Why is Today “Prime Day”?

Today is July 11, which the marketing folks at Amazon* have dubbed “Prime Day.” They’ve even created a spiffy, little banner image for it:

Ooh… pretty!

The selection of 7/11 as Prime Day was no doubt deliberate, since both 7 and 11 are prime numbers, though one has to wonder why Amazon ignored the other 52 (or 53, if it’s a leap year) dates they could have chosen:

• February
  • 2/2
  • 2/3
  • 2/5
  • 2/7
  • 2/11
  • 2/13
  • 2/17
  • 2/19
  • 2/23
  • 2/29 (some years)
• March
  • 3/2
  • 3/3
  • 3/5
  • 3/7
  • 3/11
  • 3/13
  • 3/17
  • 3/19
  • 3/23
  • 3/29
  • 3/31
• May
  • 5/2
  • 5/3
  • 5/5
  • 5/7
  • 5/11
  • 5/13
  • 5/17
  • 5/19
  • 5/23
  • 5/29
  • 5/31
• July
  • 7/2
  • 7/3
  • 7/5
  • 7/7
  • 7/11
  • 7/13
  • 7/17
  • 7/19
  • 7/23
  • 7/29
  • 7/31
• November
  • 11/2
  • 11/3
  • 11/5
  • 11/7
  • 11/11
  • 11/13
  • 11/17
  • 11/19
  • 11/23
  • 11/29

One of my favorite problems is based on the numbers 7 and 11. Here’s a modified version of it, tailored to Amazon’s special day:

An online shopper placed four items in his cart. When he checked out, his credit card was charged $7.11. Shortly thereafter, a programmer realized there was an error in the code, and total price had been calculated by multiplying the prices of the four items. The customer service department was about to alert the customer to the error, but the programmer informed them that the total price would have still been $7.11 if the prices had been added. No harm, no foul.

There was no sales tax. What was the cost of each item?

Good luck! Happy shopping!

* No, Amazon did not pay me to write a blog post about Prime Day.