Final answer:
Without the ratio of students to trees planted, it's not possible to determine the number of trees 14 students can plant or the number of students needed to plant 270 trees. This mathematical problem requires additional context or given ratios to provide accurate answers.
Step-by-step explanation:
Understanding Linear Relationships and Ratios
The question presented relates to the concept of ratios and proportionality within the subject of mathematics. If the problem stated that each student plants exactly the same number of trees, this would establish a direct linear relationship between the number of students and the number of trees planted. In say scenario, if the ratio of students to trees planted is constant, knowing this ratio is crucial for solving both parts of the question.
Without additional information, in particular the ratio of students to trees, we cannot provide a concrete answer. For the first part, we would need to know how many trees one student, or all 14 students collectively, can plant. As for the second part, provided the ratio, we can set up a proportion to find the number of students needed for 270 trees.
However, based on the given context where the concern is about seats in a campus restaurant and class enrollments, it doesn't bear direct relevance to the number of trees planted by students. Therefore, more context is needed to accurately determine the number of trees planted by 14 students or the number of students needed to plant 270 trees.