SOLUTION: The manager of a theater wants to know whether the majority of its patrons are adults or children. One​ day, 5300 tickets were sold and the receipts totaled ​$38,794. The adult

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Question 1143765: The manager of a theater wants to know whether the majority of its patrons are adults or children. One​ day, 5300 tickets were sold and the receipts totaled ​$38,794. The adult admission is ​$8.50​, and the​ children's admission is ​$6.50. How many adult patrons were​ there?
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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Let a be the number of adults.  

Then the number of children is (5300-a).


You have this "money" equation (revenue)


    8.50a + 6.50*(5300 - a) = 38794.


From the equation,


    a = %2838794+-+6.50%2A5300%29%2F%288.50-6.50%29 = 2172.


ANSWER.  2172 adults.


CHECK.  8.50*2172 + 6.50*(5300-2172) = 38794 dollars.   ! Correct !

Solved.

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It is a standard ticket problem.

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 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.