## Tuesday, December 8, 2009

You buy a cell phone and after some time decide to sell it on eBay for \$24. Interestingly, in this deal the percent that you loose is equal to the original price of the cell phone. What was the original price of this cell phone?
This puzzle is almost 300 years old and was invented by a French mathematician Étienne Bézout. Cell phones were not invented back then, so he substituted them with horses :)

Please explain your answer on our Family Puzzle Marathon site. Solve three puzzles and get a prize!

Kim said...

\$40 or \$60.

We know o * (1-o/100)=24.
We can rearrange that to be
o-(o^2)/100-24
or
O^2/100-O+24=0
this becomes o^2-100o+2400=0
(0-60)*(o-40)=0
So 0=60 or 40

Maria said...

Very creative way of defining the unknown as "o"
instead of the usual "x" or "y" or "z"!
Looks less intimidating.

Here is where Kim's first equation came from:
o - was the original price of the cell phone;
o also happens to be the percentage we lost in this sale;
If the percentage we lost is something like 5%, then in dollars it will be: original price x 5 / 100.
In our case it is: o x 5 / 100.
Even more precisely: o x o / 100, as we just assumed it is 5%.

Therefore: original price - loss = \$24
o - o x o / 100 = 24
o (1 - o/100) = 24

Kim is doing great!

Kim said...

Using "o" was definitely a mistake! When I hand wrote my notes on the paper in front of me I used a script "o" and I certainly didn't mean it to look like a zero when I typed it. Sorry if I created any confusion, but I'm glad you thought it was creative! :-)

Anonymous said...

Just so you know, and I'm aware that you're not the "English Mom", but you meant "lose" where you typed "loose".