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A 95-Year-Old Unsolved Problem?

While browsing through old newspapers in Garner (IA), I found this mathematical problem in the Garner Signal (February 11, 1914).

A Problem of Arithmetic
Who will be the mathematician to hand us in a correct solution of the following. The pupil in any school sending the first correct answer will be awarded the honors of the office:

A pretty miss with rosy cheeks,
Just merging from her teens,
Was quizzed one day about her age,
Her height, her weight, her means.

"The following I propose;
My age, height, weight and wealth
To you it will disclose.

"My age augmented by my height
And weight, then multiplied by three
Is in proportion to my wealth
As one to thirty-three.

"My height, weight and wealth combined
Increased by just a score,
Divided by one thousand, gives
My age and just no more.

"My weight, wealth and thrice my age,
Increased six and a score,
Is just two hundred times my height,
Increased by thrity-four.

"My wealth, age and thrice my height
Diminished by eighteen,
Is twenty thousand, just outright,
What must they each have been?"

Can you determine the girl's age, height, weight, and wealth? If so, you can still submit your answer to the Garner Signal, as I do not think anyone ever responded (at least by my check through through the year 1955).

Source: Garner Signal, February 11, 1914

Hint: Four variables (A, H, W, M) are involved...and a system of four equations can be set up....but the system is not easy to solve.

With four variables, guess and check is difficult. Thus, can you eliminate one or more of the variables...but beware: Do all the variables represent integer values? Plus, is height in feet or inches?

Solution Commentary: I solved it....Rather than tell you the value of the four variables, I will tell you that the value of the product AHWM = 3,502,224,000. Does that help?

Be careful, as one of the four equations in the system can be interpreted in two different ways.

GH (Vancouver) writes: "Ok, the 95 year-old problem... She is 20 years old, 66 inches tall, has \$19, 800 and weighs 114 lbs. Had to decipher the 4th paragraph properly- "two hundred times my height, Increased by thrity-four" means 200(h + 34), not 200h + 34."

Do you agree?