## Subway Tokens

Samantha purchased subway tokens from a machine. The instructions said that, for any amount of money you insert, you would receive the maximum number of tokens your money can purchase, along with your change.

Samantha put a $20 bill into the machine. She received 12 tokens and $2.60 in change.

Apparently the machine hasn’t read the instructions.

I notice that Samantha received 12 tokens and change left over. I wonder how much each token costs?

I noticed that Samantha received 12 tokens and $2.60 left over. I was wondering as to how much one token actual cost. If she only put in $15, I wonder how many tokens she wouldn’t gotten

I notice that Samantha will receive the max amount of tokens and her change for any amount of money she inserts. I noticed that when she put in $20, she received 12 tokens and $2.60. I wonder how much did each token cost? I wonder how long will those 12 tokens last her? I wonder if our subway tokens are cheaper or more expensive than other states subway tokens?

I wonder about making this a more open-ended problem by giving less information.

- What if you were told that Samantha inserted $20 and got $2.60 in change?

- What if she inserted $20 and got 12 tokens?

- What if she got 12 tokens and $2.60 in change, but you weren’t told what she inserted?

What would these discussions look like? How many answers are possible? How many of these are “reasonable”?

BTW, very funny first comment. How many people would read back in the stem of the problem to notice the machine was “broken”?