SOLUTION: Jack is as old as Diane will be when Jack is twice as old as Diane was when Jack's age was half the sum of their present ages. Diane is as old as Jack was when Diane was half the

Question 1115373: Jack is as old as Diane will be when Jack is twice as old as Diane was when Jack's age was half the sum of their present ages. Diane is as old as Jack was when Diane was half the age she will be 10 years from now. How old are Jack and Diane? Let k = Jack's age and n = Diane's age.
I thought this would work, but was wrong:
2n=1/2(k+n) where n=20 and K=15
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
You are looking for values for two variables,
so you need two independent equations.

is half the sum of their present ages.
Jack's age was equal to that
years ago.
At that point, Diane was
.
Jack will be twice as old as that= at some point in the future.
That is going to happen
years from now.
At that point Diane will be
,
and that is how old Jack is now, so
<-->
is one of the equations you need.

Diane's age 10 years from now will be .
Half of that is .
That was Diane's age at some point in the past.
That happened years ago.
At that point Jack's age was
,
and that happens to be Diane"s age now, so
<--> <-->
is another equation you can use.

The system can be solved any way you choose.
to get .

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