SOLUTION: A group of 100 people, some students and some faculty, attended a museum opening. Each student paid $10 per person for entrance to the museum and each of the faculty paid $25 per p
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-> SOLUTION: A group of 100 people, some students and some faculty, attended a museum opening. Each student paid $10 per person for entrance to the museum and each of the faculty paid $25 per p
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Question 803073: A group of 100 people, some students and some faculty, attended a museum opening. Each student paid $10 per person for entrance to the museum and each of the faculty paid $25 per person for entrance. If the total paid, for all 100 people, was $1300, how many students attended the museum opening? Answer by homeworkhedgehog(9) (Show Source):
You can put this solution on YOUR website! This is a system of equations problem, meaning that you need two equations to solve for two variables (number of students, number of faculty).
The situation is $10 x (the number of students) + $25 x (the number of faculty) = $1300 total
If we use variables, we get
The other equation we need is a bit simpler but a little more hidden in the question:
There are only two types of people (students, faculty) attending and we know the total is 100, so our equation is
From here, we can use Elimination or Substitution to solve for the number of students, s.
We'll use substitution:
If we solve
for f by subtracting s from both sides, we get
Now we can plug f back into the other equation and solve for s:
; Distribute 25 ; Combine "like" terms ; Subtract 2500 from both sides ; Divide both sides by -15
So we find out that there are 80 students.
You can check your answers by realizing that since there are 80 students out of 100, the other 20 must be faculty.
Plug s = 80 and f = 20 into your original equation of
to get
=
=
And it checks out.
