Damsel And Suitor

April 21, 2017

Chris Smith tweets mathematical curiosities at @aap03102. This one caught my eye the other day:

This is from 1779: a time when puzzles were written in poetry, solutions were assumed to be integers and answers could be a bit creepy:

Questions proposed in 1779, and answered in 1780.

I. QUESTION 742, by Mr. John Penberthy.

I’m in love with a damsel, the pride of the plain,
Have courted and talk’d in Ovidian strain;
But vain is the rhetoric us’d by my tongue,
She says I’m too old and that she is too young:
From the foll’wing equations, dear ladies, unfold;
If she be too young, or if I be too old.

x3 + xy2 = 4640y
x2yy3 = 537.6x

Where x represents my age, and y the damsel’s.

Your task is to compute the ages of the damsel and her suitor. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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