The administration has formed a 26 person planning committee. There are 5 times as many administrators as there are students and five more faculty members than students. How many students are there on the committee?
Let a = administrators
Let f = faculty
Let s = students
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a + f + s = 26
5s = a
s+5 = f
solve for s,a,f.
To determine the number of students on the committee, we first need to find the total number of administrators and faculty members.
Let's assume the number of students is "x."
We know that there are 5 times as many administrators as students, so the number of administrators would be 5x.
We also know that there are five more faculty members than students, so the number of faculty members would be x + 5.
Now, to find the total number of people on the committee, we add the number of administrators, faculty members, and students:
Total number of people on the committee = Number of administrators + Number of faculty members + Number of students
= 5x + (x + 5) + x
= 7x + 5
Since the committee has a total of 26 people, we can set up an equation:
7x + 5 = 26
Now, we can solve for x:
7x = 26 - 5
7x = 21
x = 21/7
x = 3
Therefore, there are 3 students on the committee.