenn is 9, and her mother is 36.

Edwin