Alan buys shoes from Barbara with a public account. Barbara sent Allen a $10,000 bill. Allen replied that the 200 pairs of shoes were defective, and offered to pay $6,000 and give Barbara his promissory note at a price of $1,000. Barbara accepted the offer, and Alan sent his check for $6,000 and his bill in accordance with the agreement. Barbara cashed the check and charged it on the bill, and sued Allen for $3,000 a month later. Is Barbara bound by her acceptance of the offer? please explain.