SOLUTION: there are 26 times as many students at Lincoln high school as teachers. When all the teachers and students are seated in the 900 seat school auditorium, only 9 seats are unoccupied

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Question 83365This question is from textbook Algebra: Structure and Method, Book 1
: there are 26 times as many students at Lincoln high school as teachers. When all the teachers and students are seated in the 900 seat school auditorium, only 9 seats are unoccupied. How many students are at Lincoln high? This question is from textbook Algebra: Structure and Method, Book 1

Found 2 solutions by checkley75, bucky:
Answer by checkley75(3666) (Show Source):
You can put this solution on YOUR website!
I BELIEVE YOU HAVE THE WRONG STATEMENT. THE MINIMUM NUMBER OF TEACHERS + STUDENTS IS 1+26=27. HOWEVER YOU STATE THAT THERE ARE ONLY 9 SEATS OCCUPIED.
THESE FIGURES MAKE NO SENSE.

Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website!
If the 900 seat auditorium has only 9 unoccupied seats when all the teachers and students
are seated, that means that the combined population of teachers and students is 900 - 9 = 891
.
Let T equal the number of teachers. The problem tells you that there are 26 times T students.
Add these two amounts together and, according to the problem, the result should be 891.
.
The equation becomes:
.
T + 26*T = 891
.
Combine the two terms on the left side to get:
.
27T = 891
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Solve for T by dividing both sides of the equation by 27, the multiplier of T to get:
.
T = 891/27 = 33
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So now you know that Lincoln high school has 33 teachers. You can solve for the number of
students by either subtracting 33 from the total population of 891 to get 858 students,
or you can multiply 26 times 33 which gives you the same answer of 858 students.
.
Hope this helps you to understand the problem.