## Archive for September 20, 2012

### Stolen Truck Solution

Last week, I posted a modified version of Marilyn Burn’s horse problem, and I asked you to submit your answers. I received 331 responses; thanks for participating! An analysis of the submitted responses appears below, but first, a few comments and several different solutions.

My friend Jeane Joyner of Meredith College uses this problem in teacher and parent workshops. She said:

I have folks move to corners of the room — makes money, loses money, and breaks even. Then each groups selects an ambassador to go to the other groups to see if they can persuade folks to move. Fun!

Without further adieu, here is the answer: **The man made $200.**

**Solution #1:** He spent 600 + 800 = $1,400, and he received 700 + 900 = $1,600. That’s a profit of $200.

**Solution #2:** Assume the man started with $1,000 in his bank account. He bought the truck for $600, so he had $400 left. He then sold it for $700, so his account increased to $1,100. He bought it back for $800, so he had $300 left. When he sold it for $900, his account increased to $1,200. Since he started with $1,000 and ended with $1,200, he made a profit of $200.

**Solution #3:** Use a number line to show how his amount of money changed.

After the four transactions, he is at +200 on the number line, so he made a profit of $200.

**Solution #4:** Some people find it confusing that he buys and sells the truck twice. It might be easier to think of him doing these transactions with two different vehicles. For instance, what if he bought a truck for $600 then sold it for $700, and then bought a car for $800 and sold it for $900? It might be easier to wrap your head around that.

Approached that way, his actions represent two separate events. The first time he bought and sold the truck, he paid $600 and sold it for $700. That’s a profit of $100. The second time, he bought it for $800 and sold it for $900. That’s another $100 profit. In total, he made $200.

After I posted the problem, a friend on Facebook asked, “Huh? How is that supposed to be hard?” Edward Early of St. Edwards College responded:

Sadly, I’ll only be surprised if there is a strong consensus for the correct answer. I’ve been teaching math too long to expect that to happen.

Of the 331 respondents, only 325 submitted usable responses. (Chalk this up to bad phrasing on my part. I asked folks to “enter a negative number if he lost money, 0 if he broke even, or a positive number if he made money.” I was meaning for people to enter the amount he lost or made, but some respondents entered a positive number that wasn’t possible in the context of the problem, such as 1 or 12. I think they thought they should enter *any* positive number to indicate that he made a profit. And one wiseacre responded, “a positive number.” Sorry, not even partial credit for that response!)

Of the 325 usable responses, 228 (70.1%) were correct. Answers from the other 28.9% ranged from ‑600 to 900, with 0 (28 responses) and 100 (47 responses) chosen most often. The chart below shows the distribution of incorrect responses. (Data for 200 has been removed since it overwhelms the others; its bar would be more than four times the height of the next highest bar.)

The vast majority of respondents (276) were 16 years of age or older. The 49 responses from people age 15 or younger looked like this:

Age | Responses | Correct Responses |

6 | 1 | 0 |

7 | 1 | 1 |

8 | 2 | 1 |

9 | 4 | 1 |

10 | 4 | 1 |

11 | 1 | 1 |

12 | 4 | 3 |

13 | 15 | 11 |

14 | 8 | 7 |

15 | 9 | 7 |

Interestingly, the under‑16 crowd, with 67.3% correct responses, did almost as well as the over‑16 crowd, which had 70.6% correct responses. And for the 11- to 15‑year old subset, an astounding 78.4% of the responses were correct.

From this, we can conclude that these youngsters are smarter than the rest of the population… but of course we already knew that, because teens and pre-teens know *everything*, right?