Final answer:
The scenario with Sarah's family aligns with Elder's life course principle of linked lives, illustrating the interconnectedness and mutual influence of family members' paths.
Step-by-step explanation:
The scenario with Sarah and her younger sister, Diana, best represents Elder's life course principle of linked lives. This principle suggests that the lives of family members are interconnected and what happens to one member affects others.
In the case provided, Diana's illness and the subsequent financial decisions made by the parents to afford her experimental treatment directly impact Sarah's opportunity to attend university. The choices and life paths of one family member are inextricably linked to and influence the others, demonstrating the principle of linked lives.