Christopher M. answered 11/02/22
Professional Law School Tutor - Legal Writing and Doctrinal 1L Courses
The legal doctrine applicable to this question is the mailbox rule. The mailbox rule pertains to the timing of acceptance. The mailbox rule states that acceptance by mail or similar means is effective at the moment of dispatch. In other words, the acceptance is effective as soon as the offeree places his acceptance in the mail.
In your question, the offeree properly accepted the offer to buy the product when he sent a letter accepting the offer. Therefore, the valid contract is for sale of the product at $100 and any subsequent acceptance does not matter.