SOLUTION: A movie theater has a seating capacity of 287. 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 1150052: A movie theater has a seating capacity of 287. 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 $ 2072 on a sold out night, how many children, students, and adults attended?
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

Let x be the number of adults.

Then the number of children is 2x  and the number of students is (287-x-2x) = 287 - 3x.


Now you can write the equation for total money


    5*(2x) + 7*(287-3x) + 12*x = 2072.


Simplify and solve for x


     10x + 7*287 - 21x + 12x = 2072

       x                     = 2072 - 7*287 = 63.


ANSWER.  63 adults, 2*63 = 126 children and  287-63-126 = 98 students.

Solved.

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The lesson to learn from my solution is THIS : 

    This problem is to be solved using one equation and one unknown.


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