How Much Does Your Name Cost?

Here’s a contrived yet fun math problem that I shared with my sons recently:

A local hardware store sells bronze letters. However, the letters vary in price; some are more expensive than others. When I was at the store the other day, four people purchased the letters in their names. Their names and the prices they paid were:

Aiden $491  •  Ned $225  •  Dane $399  •  Ed $135

The price of a name is equal to the sum of the prices of its letters. The price for uppercase and lowercase letters is the same, and there is no additional surcharge or tax. How much would the following people pay to buy the letters in their names?

Edna  •  Ian  •  Nadine

Those of you who know a little algebra will have no trouble with that problem. Those of you who don’t shouldn’t have too much trouble, either.

But then, I realized I could extend the problem for some added fun. And who am I to keep fun things to myself? So, here ya go.

I saw this sign in a window the other day:

At first, I thought the store was engaging in human trafficking. But then I realized that $269 was the price for the bronze letters that had been used to spell the name Eli. Inside the store was a price list for other names:

AIDEN – 491	AL – 248	ART – 267	BEA – 290
EARL – 415	DANE – 399	ED – 135	ELI – 269
FAY – 220	GABI – 289	HAL – 284	IVY – 143
JACK – 234	JAY – 232	KO – 60	KAI – 283
LEXI – 272	MAVIS – 363	MAX – 215	NED – 225
PAT – 210	PERRI – 330	QI – 93	QUIN – 199
SAMMY – 338	WILL – 243	ZENO – 243

The store didn’t have a list of prices for the individual letters, but then I realized that I didn’t need one. From the table above, I could figure out how much my name  would cost.

Can you figure out how much your name would cost?

You can download both of these problems for use in a classroom (or at a mathy party) from the following link:

Name Letters (PDF)

And while I don’t believe in answer keys, you can check your work by using the form found on this page.

Name Letter Form

For what it’s worth, the longest name ever — according to Wolfe + 585, Senior, who has a pretty long name himself — is Rhoshandiatellyneshiaunneveshenk Koyaanisquatsiuth Williams. Her entire name name would have cost $4,073 at this store — an astounding $2,359 for her first name, $1,119 for her middle name, and a veritable bargain at $595 for her tame-by-comparison last name. (Incidentally, this is the name that appeared on her birth certificate. As the story goes, her father later increased her first name to 1,019 letters and added an additional 36 letters to her middle name. You know… just in case the name wasn’t long or unique enough already.)