Question 1114919
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<pre>
It is not a rational way to solve this problem using system of equations.


Since the problem asks for only ONE unknown ("the number of student tickets"), it is much more reasonable, simple and straightforward way 
to solve it using a single equation for only one unknown x, which is the number of student tickets.


The equation is 

3x  + 5*(584-x) = 2112.


3x + 5*584 - 5x = 2112

-2x = 2112 - 5*584 = -808  ====>  x = {{{(-808)/(-2)}}} = 404.


<U>Answer</U>.  The number of student tickets sold is 404.
</pre>

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It is a standard ticket problem.


Read the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/Using-systems-of-equations-to-solve-problems-on-Tickets.lesson>Using systems of equations to solve problems on tickets</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/Three-methods-for-solving-standard-typical-problem-on-tickets.lesson>Three methods for solving standard (typical) problems on tickets</A>

in this site.


Learn from these lessons on how to solve such problems once for all.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


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