document.write( "Question 1132189: A movie theater has a seating capacity of 383. 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 $ 2778, How many children, students, and adults attended? \n" ); document.write( "

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A movie theater has a seating capacity of 383. 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 $ 2778, How many children, students, and adults attended?
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Let number of students and adults be S, and A, respectively
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document.write( "Then number of children = 2A
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document.write( "We then get: S + A + 2A = 383 =====> S + 3A = 383 =====> S = 383 - 3A ------- eq (i)
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document.write( "Also, 5(2A) + 7S + 12A = 2,778 ------- eq (ii)
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document.write( "5(2A) + 7(383 - 3A) + 12A = 2,778 ------- Substituting 383 - 3A for S in eq (ii)
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document.write( "10A + 2,681 - 21A + 12A = 2,778
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document.write( "10A - 21A + 12A = 2,778 - 2,681
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document.write( "A, or number of adults = 
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document.write( "Number of children: 
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document.write( "Number of students:  \n" );
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