The Missing Dollar?

Question

I saw a shirt, which cost $97. I borrowed $50 from mom, and $50 from dad. I bought the shirt, with $3 of change.

I gave $1 back to mom, $1 back to dad, and kept the other $1 myself.

Now this means I owe my mom $49 and my dad the same, $49 – since I borrowed $50 from and gave back $1 to, each of them.

$49 + $49 = $98
$98 + my $1 = $99

Wait!! Where did the other $1 go??

Solution

This is a classic.

The last equation 98 + 1 = 99 means this “in words”:

“money which I still owe toward mom & dad” + “money remaining in my pocket”

Which equals to

“initial borrowed money resultantly”

“This money” was “used” equivalently like this:

“initial money borrowed from mom & dad” – “part of this money which is not returned back to them”
= 100 – 1
= 99

So, in other words, the “fault” is to “think” (being misled by the numbers cleverly chosen for this infamous example) that “98 + 1” must equal “initial borrowed amount” which need “not” be so because:

Consider, “98 + 1” in “words”:

It’s equivalent to “part of initial borrowed money used to buy shirt (97) and 1 dollar change in my pocket + 1”, that is the last “1” is “simply added” and does “not” refer to the 1 dollar change in your pocket.