Math Puzzle — When $5 is not worth $5

I recently had an odd customer shopping experience at Whole Foods, thanks to a black-box software algorithm. I had come into possession of a “$5 off $25” coupon, which doesn’t happen very often, so went off to Whole Foods to buy some groceries. Turns out that at Whole Foods, a $5 coupon isn’t always worth $5.

With the purchase by Amazon, Whole Foods introduced some new discount types for Prime members. Two of them are:

  • An extra 10% off of sale items (yellow tags). Sales prices are available to all shoppers, but Prime members get an extra 10% off at checkout.
  • Prime deals — super-low pricing on certain items (blue tags). These are labelled at the full price, but have a discount taken at checkout.

I found a mixture of Prime deals, sale items, and non-sale items totaling around $75. At checkout though, here is what I saw for the “Prime deal” on my ticket — steak that was supposed to be $5.99/lb showed up with only a partial discount (priced at $7.16/lb):

Whole Foods Ticket Showing Weird Discount
Whole Foods Ticket Showing Weird Discount

Um, what?? 2.23 lbs at $5.99/lb should be … $13.36. But they charged me $15.97??

Over the next 10 minutes, three employees tried explaining the math to me through various combinations of the 10% Prime discount + the $6.31 reduced price, but they could never get the numbers to match up on my ticket. Running the math myself, it turned out that the computer somehow took $2.61 of my coupon and applied it towards my $5.99/lb “Prime deal” — definitely non-transparent, confusing, and I feel slightly unethical. So my $5 coupon became worth $2.39.

Typically, my experience with such coupons are one of the following two things:

  1. $5 off is applied at the end of the ticket, where a whole $5 is removed from the final price. Or, if there are sales items:
  2. $5 is taken off the total ticket, but divided equally across all items. And then any additional sales discounts are taken. For example, in this case I bought $7.50 worth of chicken — about 10% of the ticket total. That means the coupon would have reduced the price of the chicken to $7.00, and then the extra 10% off of sales prices would have been $0.70 off (instead of the $0.75 non-coupon amount). Other store tickets, like CVS, are very transparent about this and show line-by-line how the various discounts interact.

Understandably, this coupon had fine print of cannot be combined with other discounts or pricing, in which case I would have assumed the $5 would have been taken off of non-sales and non-discounted items, of which I had purchased over $25 worth. Of course I could have achieved the same effect by splitting my ticket into two, which would have saved everyone time compared to the 10 minutes of math lessons.

However, in this case $2.61 of the coupon was applied towards a “reduced price” item, making one of the following two things true for my Prime deal + coupon combination:

  1. The advertised “Prime deal” of $5.99/lb changed to $7.16/lb once my coupon was introduced.
  2. My $5 off coupon became worth $2.39.

Either way, I felt like the pricing algorithm that calculated the ticket was dishonest and unethical (and I blame the pricing strategists / programmers, not the store employees). A cynical person might wonder if the algorithm calculated a “Prime” discount based on some ML model that returns a discount that the average shopper wouldn’t notice or complain about, because there is no straightforward, mathematical way that I can figure out how my $5 coupon got reduced to $2.39. If anyone can provide a logical, mathematical explanation of my ticket, I would love to see it!

Overall, extremely disappointing nickel-and-dime behavior for “Earth’s Most Customer-Centric Company”, so I will be taking my money (and shopping data) elsewhere.