Question 167513
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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Let anna be x yrs old now.
Let mother be y yrs old now.
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EQUATIONS:
x+7 = (1/2)(y+7)
Y-13 = 6(x-13)
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Rearrange to solve:
2x - y  = -7
6x -y  = -7*-13
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Subtract 1st equation from 2nd to get:
4x = -7*-14
x= 24.5 yrs old now (Anna's age now)
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Cheers,
Stan H.