Question 1198443: A movie theater has a seating capacity of 151. The theater charges $5.00 for children, $7.00 for students, and $12.00 for adults. There are half as many adults as there are children. If the total ticket sales was $ 1084, How many children, students, and adults attended?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52780)   (Show Source):
You can put this solution on YOUR website! .
A movie theater has a seating capacity of 151.
The theater charges $5.00 for children, $7.00 for students, and $12.00 for adults.
There are half as many adults as there are children.
If the total ticket sales was $ 1084, How many children, students, and adults attended?
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x adults, 2x children and the rest (151-x-2x) = (151-3x) are the students.
Write the total money equation
12x + 5*(2x) + 7*(151-3x) = 1084.
Simplify and find x
12x + 10x + 7*151 - 21x = 1084
x = 1084 - 7*151 = 27.
ANSWER. 27 adults, 54 children and the rest 151-27-54 = 70 are students.
Solved.
Three unknown are found using one equation, which is a kind of miracle.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
The statement of the problem is faulty. As stated, there are four different combinations of tickets at the different prices that make the total ticket sales $1084.
Only one of those combinations has tickets sold for all 151 seats in the theater (see solution from the other tutor). But the statement of the problem only tells us the seating capacity of the theater; it doesn't say that tickets were sold for all 151 seats.
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