SOLUTION: There were 480 people at a play. The admission price was $3 for adults and $1 for children. The admission receipts were $840. How many adults and how many children attended?

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Question 1162627: There were 480 people at a play. The admission price was $3 for adults and $1 for children. The admission receipts were $840. How many adults and how many children attended?
Found 2 solutions by ikleyn, math_helper:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

x adults and (480-x) children.


The revenue equation is


    3x + 1*(480-x) = 840   dollars.


From the equation,  


    3x - x = 840 - 480


    2x     = 360

     x     = 360/2 = 180.


ANSWER.  180 adults, and the rest  480 - 180 = 300 children.


CHECK.   180*3 + 300*1 = 840  dollars.   ! Precisely correct !

Solved.

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It is a standard tickets problem.

There are different methods of solving such problems.
In this site, there are lessons
    - Using systems of equations to solve problems on tickets
    - Three methods for solving standard (typical) problems on tickets
explaining and showing all basic methods of solving such problems.

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 lesson is 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.



Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!




A + C = 480    ("... 480 people at a play") ... attendance equation

3A + C = 840   ("The admission receipts wer $840") ... money equation



Subtract the top equation from the bottom one, solve for A then plug in to either equation and solve for C.  Check you answer...