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Hello:

The dorm charges $6300 for 35 students for 24 days. In how many days will the dorm charges be $3375 for 25 students?

I think it is 18 days.

Here is an answer and solution:

6300 dollars/(35 students × 24 days) = 6300 dollars/(840 student days) = 7.50 dollars/(student day)

3375 dollars/(25 students) × 1 student day/(7.50 dollars) = 18 days

25 students will be charged $3375 for 18 days.

Can you explain the development of the above calculation? For example, why divide 6300 dollars by 35 students X 24 days and so forth.

What is the reasoning used for determining the answer as is shown in the calculation?

The simplest approach is to determine the unit rate, i.e., how much is charged one student for one day.

The charge is 7.50 dollars/(student-day), so 25 students are charged 25×7.50 = 187.50 dollars per day.

3375 dollars × 1 day/(187.50 dollars) = 18 days

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