A boy saw a shirt for \$97 but does not have enough cash. So he borrowed \$50 from his mom and another \$50 from his dad.

He bought the shirt, and got back \$3 as change. He gave his dad \$1 and his mom \$1 and kept the other \$1 for himself.

Now mom and dad paid \$50 each and got back \$1 each. So they paid \$49 each, totaling \$98. The boy has another \$1, adding up to \$99. Where is the missing dollar?

The problem is that the question is cleverly phrased to conceal what is really going on.

Let’s locate all that money. There are two ways to think about how much money is out there to be found.The way that this question is tricky is that it combines that two ways.

The first way is this. How much money did mom and dad pay originally?

The second way is this. How much money did they end up paying?

So if it is the first way, then clearly the total we need to account for is the \$100.

So let’s see what happens to that \$100. The shirt costs \$97, the boy keeps \$1 and mom and dad get \$1 back. That adds up fine.

Now let’s look at the second way. How much money did they end up paying? Well \$98 dollars, and \$97 of it went for the shirt and \$1 to the boy. Now, that adds up too.

The problem with the question is that the the \$1 that the boy keeps is contained in the \$98 that they end up paying so we shouldn’t expect them to add to anything meaningful.

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