To determine which supporting detail best supports the central idea, we need to know what the central idea is. However, among the provided options, each response covers different aspects of a person's experience, likely related to challenges, determination, and personal preferences in a shelter environment.
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"Along the way, we stumbled and we started struggling as a family," she says. - This detail emphasizes family struggles, potentially supporting a central idea about the challenges of family life or homelessness.
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"Among the many frustrations of shelter life are long security checks and noise." - This focuses on the negative aspects of living in a shelter, supporting an idea about the difficulties faced in such environments.
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"I just know when I have a goal, I try not to let anything get in the way, she says." - This highlights determination and perseverance, which could support a central idea about striving for personal goals despite obstacles.
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"I try to stay out as late as possible," she says. "I would say it's my favorite place." - This suggests a personal perspective on the shelter, perhaps indicating comfort or avoidance of issues within.
If the central idea revolves around perseverance and determination in the face of struggles, then the third option ("I just know when I have a goal, I try not to let anything get in the way, she says.") would likely best support that idea. If it focuses more on the struggles of shelter life, the second option would be stronger.
Ultimately, the best supporting detail depends on the specific central idea being analyzed.