Acquiring mathematical literacy requires students to apply mathematics in various real-world contexts. However, mathematics classes often provide brief, content-focused descriptions of reality-based tasks and tasks that describe the situation as more complex, closer to reality, are still lacking. Students with different sociodemographic characteristics and cognitive factors have difficulties in solving reality-based tasks in mathematics lessons. The relationship between sociodemographic characteristics and cognitive factors (language and mathematical competence) concerning complex situation descriptions has not yet been investigated. To identify disadvantaged students in integrating such complex-situation tasks in mathematics lessons, this study aims to investigate which sociodemographic characteristics predict the solving of complex-situation tasks and whether cognitive factors mediate the relationship. Experts created 30 complex situations with different mathematical questions. A total of 519 9th- and 10th-grade students participated in a paper–pencil test. Path analysis revealed that the competence to solve complex-situation tasks is directly linked to gender and social background, with mathematical content-related skills and language competence mediating this relationship.