Final answer:
The total number of students at the college is calculated by dividing 7000, the number of students living in dormitories, by the given fraction (5/9), resulting in 12600 students in total at the college.
Step-by-step explanation:
The question asks us to calculate the total number of students at a college based on the information that five-ninths of them live in dormitories and that there are 7000 students living in dormitories. To find the total number of students, we set up the equation where the fraction of students living in dormitories (five-ninths) multiplied by the total number of students equals 7000. The equation can be formulated as (5/9) * total students = 7000.
To isolate 'total students,' we divide both sides of the equation by (5/9), giving us:
total students = 7000 / (5/9)
total students = 7000 * (9/5)
total students = 12600.
Therefore, there are 12600 students in the college.