Let's take this scenario out of the bowling alley and look at it in real life....
You are getting repairs done to your home.....a "friend" who is a contactor tell you he can do it for you for $300....and the lowest bid you have from any other contractor is $1000, so you ok. Nothing in writing, he is a friend, no need to have it in writing. After about 2-3 weeks of doing the work on the weekends, he comes back and says....well I need to charge you $600 now. Would you agree? Probably because it is still less then the bids you got. But what if he says it will be $1200 or $1500 now?
This is the crux of the matter. Carlos was told/promised something. Was it something he didn't deserve, yes. He only deserved to get paid for the weeks he was there, not a full share. Just like in the sceanrio above where you were trying to get something you didn't deserve, repairs done for less then reasonable wages. If the captain made this claim on his own, he needs to live by it. If that means he pays either Carlos or Bowler B out of his own pocket, so be it. The captain was desparate to make sure they had a bowler so they could remain competitive, I would assume. So he made an offer Carlos could not refuse in order to make sure he would say yes. No matter what is the correct way to handle things, this was the offer he chose to make. Why should he be let out of his offer now? Just like the contractor friend, you would tell them tough, you said you could do it for $300, if it costs you more then that, it's on you, not me.
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Jorge300