# Tag Archives: groceries

## Some more grocery store math

### Problem 1

A Fruit Roll Up weighs 0.5 oz & is a 12.5 by 11 cm parallelogram.

A Fruit by the Foot weighs 0.75 oz & is rectangular. One dimension of this rectangle is 2.2 cm. What is the other dimension?

(Be sure to state your assumptions, and any other information you draw upon in your solution.)

### Problem 2

There are now Cheez-Its BIG. They claim to be “Twice as Big” as ordinary Cheez-Its. One serving of regular Cheez-Its consists of 27 crackers and weighs 30 grams. One serving of BIG Cheez-Its also weighs 30 grams.

(A) How many crackers should one serving of BIG Cheez-Its contain?

(B) How many does it contain?

## More junk food math

You’ve seen the billboards for these, right?

Basically, they’re mini McNuggets.

McNuggets have a lot of fat. Most of it (as with all fried foods with the possible exception of cheese curds) is in the outer coating.

So what happens when we shrink the McNugget?

We could model the chicken by volume and the outer coating by surface area. In this case, shrinking the McNugget by a factor 1/2 would yield a doubling of the ratio of coating to chicken. As a result we predict a substantial increase in fat as a percentage of weight.

But that’s a crude model-the coating isn’t infinitely thin.

A more realistic model might treat the coating as having a thickness, and thus a volume. When we shrink the McNugget to make a McBite, do we shrink the thickness of the coating proportionately? This seems unlikely. But even if we do, the ratio of coating to chicken increases.

More likely is that the coating is of constant thickness. In other words, McBites are probably smaller chicken bits covered with the same coating as McNuggets. Once again, we increase the ratio of coating to chicken, and we predict a substantial increase in fat as a percentage of weight.

Heading over to McDonald’s online Nutrition Information, we learn that McNuggets have about 12 grams of fat for a 65 gram serving. That’s about 18% fat by weight. This figure is consistent across serving sizes.

Mc Bites? 19 grams of fat for an 85 gram serving. That’s about 22% fat by weight. Also consistent across serving sizes.

How different is 22% fat from 18% fat, you ask? Very different. They’re both bad news, but 22% fat is (coincidentally) 22% more fat than 18% is. So take a serving of McNuggets, which has a lot of fat. And put almost a quarter more fat in. That’s McBites. Oh, and also increase the portion size from 97 grams (6 piece McNuggets) to 128 grams (Regular size McBites).

Middle school math will get you far, kids.

Now if we can get an estimate of the McNugget to McBite scale factor, we can set up a system of equations and figure out just how much of that fat is in the coating.

## I was wrong…(Oreos, cont.)

This Oreo thing has gotten out of hand. Here is where we stand (with surprise dénouement at the end):

@JWDixonizer observed via Twitter that it must be volume that is doubled. I tried to refute that, but could not. Here are five manufactured Double Stuf Oreos next to five made the old-fashioned way.

The Double Stuf come out a tad shorter, but within any reasonable margin of error. Ergo, Double Stuf has double the volume of stuf. In an appearance that delights me no end, Al Sicherman himself confirms this:

My best evidence [that Double Stuf is in fact double stuf] follows not from all that pointless weighing but from noting that a stack of nine Double Stufs is approximately the same height as 11 originals: about 5 3/16 inches.

Sicherman then establishes his own system of equations and finds the stuf in a regular Oreo to measure approx. 0.1 inches and the stuf in a Double Stuf Oreo to measure approx. 0.2 inches.

But double volume doesn’t mean it’s Double Stuf.

Consider the case of whipped cream. Or popcorn.

Then Chris Lusto did an analysis. He argued that Nutrition Facts constitute imprecise data, and that we shouldn’t be surprised by conflicting results from two imprecise systems.

But Lusto didn’t touch any cookies in his first go. He didn’t measure mass and he didn’t run computations on fat grams.

Al Sicherman did. Not only that, he thought to measure the diameters of the wafers. I paired them up and they looked fine to me. But he lined up 10 regular wafers and 10 Double Stuf wafers. He claims to have photographic evidence that Double Stuf wafers have a larger diameter.

I have yet to run the numbers on this observation.

# Hold the presses!

In a late development, Lusto has cracked the case.

After taking grief for his hands-off approach to Oreo research, Lusto busted out a scale and honed his stuf-scraping techniques. He has now demonstrated definitively that Double Stuf is doubly stuffed.

I am humbled and chagrined. It turns out the Triple-Double really is a different beast. That chocolate stuf is deceptive.

On the plus side, if you solve the system of mass equations,

$\begin{cases} 10w+10s=113 \\ 20w+20s=145 \end{cases}$

the solution matches Lusto’s finding: One stuf weighs a bit more than 3 grams.

So there’s that.

## My Oreo manifesto, part 3

What? You think my reductio technique is sloppy?

You object to my introduction of the Triple-Double when it wasn’t stated in the set up of the proof? You think that chocolate filling is the problem and so you question my results?

