SOLUTION: Bob is as old as John will be when Bob is twice as old as John was when Bob's age was half the sum of their present ages. John is as old as Bob was when John was half the age he w

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Question 131188: Bob is as old as John will be when Bob is twice as old as John was when Bob's age was half the sum of their present ages. John is as old as Bob was when John was half the age he will be ten years from now. How old are John and Bob?

...I have no idea where to start...
Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
Let Bob's current age =
Let John's current age =
Let half the sum of their present ages =
Let half John's age ten years from now =
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The problem could now be restated:
"Bob is as old as John will be when Bob is twice as old as John was when Bob's age was . John is as old as Bob was when John was
Find and "
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Assume John is older than Bob. At any time, the difference in
their ages will be
When Bob was , John was
Twice that age is
When Bob is that age, John will be
It says Bob is this old

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When John was , Bob was
It says that John is this age

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The equations I have now are:

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substituting,

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substituting,

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substituting,

Bob's age is 20/7, John's age is 10/7
check:

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OK

OK
Unless I messed up along the way, that's it