SOLUTION: 584 tickets have been sold for the schools play. An adult ticket costs $5 and a student ticket costs $3. The total ticket sales are $2112. Use a system of equations to solve for th

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Question 1114919: 584 tickets have been sold for the schools play. An adult ticket costs $5 and a student ticket costs $3. The total ticket sales are $2112. Use a system of equations to solve for the number of student tickets that have been sold to the play.
Found 2 solutions by ikleyn, addingup:
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
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 =  = 404.


Answer.  The number of student tickets sold is 404.

----------------
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.

Learn from these lessons 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".


Answer by addingup(3677)   (Show Source): You can put this solution on YOUR website!
To solve as a system of equations:
Equation for the number of tickets sold:
a + s = 584
multiply all elements in this equation times 5:
5a + 5s = 2920 (1)
Equation for the total $ tickets sold:
5a + 3s = 2112 subtract this equation from (1):
----------------------------------------------------------
5a + 5s = 2920
-
5a + 3s = 2112
--------------
0a + 2s = 808
rewrite, since the value of a is 0:
2s = 808
s = 404
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