I went back to my old high school last night to attend the final concert of the choir director that presided over so many of my formative moments. I got to hang out with some of the same people with whom I used to have the kind of deep, meaning-of-life conversations that only happen in movies or in real life when you’re between the ages of 15 and 17. A good number of them are teachers now, as it turns out. Their students are lucky to have them.

I went back with a few of the people who helped make me into me, to honor a man who helped shape all of us. I saw a fantastic concert. I had a lot of hugs and handshakes. I found a plaque that still has my name on it. And then I drove home listening to a record I listened to a lot back then. Now I’m sitting in my apartment back in New York, wistful and weary. HOLD ON TO THESE MOMENTS WITH BOTH HANDS. DRINK FULLY AND RICHLY FROM THE CUP OF YOUTH. AND RETURN FOR SECONDS.

Anyway, here’s a challenge question! First correct response gets a free copy of the Math Guide.

Louis and Rebecca each had x dollars on Monday morning. On Monday afternoon Louis paid Rebecca 20% of his money for a computer that she was selling. On Tuesday morning, Rebecca paid Louis 20% of her money for a lawnmower that he was selling. On Wednesday morning, both Louis and Rebecca paid 20% of their money to Steven for…something. I don’t know. Steven was selling something. Assuming they did not spend or receive any other money in that period, how much money did Steven receive, in total, from Louis and Rebecca in terms of x?

Leave your answers in the comments. I’ll post a solution on Monday (assuming someone gets it by then).

In order to win a book, you must not comment anonymously. I need to be able to get in touch with you to get your shipping info, etc. Also, while you can still win a free book if you don’t live in the US, you’re going to have to pay for shipping. So the book is only sorta free if you’re international.

Good luck!

UPDATE: Congratulations to Jason, who nailed it with alarming speed, and to whom a Math Guide will be en route. Solution below the cut.

There’s a fast way to do this problem, and then there’s a very fast way to do this problem. I’m gonna give you both.

First, the fast way. Plug in. Say x = 100. Here’s how the money flows:

Day and time Louis Rebecca Steven
Monday morning $100 $100
Monday afternoon $80 $120
Tuesday morning $104 $96
Wednesday morning $83.2 $76.8 $20.80+$19.20=$40

$40 is 40% of x (which, as you’ll recall, we said was 100), so the answer is 40% of x, or 0.4x.

As you look at the table, you might notice that each row adds up to $200. Interesting, no? Which brings us to the very fast way to do the question. Regardless of the money that changes hands between Louis and Rebecca, the total amount of money they have together never changes. So we can just, from the get-go, say that the amount of money that gets handed to Steven is 20% of the total money Louis and Rebecca begin with.

They start with, in total, 2x dollars. 20% of 2x is 0.4x.

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