SOLUTION: Anna made the following announcement: "In 7 years, i will be half my mothers age. Thirteen years ago, she was 6 times as old as i was then." How old is Anna?

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Question 1020390: Anna made the following announcement:
"In 7 years, i will be half my mothers age. Thirteen years ago, she was 6 times as old as i was then."
How old is Anna?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
x= Anna's age
y= Anna's mother's age
y%2B7= Anna's mother's age in 7 years
x%2B7= Anna's age in 7 years
We know that x%2B7=%281%2F2%29%28y%2B7%29 because Anna said
"In 7 years, i will be half my mothers age."
x%2B7=%281%2F2%29%28y%2B7%29<-->2%28x%2B7%29=y%2B7<-->2x%2B14=y%2B7<-->2x%2B7=y

x-13= Anna's age thirteen years ago
y-13=2x%2B7-13=2x-6= Anna's mother's age thirteen years ago
We know that 6%28x-13%29=2x-6 because Anna said of her mother
"Thirteen years ago, she was 6 times as old as i was then."

So we solve 6%28x-13%29=2x-6
6%28x-13%29=2x-6<-->6x-78=2x-6<-->6x-2x=78-6<-->4x=72<-->x=72%2F4<-->highlight%28x=18%29 .
Anna is highlight%2818%29 years old.

NOTE/CHECKING:
In 7 years Anna will be 18%2B7=25 and her mother will be 2%2A25=50 .
They are 50-25=25 years apart,
so right now Anna's mother's age is 18%2B25=43 .
Thirteen years ago, Anna's age was 18-13=5 ,
and her mother's age was 43-13=30 .