Question 167513
In 7 years, I will be half my mother's age. Thirteen years ago, she was 6 times as old as i was then. 
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Let A = Anna's age
and M = Mother's age
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From:"In 7 years, I will be half my mother's age"
A+7 = M/2 (equation 1)
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From:"Thirteen years ago, she was 6 times as old as i was then"
6(A-13) = M (equation 2)
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Using the definition of M from equation 2, substitute it into equation 1 and solve for A:
A+7 = M/2 
A+7 = (6(A-13))/2
A+7 = 3(A-13)
A+7 = 3A - 39
7 = 2A - 39
46 = 2A
23 years = A