Word age problem with age ratio's.

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platinum983

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Last day of each calendar year, Ana and Josh order chocolate cake. Ana and josh split cake in the ratio of their years
(For example, if they are the same age, they split half-half). If 2015. Ana got double the piece than 8 years earlier,
how old are Ana and Josh?

If x is the age of Ana, and y is the age of Josh I've got y=(x(x+25))/(8-x). I get a solution by guessing a few options, but couldn't get
a clear solution. (Sorry for bad English)
 
Please explain how you got that equation; I don't see where 25 came from (or the rest, either).

Also, what is your answer, and the check you did? That will help me see whether we are interpreting the problem the same way.

I have an algebraic (Diophantine) solution, with two feasible answers. My equation is very different.
 
platinum983 said:
Last day of each calendar year, Ana and Josh order chocolate cake. Ana and josh split cake in the ratio of their years
(For example, if they are the same age, they split half-half). If 2015. Ana got double the piece than 8 years earlier,
how old are Ana and Josh?

If x is the age of Ana, and y is the age of Josh I've got y=(x(x+25))/(8-x). I get a solution by guessing a few options, but couldn't get
a clear solution. (Sorry for bad English)
Click to expand...
Please explain how you derived your equation.
 
That appears to be the solution for the same problem but with 8 replaced with 11. Apart from that, the equation is what I started with, and much of the work agrees with me, with a number change. For the last part, I found it sufficient to try values for "a" to find integer solutions that yielded possible ages for both. (They seem to be ignoring that little detail.)

But still, where did your wrong equation come from? There may be something for you to learn from your mistake, rather than just from seeing someone else do something correct.
 
Why are the answers in this form: (21, 21^2/20), (20, 20^2/21), (18, 18^2/22)?? I don't believe in coincidences.
 
Jomo said:
Why are the answers in this form: (21, 21^2/20), (20, 20^2/21), (18, 18^2/22)?? I don't believe in coincidences.
Click to expand...
... and if you think through it (perhaps starting at the form [MATH]b = \frac{a^2}{22-a}[/MATH]), you can see why!

A similar thing happens in the original problem, with 8 rather than 11. But I suspect that with different numbers, it might be a little less regular.
 
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