194 children, 92 students, and 97 adults attended
Step-by-step explanation:
The given is:
We need to find how many children,
students, and adults attended
Assume that x represents the number of children, y represents the number of students, and z represents the number of adults
∵ There were x children, y students and z adult attended
∵ The movie theater has a seating capacity of 383
∴ x + y + z = 383 ⇒ (1)
∵ The theater charges $5 for children, $7 for students, and
$12 for adults
∵ The total ticket sales was $2778
∴ 5x + 7y + 12z = 2778 ⇒ (2)
∵ There are half as many adults as there are children
- Half means 0.5
∴ z = 0.5x ⇒ (3)
Substitute equation (3) in equations (1) and (2)
∵ x + y + 0.5x = 383
- Add like terms
∴ 1.5x + y = 383 ⇒ (4)
∵ 5x + 7y + 12(0.5x) = 2778
∴ 5x + 7y + 6x = 2778
- Add like terms
∴ 11x + 7y = 2778 ⇒ (5)
Let us solve equations (4) and (5) to find x and y
Multiply equation (4) by -7 to eliminate y
∴ -10.5x - 7y = -2681 ⇒ (6)
- Add equations (5) and (6)
∴ 0.5x = 97
- Divide both sides by 0.5
∴ x = 194
Substitute the value of x in equations (4) and (3) to find y and z
∵ 1.5(194) + y = 383
∴ 291 + y = 383
- Subtract 291 from both sides
∴ y = 92
∵ z = 0.5 (194)
∴ z = 97
194 children, 92 students, and 97 adults attended
Learn more:
You can learn more about the system of linear equations in brainly.com/question/6075514
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