Nov 23, 2002
RAY: Let me set the scene. The owner of a record store hires a pimply faced, high-school kid to work on Saturdays.
He says to the kid, "You know what to do. But I got one little extra thing for you. I've got two piles of used 45-PM records that I'm selling for my friend Sam. Each pile consists of 30 records.
"The records in the first pile are two for a buck. The other pile is three for a buck. I don't want you to put the money in the register. I've got to give it to Sam. Put the money into the cigar box under the counter."
At the end of the first day, the owner comes back to the store, finds that all of the records have been sold and there is $25 in the cigar box. The two-for-a-dollar records sold for a total of $15, and the three-for-a-dollar records sold for a total for ten bucks.
Encouraged by the rapid sales, the next week Sam shows up with 60 more records.
The owner gives the kid the same instructions. This time, the kid says, "I noticed last week that people were taking two records from one pile and three records from another pile, so I decided that this week I'm going to sell five for two bucks."
The fellow who owns the record store says, "Seems like a good idea."
At the end of the day, though, the owner opens the cigar box and there's $24 in there. He says, "You're missing a dollar!"
The kid says, "No, I sold all the records."
And that's the question. Where's the missing dollar?
RAY: Here's the answer:
In the record sale in Week #1, the records in the pile marked 2 for $1 were priced at 50 cents each. And the records in the pile marked 3 for $1 were priced at 33.33 cents each.
In the record sale in Week #2, the records were all marked 5 for $2, which averages out to 40 cents per record. And that average price is the problem.
Because if you averaged the price of the records for sale in Week #1, the true average is 41.67 cents.
To make $25 in the record sales in Week #2, the clerk should have priced the records at 5 for $2.08 to reach a total sales figure of $25.