Consideration and Intention problem

Can you help me answer the following problem contract law question using the IRAC method and quoting any relevant case studies please?

Arthur's daughter, Belinda, aged 21, was studying for some accountancy exams at Ademup College. It was a contractual requirement that students in residence at the College were non-smokers, and Belinda therefore gave up smoking. Arthur, however, was worried that under the pressure of preparing for exams Belinda would start smoking again, and so he promised to pay her 200 if she did not smoke at all until she had completed the course. Arthur runs a small business, and asked Belinda to prepare a short report for him on the taxation of companies. He was very pleased with the result and promised to give her 250 'for all her hard work'. Belinda passed her examinations and has not started smoking again. Arthur has not made either of the promised payments. He seeks your advice as to whether he is legally obliged to do so.

Please note this for my individual research and learning purposes only.