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You want to buy a shirt that costs $97. To buy the shirt, you borrow $50 from your mom and $50 from your dad. You now have $100.

You buy the shirt and get $3 in change. You give $1 to your mom, $1 to your dad, and you keep the last $1 for yourself.

Now you owe your mom $49 and your dad $49.

$49 + $49 + $1 (the dollar you kept) = $99.

Where did the last dollar go?

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There is no missing dollar. First of all, don't consider how in debt he is of his parents. Think of it like this: the store has $97, and they each have $1 at the end. That's it - no debt calculation needed.

Now like this: you took $100 and now you need to pay back $100. You give $1 to each parent. Now you have $98 to give back. You owe $49 to each so $49*2 = $98. You owed $100 and you paid them back $2 and now you owe $98. The $49*2 + $1 math is wrong.

For example, if you had not given you parents any change back (you had kept the $3), then you would owe your parents $50 each. Would you say $50 * 2 + $3 = $103? No - that doesn't makes no sense.

To you parents, you took $98 to spend (shirt for $97 and $1 for yourself). What you do with the $1 is irrelevant and so is the fact that you have it; it's all about what you owe if we're calculating it like this. Ok now $98 to spend out of $100 and you give them the change ($2). So you owe $98 at this point (not $100). Now you owe $49 to each. $49 * 2 = 98. Or, $98 / 2 = $49 each.

If you add what you owe and what you paid towards what you owe, its ($49 * 2 + $1 * 2 = $100), where the $100 is what you owed at the start.
The general equation would be: initial money owed = current money owed + money paid towards initial money owed.

So the problem is that the $1 is irrelevant in $49 * 2 + $1. It's supposed to be $49 * 2 = $98 where $98 is what you owe and what you spent.