Tuesday, May 7, 2013

Crime Doesn't Pay...Especially If You're Bad at Math

I had one of those teachable moments today.

My uncle told me that he had two pick-up trucks filled with aluminum cans. He took them to the recycling center where they were paying $0.56 per pound. He left with $222.

I presented the same problem to my class today. I didn't pose a question...but naturally my students wondered...how many cans is that?

Many took notice that it wasn't solvable. They didn't know the number of cans in a pound. I didn't either, but I had a triple-beam balance and a can. So we weighed it...16 grams for a can.

Next they wanted to know the number of grams in a pound. (They're very annoying.) I didn't know this either, so we googled it...about 453 grams.

We solved the problem, thought about how long it would take to collect all of those cans, how much soda you would have to drink, etc.

When we finished, a student told me how he and his family trick the system....

Jack: We get more money at the recycling center for our cans because we put a penny in each can.

Me: Jack, not only does that sound unethical, but...that doesn't sound right to me. You're making the cans weigh more, but those pennies are valuable. Are you sure that you're really getting more money that way? 

Jack: Yeah, we've been doing it for years.

Me: That doesn't sound right. What if I take one pound of pennies for recycling? No cans...just pennies. Each penny weighs...[googling]...2.5 grams which means there are...[calculating]...181 pennies in a pound. Those pennies are worth $1.81. You just traded them in for $0.56. You just lost...$1.25.

Jack: No no no no. But we put one penny in each can. That changes things. You have to figure it out with the cans.

Me: Are you sure? Ok, let's assume that you put one penny in 181 cans. How much would 181 cans with 181 pennies in them weigh?

Jack: ......6.38 pounds for the cans....1 pound for the pennies...so that's 7.38 pounds.

Me: And how much money are you getting for the 7.38 pounds?

Jack: .....$4.13. You see, I was right. That's more than $1.81.

Me: Yeah...but we're not done yet. You got $4.13, but you lost $1.81 from the pennies. So you are really only making $2.32, right?

Jack: Yeah, so?

Me: What if you didn't put the pennies in the cans? How much money would you have gotten for that?

Jack: ...[calculating].......ok, never mind.

Me: Don't "never mind" me. What did you get?

Jack: (quietly)...$3.57.

Me: Right. So if you put pennies in the cans, you make $2.32. No pennies...$3.57. How long has your family been putting pennies in cans Jack?