You have a point on that first count. But the second count? Come on! Seriously?!? The calorie count of a chocolate filling is gonna be substantially different from that of a vanilla filling? Please.

Go check the Nutrition Facts on Vanilla Oreos, and then we’ll talk.

While you’re driving to the grocery store (or walking to your pantry), here’s some more data.

I weighed 10 of each kind of cookie.

• 10 regular Oreos weighed 113 grams
• 10 Double Stuf Oreos weighed 145 grams
• 10 Triple-Double Oreos weighed 210 grams

I solved the regular/Triple-Double system and concluded that each wafer weighs about 1.7 grams and each unit of stuf is about 8 grams.

Using my new assumption-that Double Stuf is not double stuff and a side calculation (complicated, but interesting) which suggests that Double Stuf is really $1 \frac{5}{12}$ stuff, the solution to the regular/Triple-Double system is consistent with the solution to the regular/Double Stuf system.

And that means the Oreo below is not a duoseptuagenuple stuf Oreo, Doc Blades’ claim notwithstanding. Nope, that bad boy isn’t any better than unopentuagenuple.

Man do I wish I had taken this photograph!

UPDATE: I corrected “vanilla filling” to “chocolate filling” in paragraph 3. Also, further objections (beyond those noted above) have been raised in the Twitterverse. I’ll update these in a new post shortly.

Meantime, y’all know how to comment on a blog, right?

## My Oreo manifesto, part 2

So you read my previous blog entry in which I paid homage to the culinary sleuthing of Al Sicherman and alleged that Double Stuf isn’t really double stuf.

When we left off, we had been working with the assumption (soon to be demonstrated false) that Double Stuf is double stuf. We had learned that a single unit of stuf has about 17 calories and a single wafer has about 19 calories.

Enter the Triple-Double.

Again, we use Nabisco’s own data. One serving Triple Double Oreos has 1 cookie and 100 calories.

Translation: One serving of Triple-Double Oreos is 3 wafers (that’s the triple part), 2 stufs (that’s the double) and 100 calories (that’s the OMG! part).

Comparing the Triple Double to the Double Stuf, we can see that the only difference between one Double Stuf cookie and one Triple-Double cookie is 1 wafer and 30 calories.

What can we conclude? That a wafer has 30 calories. But wait! That’s over 50% more calories than we got under the assumption that a Double Stuf has double stuf. We have reached a contradiction, which means we need to reject our initial assumption.

Double Stuf ain’t double stuf.

QED.

## My Oreo manifesto

Math is powerful.

No one has demonstrated this more frequently and more convincingly than Al Sicherman of the StarTribune. In his Tidbits column, Sicherman keeps tabs on prices and variations of processed foods. A favorite category for him recently has been Oreos. Writing recently on the topic of the new Peppermint Creme Oreos (which he describes as toothpastey), Sicherman says:

All of that is not to say that there is no significant difference between Cool Mint Creme Oreos and Peppermint Creme Oreos: They are the same price on the shelf, but the package of Cool mint Oreos is 15.25 ounces (30 cookies), and that of Peppermint Creme Oreos is 10.5 ounces (20 cookies). So Peppermint Creme Oreos cost 45 percent more per ounce — or 50 percent more per cookie.

Whoomp! There it is! Math, baby!

Gotta love this guy. (But seriously, would it kill the Strib to dispatch a photographer with a camera that has more than 1 megapixel?)

Inspired by his example, I’m prepared to turn up the heat on Nabisco’s Oreo division. Are you ready?

Double Stuf isn’t double stuf.

Let me say that again…DOUBLE STUF IS NOT DOUBLE STUF!

How do I know? Math.

How should we do this? Reductio ad absurdum? Let’s assume it is double stuf. Then, according to Nabisco’s own data (found on the Nutrition Facts), one serving of Oreos is 3 cookies and 160 calories. Double Stuf is 2 cookies and 140 calories.

Let me translate that for you. One serving of regular Oreos has 6 wafers, 3 stufs and 160 calories. Meanwhile one serving of Double Stuf Oreos has 4 wafers, 4 stufs and 140 calories.

That’s hard to compare. So let’s consider two servings of regular Oreos (6 cookies, 12 wafers, 6 stufs, 320 calories) and three servings of Double Stuf (6 cookies, 12 wafers, 12 stufs and 420 calories).

Those Double Stuf Oreos account for 6 additional stufs and 100 additional calories (same number of wafers, remember). We conclude that each stuf is approx. 17 calories. And from this we can conclude that each wafer has approx. 19 calories.

What, you prefer the formal mathematical solution? Fair enough:

Let w be the number calories in a wafer and f be the number of calories in a unit of stuf. Then Nabisco’s calorie claims yield this system of equations:

$\begin{cases} 6w+3f=160 \\ 4w+4f=140 \end{cases}$

We can rewrite this equivalently as:

$\begin{cases} 12w+6f=320 \\ 12w+12f=420 \end{cases}$

And then solving by combination, we get:

$6f=100$ or $f=16 \frac{2}{3}$

You’re comfortable with that. No problem, right?

Tune in tomorrow for the dénouement.