Question 118138
Consecutive odd integers are 2 numbers apart. (Think of 3 and 5 being consecutive odd integers
or 9 and 11 ... both pairs are 2 numbers apart).
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If x is the unknown odd integer, then x + 2 is the next consecutive odd integer.
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So the younger sister is x years old and the older sister is x + 2 years old.
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How old was each sister 12 years ago? The younger sister would have been x minus 12 years old
and the older sister would have been x + 2 minus 12 years which simplifies to x - 10 years
old. And since at that time (12 years ago) the sum of their ages was 8 you can write the
equation for the sum of their ages as:
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(x - 12) + (x - 10) = 8
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On the left side, combine the two terms that contain x to get:
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2x - 12 - 10 = 8
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Then combine the two numbers on the left side and you have:
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2x - 22 = 8
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Get rid of the -22 on the left side by adding 22 to both sides and you have:
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2x = 30
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Finally, solve for x by dividing both sides by 2 and the result is:
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x = 15
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This tells you that the younger sister is 15. The older sister's age is the next consecutive odd
integer (two numbers higher than 15), so the older sister is 17.
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Check. 12 years ago the younger sister would have been 15 minus 12 or 3 years old. And the
older sister would have been 17 minus 12 or 5 years old. The sum of their ages at that time
would have been 3 plus 5 and that equals the 8 years, just as the problem said it was supposed
to. 
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Therefore, the answer to this problem is that the two sisters are currently 15 and 17 years old.
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Hope this helps you to understand the problem and how to work it.
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