Question 166972: Anna made the following announcement:
" In 7 years, I will be half my mother's age. Thirteen years ago, she was 6 times as old as I was then."
How old is Anna now?
My teacher gives us a "problem of the week" every week and this is it. I'm not sure how to figure out the answer.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Anna made the following announcement:
" In 7 years, I will be half my mother's age. Thirteen years ago, she was 6 times as old as I was then."
How old is Anna now?
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A = Anna's age
M = Mother's age
In 7 years, I will be half my mother's age.
M+7 = 2*(A+7)
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Thirteen years ago, she was 6 times as old as I was then.
M-13 = 6*(A-13)
Now there are 2 eqns in 2 unknowns.
M + 7 = 2A+14 eqn 1
M -13 = 6A-78 eqn 2
3M+21 = 6A+42 eqn 1 times 3
Subtract
-2M-34= -120
-2M = -86
M = 43 (Mother's age)
Sub into eqn 1
43+7 = 2A + 14
2A = 36
A = 18 (Anna's age)
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Check:
13 years ago, they were ages 5 and 30, = 6 times.
In 7 years, they'll be 25 and 50, 2 times.
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