Question

You see a shirt for 97 dollars.
You don't have the cash so you borrow 50 bucks from your mom and 50 bucks from your dad,
50+50=100.
So you buy the shirt and you have 3 dollars change.
You give your dad 1 dollar and your mom 1 dollar, and you keep 1 dollar.
Now you owe your mom 49 dollars and your dad 49 dollars. 49+49=98 + your 1 dollar=99 dollars.
Where is the missing 1 dollar?

Answer 1

There is no missing dollar. You're comparing things that shouldn't be compared.

You start with 0 dollars. Get get 100 dollars, and incur 50 dollars of debt from your mom and 50 dollars of debt from your dad. Let's call them D(m) and D(d), respectively.

You have 100 dollars. You spend 97 on a shirt, so you now have 3 dollars. D(m) is still 50 dollars, D(d) is still 50 dollars.

So, you decide to give 1 dollar to mom, and 1 to dad. You have now spent 99 dollars of 100, leaving you with 1 dollar left over.

D(m) is now 49, as is D(d). If you combine them, you are 98 dollars in debt with 2 paid back.

So... in short.. we have two different systems. Cash you have and debt you need to pay back. They are NOT the same, and both balance out well. So, no missing dollar.

$100 - $97 - $1 - $1 = $1 < - Cash you have in person
$100 - $1 - $1 = $98 < - Cash you still owe your parents