Cheerful Charlie and the Cupcakes

My good friend Cheerful Charlie, I told the third and fourth graders, was having a party, at which he planned to serve cupcakes. One hundred cupcakes, to be precise. I'm not sure who-all is on his guest list (other than me, of course), but he's either inviting a lot of people, or a few big eaters, or else he just wants a lot of leftovers.

Cheerful had (wisely) decided not to make these cupcakes from scratch (his measuring skills aren't what you would call real accurate), but was having some trouble determining which store he should go to. He had three choices, I explained, and he wanted to spend as little money as he could and get as good a deal as possible, and if the students could advise him that'd be great.

So, there was Cupcakes R Us, I told the kids, which sold baskets of 50 cupcakes at a shot, and each basket cost $40 but he also had to pay a fee of $5 to park.

And there was Cupcake Depot, where cupcakes were $9 per bag for a bag of 10, plus which Cheerful had a coupon for $5 off his total purchase.

And there was Cupcake's Discount Warehouse...

Look at all the information, I told them, and do some calculations if you need to, and decide if there are other considerations Cheerful should be thinking about, and then write Cheerful a letter suggesting what he ought to do. The students could turn in a handwritten letter which we'd forward on to Mr. Charlie, I explained, or they could email him directly at cheerful.charlie@yahoo.com, an account which he checks but not as regularly as he should because he often forgets or mistypes the password.

For some students, the assignment was just a relatively straightforward problem in arithmetic. You determine how many bags, boxes, or baskets of cupcakes Cheerful needs to buy at each store so he has 100 cupcakes in all; you multiply that number by the cost per box/bag/bucket/basket; you add the parking fee or membership fee, you subtract the coupon...and if you've done it right, you inform Cheerful that the cost at all three stores is the same, eighty-five bucks, and he can go wherever he likes and it doesn't make any difference. And this is a fine way of looking at it.

But what makes the problem interesting is the real-world nature of it. Sure, price is important. But is the lowest price always the best deal? I remember when my wife and I discovered WHY generic spaghetti sauce was so cheap (hint: it contained mostly water)... So the question becomes, what other things should Cheerful be taking into account?

Well, a lot of kids came up with lots of ideas.

"You should go to Cupcake's Discount Warehouse," one student wrote. The membership fee of $5 was annoying, she pointed out, "but if you have to go back again you will have your membership card so it'll be cheaper."

"Maybe you can walk to Cupcakes R Us," said somebody else. "Or ride a bike. Then you might not have to pay to park." (Note the "might." Hedging your bets, we call it.)

"It depends," wrote another student. "How far away are the stores?" A good question. If the nearest Cupcakes R Us outlet is in Albany, Scranton, or Paramus, it isn't worth the time and the gas to get there.

"You should ask them each for a free sample," suggested one optimist. "If you say you'll buy a lot they'll probably let you have one. Buy the one that tastes best." Not much point in saving five dollars if the cheaper cupcakes tasted like sawdust or carbon paper. --Or were made primarily of water, like the generic spaghetti sauce referred to above.

"Buy them in bags of 10," someone else advised. "The prices are all the same but if you need more then you only have to buy 10 more, not 20 or 25 or 50, and that will save you money."

And another student went right to the heart of the matter: Measure the cupcakes. "Buy the ones that are biggest," he suggested.

Unfortunately, Cheerful (who likes things simple) is still uncertain what to do: he's definitely bummed at the prospect of needing to find more information. We'll keep you posted. In the meantime, it was nice to see how many students recognized that there might be other considerations besides the cost of the cupcakes. We like to remind kids that math is about real-world situations, and in particular we like to point out that answers may not be as cut and dried as the textbooks sometimes suggest they are. This was a good example of both--and a good example of how a little knowledge can be a dangerous thing.

(Though regarding "other considerations," you CAN have too much of a good thing: see one of my favorite cartoons of all time, http://xkcd.com/309/. --Cut and paste the URL into your browser window if the link doesn't work for you. The two folks on the extreme right? That would be me and my wife...)