SOLUTION: A movie theater has a seating capacity of 315. 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

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Question 1130098: A movie theater has a seating capacity of 315. 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 $ 2282, How many children, students, and adults attended?
Answer by ikleyn(52832)   (Show Source): You can put this solution on YOUR website!
.
Let x be the number of adults.


Then the number of children is 2x, according to the condition,
and the number of students is the rest (315-x-2x) = (315-3x).


The "money" equation (the revenue equation) is


    12x + 5*(2x) + 7*(315-3x) = 2282.


    12x + 10x + 7*315 - 21x = 2282

    x = 2282 - 7*315 = 77  is the number od adults.


ANSWER.  77 adults;  2*77 = 154 children and the rest (315-77-154) = 84 students.

Solved.

The lesson to learn from the solution is THIS : 

     This problem is to be solved using ONE unknown - not three.


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