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A new movie is currently showing at the local movie theater. For the 6:00 pm showing, the theater sold 36 student tickets and 24 adult tickets for a total of $423. The theater sold 41 student tickets and 38 adult tickets for a total of $585.75 for the 8:30 pm showing. If x represents the number of student tickets sold and represents the number of adult tickets sold, which of the following systems of equations correctly models the situation? Group of answer choices

Sagot :

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Answer:

36x + 24y = 423 (1)

41x + 38y = 585.75 (2)

x =$5.25

y = $9.75

Step-by-step explanation:

x = the number of student tickets sold

y = the number of adult tickets sold

36x + 24y = 423 (1)

41x + 38y = 585.75 (2)

Multiply (1) by 38 and (2) by 24

1368x + 912y = 16,074 (3)

984x + 912y = 14,058 (4)

Subtract to eliminate y

1,368x - 984x = 16,074 - 14,058

384x = 2,016

x = 2,016/384

x = 5.25

Substitute x = 5.25 into (1) to find y

36x + 24y = 423

36(5.25) + 24y = 423

189 + 24y = 423

24y = 423 - 189

24y = 234

y = 234/24

y = 9.75

x =$5.25

y = $9.75

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