Recently presented Large Language Models (LLM) exhibit problem-solving capabilities that can be exploited in educational settings. This paper explores the utilization of LLMs in constructing virtual agents capable of emulating student behavior and engaging with learning platforms. The results obtained by using a modest-sized LLM on an Intelligent Tutoring System for the teaching and learning of word problem-solving validate the feasibility of the approach and its potential applicability to other systems with limited computational resources. In our particular case, the efficacy of the implemented agent in solving word problems varied according to the complexity level of the task, as happens with human users. Success rates ranged from 92% for single-step problems to 14% for relatively complex problems. The potential applications of the presented approach are diverse. They extend from crafting collaborative learning settings in which individual students engage with other synthetic counterparts, to serving as invaluable tools for enhancing teacher training programs.