I just had a Subway sandwich, and I notice on the packaging the following information:

Subway sandwiches with 6 grams of fat or less include:

- Ham (4.1g fat Aus; 4.5g fat NZ)
- Veggie Delight(3.1g fat Aus; 3.1g fat NZ)
- Turkey & Ham (4.9g fat Aus; 4.9g fat NZ)
- Turkey (5.1g fat Aus; 4.9g fat NZ)
- (some others)
Prepared according to standard recipes […]

This presents some interesting observations. Firstly, notice that the amounts of fat are different for Australia and New Zealand. I’m guessing this is because here in Australia Subway uses leaner ham than in NZ, while conversely we get fattier turkey than in NZ.

Secondly, the veggie sub, which has negligible fat content in the filling (essentially just lettuce, tomato, onion, carrot, and cucumber – the “6 grams of fat or less” subs are defined to have “no cheese or condiments”) must be getting all of its fat content from the bread. The fact that this is the same in both countries is mildly reassuring.

Thirdly, the combined Australian ham & turkey sub contains a fat content that is, understandably, between the fat content of the ham or the turkey alone – assuming it contains a fraction of the ham plus a fraction of the turkey of the individual subs, not just both lots added together. The NZ ham & turkey is a bit more puzzling, since it contains the same amount of fat as a turkey sub alone! Yet we can see the turkey is fattier than the ham, so if we remove some turkey and add an equal amount of ham, the total fat content should drop.

Fourthly, the “prepared according to standard recipes” implies that the same proportions of ingredients are used in both countries to make the same sandwiches. (This may not actually be the case, but run with me here.)

Well, given these data, let’s see what we can deduce. Let’s call the amount of ham in a ham sub a “serve of ham”, and the amount of turkey in a turkey sub a “serve of turkey”. Then in Australia a serve of ham contains 1 gram of fat and a serve of turkey contains 2 grams of fat, while in NZ they contain 1.4 and 1.8 grams of fat respectively.

Now let *h* be the number of serves of ham in a ham & turkey sub and *t* be the number of serves of turkey. Then, subtracting the 3.1 grams of fat from the bread (the same for each sandwich), we have:

- In Australia: 1
*h*+ 2*t*= 1.8 - In New Zealand: 1.4
*h*+ 1.8*t*= 1.8

Plugging this into *Mathematica* (hey, I could solve it by hand if I wanted, but I have *Mathematica* sitting right here, so why not use it?) gives:

*h*= 0.36*t*= 0.72

So, this means:

- A ham & turkey sub contains exactly twice as much turkey as ham!
- The total amount of meat in a ham and turkey sub is 1.08 serves!

But wait, there’s more! That 1.08 serves is made up of 0.36 serves of ham and 0.72 serves of turkey. If the serves are the same size, then you get *more* meat in a ham & turkey sub than in either a ham or a turkey sub alone. But let’s say the size of a serve of ham is *H* and the size of a serve of turkey is *T*. Then setting the size of a standard serve of “ham & turkey” to be the same size as a serve of turkey, we get:

- 0.36
*H*+ 0.72*T*=*T*

Solving for T in terms of H, this gives:

*T*= 9*H*/7

In other words, if a serve of turkey is more than 9/7 the size of a serve of ham, then a ham & turkey sub gives you *less* meat than a turkey sub. But if a serve if turkey is less than 9/7 the size of a serve of ham, then a ham & turkey sub gives you more meat than either a ham sub or a turkey sub alone. A sensible assumption is that Subway is likely not going to give you less meat on a ham & turkey sub than on a turkey sub, so we can be pretty sure that a turkey sub contains no more than 9/7 the amount of meat of a ham sub.

This then allows us to calculate that, in Australia, turkey is at least (2/1)/(9/7) = 1.56 times as fatty as ham, while in New Zealand turkey is at least (1.8/1.4)/(9/7) = 1 times… at least as exactly fatty as ham!

What this in turn says about turkey and pig farming practices in Australia and New Zealand is left as an exercise for the reader.

I had a meatball sub in New Zealand (I always have meatball) and I think their sauce was completely different!

Your next Subway Math post should be on the tessellation of cheese. Any your poor math teacher, solving a basic simultaneous equation by computer. Next we’ll all be forgetting long division or coopering.

That. Was. Awesome.