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I mean, is there any other solution? There are certainly no integral solutions to the problem, but there is a unique (rational) solution.

I feel like I’m missing something entirely, though...

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I was also stuck thinking in integers for a few seconds, perhaps because of the context. But yeah, a 10-year-old would already know about fractions.

I also mentally started thinking about integral solutions. I wonder if it's also because of the variable names... a,b,c tend to be used to represent integers (e.g. Fermat's Last Theorem, Euclid's algorithm etc).

x and y are more commmonly used to represent real numbers.

Random aside: once in high school I took a math puzzle test. The only problem I skipped was because they asked for "integral solutions." I knew the word "integral" only as belonging to calculus, about which I knew nearly nothing at the time. If I had realized in context it just meant "integer" I could have done it!

They did make it a tricky question!

Thanks for pointing that out. I'll use X and Y next time I share this story. Of course my daughter wouldn't have known at the time about the distinction, and neither did I - it having been too long since doing algebra ;)

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