38. Where Did the Extra Dollar Go?
I want to buy a pair of shoes that I think costs $50, so I borrow $25 from my mom and $25 from my dad—$50 in total.
When I get to the store I discover the shoes are on sale for $45, so I buy them and receive $5 change. I give $3 of that change to a friend who asked to borrow it, leaving me with $2.
I use those $2 to pay back $1 to my mom and $1 to my dad. Now I still owe them $24 each.
Here is the seeming paradox:
- I owe my parents $24 + $24 = $48.
- My friend has $3.
$48 + $3 = $51, yet I only ever had $50. Where did the extra dollar come from?
Added 17 December 2012
Hint: Be careful what you add. Debts should be compared with the money that remains unaccounted for, not with money that is in someone else’s hands.
Solution:
The $3 your friend now holds is part of the $48 you still owe. The correct accounting is:
- You owe your parents a total of $48.
- You possess no cash.
- Of the $48 you owe, $45 is represented by the shoes you bought, and $3 is with your friend.
$45 (shoes) + $3 (friend) = $48, exactly matching the debt. Adding $48 (debt) to $3 (friend’s money) counts the same $3 twice, creating the false total of $51. There is no missing or extra dollar—just a misleading addition.
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