1. ## Three Ages

Transpsing the two digits of Alices age gives Billies age. The difference between their ages is twice Carlas age and Billie is ten times as old as Carla. What are their ages?

2. ## Re: Three Ages

I think this is a "moderate cheat"
<span style="background-color: #FFFF00; color: #000000; font-weight: bold"><font color=yellow>Ages should be integers! Though I guess at that age they still use the half!
Alice is 54
Billie is 45
Carla is 4.5
45 = 10*4.5
54=45 = 9 = 2*4.5</font color=yellow></span hi>

Steve

3. ## Re: Three Ages

Steve, You got me! And you're correct <img src=/S/cheers.gif border=0 alt=cheers width=30 height=16>

4. ## Re: Three Ages

I don't see this as a "cheat" at all Steve. It's the only solution within the constraints of the problem. From the information given I determine that: <span style="background-color: #FFFF00; color: #000000; font-weight: bold"><font color=yellow> the digits in the ages of A & B must be related by 5p = 4q, where the ages are pq and qp. The only single digits able to satisfy this condition are 4 and 5. The fractional age is a consequence of this.</font color=yellow></span hi>

Alan

5. ## Re: Three Ages

I did find the solution even with this "cheat" and I admit it is only a "moderate one"

I just don't think it is NORMAL practice to use half years. I would have also complained if it reguired other "decimal" dates. Though I suppose one could argue that if a child is < 2 years using deciamls that correspond to MONTHS fractions is acceptable, since we give ages of 18 months etc, ir if < about 10 to give half years as is the practice of many children.

Over these ages I think the practice is never done. "I am 45 and a half" is not said, but I am "8 and ahalf" is.

Steve

6. ## Re: Three Ages

At this stage of the game, I just say "I'm under 50" and leave it at that. <img src=/S/grin.gif border=0 alt=grin width=15 height=15>

Alan

7. ## Re: Three Ages

And I can't even say that any more, at least not truthfully <img src=/S/sad.gif border=0 alt=sad width=15 height=15>

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