SOLUTION: The ages of two sisters can be represented as consecutive odd integers. Twelve years ago, the sum of their ages was 8. How old is each now?

Question 118138: The ages of two sisters can be represented as consecutive odd integers. Twelve years ago, the sum of their ages was 8. How old is each now?
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
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).
.
If x is the unknown odd integer, then x + 2 is the next consecutive odd integer.
.
So the younger sister is x years old and the older sister is x + 2 years old.
.
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:
.
(x - 12) + (x - 10) = 8
.
On the left side, combine the two terms that contain x to get:
.
2x - 12 - 10 = 8
.
Then combine the two numbers on the left side and you have:
.
2x - 22 = 8
.
Get rid of the -22 on the left side by adding 22 to both sides and you have:
.
2x = 30
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Finally, solve for x by dividing both sides by 2 and the result is:
.
x = 15
.
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.
.
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.
.
Therefore, the answer to this problem is that the two sisters are currently 15 and 17 years old.
.
Hope this helps you to understand the problem and how to work it.
.

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