Question 83365
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
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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.
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The equation becomes:
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T + 26*T = 891
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Combine the two terms on the left side to get:
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27T = 891
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Solve for T by dividing both sides of the equation by 27, the multiplier of T to get:
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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.
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Hope this helps you to understand the problem.