## Friday, March 30, 2012

### A Pawn Stars Puzzle

My 12-year old son recently became a fan of the Pawn Stars TV show.  I have been trying to decide for a while what I think about this show. It is a Las Vegas Pawn Shop, run by three generations: an aging, cursing, revengeful dad; nice encyclopedically knowledgeable, cursing son, and a heavy, tattooed, Harley Davidson-riding, cursing grandson.  Just as I was about to tease our son for watching this strange thing, my dad (who is frequently with us helping me with the new baby) fell into the traps of the show too. What can I say. It is informative,  fast paced and the objects traded are very cool. So, here it is: a Pawn Stars Puzzle created in collaboration with my son.

A woman got the following objects at the Brentwood Estate Sale: a 16th century beheading sword and a diamond encrusted Rolex. A few months later she needed money and drove to the TV-featured Pawn Shop to trade these objects. She got \$5,000 for each. On one of them she lost 15% as compared with the price she got it for, on the another she gained 15%.  Did she get even in this whole buy-and-sell adventure, or did she lose or gain money?

Your answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.

James said...

She spent 5000/.85 +5000/1.15 = 10,230.18 while buying. But she has got only 10000 while selling.

Tom said...

x = price paid for first item
y = price paid for second item

x - .15X = 5000
0.85x = 5000
x = 5000 / .85 = \$5882 approx lost \$882 on first item

y + .15y = 5000
1.15y = 5000
y = 5000 / 1.15 = 4347 approx gain 652 on second item

ratna srinivas said...

she lost 2.3%

Annie said...

She lost money.

For the item where she gained 15%, 1.15x = \$5000. She paid roughly \$4348. for it and made \$652.

For the item where she lost 15%, .85x = \$5000. She paid about \$5882. and lost \$882.

Total loss was \$882. - \$652. = \$230.

Ilya said...

Original prices paid are 5K/.85 and 5K/1.15. Simplified fractions give us 5K*(20/17 + 20/23) = 5K*800/391, which comes out to more than 5K*2, which means she lost some money as a result.

She came out ahead in her deal. One item must have been worth \$5,882.35, but she got 15% less than full value meaning she missed out on 5882.35 - 5000 = \$882.35. The other item must have been worth \$4347.83, but this time she got 15% more than full value meaning she got 5000 - 4347.83 = \$652.17 extra. Combining these we see that her items were valued at 882.35 - 652.17 = \$230.18 more than they were really worth. She gained money.

If you wanna get fancy, you can write it up in one expression,
(5000/.85 - 5000) - (5000 - 5000/1.15) = \$230.18

Jerome said...

My guess is that she broke even.

It would go something like this.

0.85x + 1.15x = 2x

In this case x = 5000 dollars. She paid 5000 for each item to begin with, so she must have gone 750 up on one of them and the same amount down on the other. She spent 10000 on both and got 10000 back.

Jerome said...

I misread the question -- not an uncommon thing for me to do.

These guys aren't in business to do anyone any favors.

The one she lost 15% is set up like this.
0.85*x = 5000
x = 5882.35

The one she gained 15% is set up like this
1.15 y = 5000
y = 4347.83

x + y = 10230.18

She lost 230.18 dollars.

Anonymous said...

its 2.3% loss

TracyZ said...

The woman lost money overall on the purchases.

Woman bought two items at an estate sale
Estate sale price of the 1st item: x
Trade value at the pawn shop: 0.85x = \$5000

Estate sale price of the 2nd item: y
Trade value at the pawn shop: 1.15y = \$5000

Question:
Is \$10,000 > x + y (she gained \$ at the pawn shop) or \$10,000 < x + y (she lost \$)

x = \$5000/0.85 ---> x = ~\$5,882.35
y = \$5000/1.15 ---> y = ~\$4,347.83

x + y = ~\$10,230.18

\$10,000 < \$10,230.18 ---> she lost \$

Maria said...

Yes, she did lose about \$230 or 2.3% of the \$1,000 she got. The 15% gain/loss is a known shopping trick. The percentage is the same (15%) but it is taken from a larger number when it is a loss and applied to a smaller number when it is a gain (to result in \$1,000). Therefore, loss is larger than the gain. Puzzle point for everyone who answered: James. Tom, ratna srinivas, Annie, Ilya, Thad, Jerome and TracyZ.

Anonymous said...

FYI, you don't need to do all the math to get the answer (the question was loose, gain, or break even, not by how much).

From reading the question, she lost 15% of an amount greater than \$5000, while only gaining 15% of an amount less than \$5000 - therefore she lost money.

Jerome said...

The questions we generally get here require that we prove what we say. These are math questions, not multiple choice.