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 faculty paid$25 per person

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Question 1145257: 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 faculty paid$25 per person for entrance. If the total paid, for all 100 people, was $1300, how many students attended the museum opening?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39616)   (Show Source): You can put this solution on YOUR website!

therefore for easier calculation, T for number of faculty (teachers), and for number of students.

---------solve for T. Evaluate .
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.

            It can be solved MENTALLY, without using equation/equations. 


Let assume for a minute that all 100 bought tickets were student tickets.

Then the total would be 100*10 = 1000 dollars.


But it was 1300 dollars.  


The shortage of 1300 - 1000 = 300 dollars is due to the assumption that all tickets were student tickets.


Hence, we should correct our assumption, by replacing some of 100 tickets (that we assumed to be student tickets)

by faculty tickets.


Each replacement diminishes the shortage of 300 dollars by (25-10) = 15 dollars.

Hence, we should replace  300/15 = 20 tickets.


It means that there were 20 faculty tickets and 100-20 = 80 student tickets.



CHECK.  80*10 + 20*25 = 800 + 500 = 1300 dollars.   ! Correct !


Completed.

---------------

It is a standard tickets problem.

There are different methods of solving such problems.
Read the lessons
    - Using systems of equations to solve problems on tickets
    - Three methods for solving standard (typical) problems on tickets
in this site.

From these lessons,  learn on how to solve such problems once and for all.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Systems of two linear equations in two unknowns".

Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.


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