Question

A movie theater has a seating capacity of 225. 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 $

1622, How many children, students, and adults attended?

Answer 1

Based on the information, there were 94 children, 47 adults and 84 students.

Let there be x number of children, y number of students and x/2 number of adults. Forming the first equation based on number of students -

x + y + x/2 = 225 : Equation 1

Multiply equation 1 with 2

2x + 2y + x = 450 : Equation 2

3x + 2y = 450 : Equation 3

y = (450 - 3x)/2 : Equation 4

Forming second equation based on cost -

5x + 7y + 12x/2 = 1622 : Equation 5

Rewriting this equation

5x + 7y + 6x = 1622 : Equation 6

11x + 7y = 1622 : Equation 7

Keep the value of y from equation 4 in equation 7

11x + 7(450 - 3x)/2 = 1622

11x + (3150 - 21x)/2 = 1622

22x + 3150 - 21x = 3244

x = 3244 - 3150

x = 94

Keep the value of x in equation 4

y = (450 - 3×94)/2

y = (450 - 282)/2

y = 168/2

y = 84

Number of adults = 94/2

Number of adults = 47

Thus, there were 94 children, 47 adults and 84 students.

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