SOLUTION: Jamie is 5 years older than her brother. Five years ago she was 2 times older than her brother. How old are they?

Question 1132219: Jamie is 5 years older than her brother. Five years ago she was 2 times older than her brother. How old are they?

Found 2 solutions by Alan3354, greenestamps:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Jamie is 5 years older than her brother. Five years ago she was 2 times older than her brother. How old are they?
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Five years ago she was 2 times older than her brother.
1 time older = 2 times as old.
2 times older = 3 times as old.
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The difference is always 5 years.
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5 years ago:
J = B + 5
J = 3B
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Sub for J in the 1st eqn
3B = B + 5
2B = 5
B = 2.5
J = 7.5
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Add 5
===============
B = 7.5
J = 12.5
=====================================
"2 times older" shows the author of the problem should find other work.
But, at least it's not "2 times younger."

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The solution by the other tutor shows that the statement of the problem is faulty, because the answers are not whole numbers of years.

The other tutor correctly points out that "two times older" is NOT the same as "two times as old". Unfortunately, most people don't make a distinction between the two phrases. (I have even seen problems on practice SAT tests where the wrong interpretation of "x times older than" is used!)

So the intended statement of the problem is this:

Jamie is 5 years older than her brother. Five years ago she was 2 times AS OLD AS her brother. How old are they?

The difference in their ages is always 5 years. So when she was twice as old as her brother, she was 10 and he was 5. Since that was 5 years ago, they are now 15 and 10.
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