SOLUTION: Please help me and show steps. I have did this question 10 times and still comes up with the wrong answers. Thanks A movie theater has a seating capacity of 333. The theater cha

Question 1001637: Please help me and show steps. I have did this question 10 times and still comes up with the wrong answers. Thanks
A movie theater has a seating capacity of 333. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 2422, How many children, students, and adults attended?
These are the answers I got.
children 144
students 120
adults 69
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
The seating capacity but no given total number of attendees suggests this includes an inequality.

c children, s students, a adults;
----Half as many adults as children;

Account for ticket sales:
and then sub for a:

Account for seating capacity:
and subst for a:

You have two algebraic statements in the unknown variables c and s. You COULD be looking for a solution for c, s, a, which is an inequality, or a set of combinations of these variables. You might simply try to use both statements as equations assuming capacity was full.

Maybe work with ticket sales equation this way:

-
Now you MIGHT want to try to graph this system of statements and look for the whole number solution values for s and c:

My guess, without having tried fully yet, is that your desired points (c,s) might be ON the line; maybe, just maybe, the intersection might work, but ...?

You would want a solution which is ON THE line in order to be consistent with ticket sales.
Answer by MathTherapy(10555) (Show Source): You can put this solution on YOUR website!
Please help me and show steps. I have did this question 10 times and still comes up with the wrong answers. Thanks
A movie theater has a seating capacity of 333. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 2422, How many children, students, and adults attended?
These are the answers I got.
children 144
students 120
adults 69

Sorry! Your answers are incorrect, and so is the person's who tried to help you, whatever that answer may be!
Number of children:
Number of students:
Number of adults:
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