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(52778)   (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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