The Fabulous Fox Theater in St. Louis, Missouri, offers several levels of seating, among them...

Nash Frank

Nash Frank

Answered

2022-07-27

The Fabulous Fox Theater in St. Louis, Missouri, offers several levels of seating, among them mezzanine, lower balcony, and middle balcony. One group of patrons buys 4 mezzanine tickets and 6 lower balcony tickets for dollar-sign 558 point Another group spends $787 for 2 mezzanine tickets, 7 lower balcony tickets, and 8 middle balcony tickets. A third group purchases 3 lower balcony tickets and 12 middle balcony tickets for $615. What is the individual price of a mezzanine ticket, a lower balcony ticket, and a middle balcony ticket?

Answer & Explanation

Tolamaes04

Tolamaes04

Expert

2022-07-28Added 12 answers

let cost of mezzanine ticket =x , cost of lower balcony ticket =y , cost of middle balcony =z ,
given One group of patrons buys 4 mezzanine tickets and 6 lower balcony tickets for dollar-sign 558 point
4 x + 6 y = 558 x = ( 558 6 y ) 4 x = 139.5 1.5 y
Another group spends $787 for 2 mezzanine tickets, 7 lower balcony tickets, and 8 middle balcony tickets
2 x + 7 y + 8 z = 787
A third group purchases 3 lower balcony tickets and 12 middle balcony tickets for $615.
3 x + 12 z = 615 z = 615 3 y 12 z = 51.25 0.25 y
put x = 139.5 1.5 y ,   z = 51.25 0.25 y in 2 x + 7 y + 8 z = 787
2 ( 139.5 1.5 y ) + 7 y + 8 ( 51.25 0.25 y ) = 787 279 3 y + 7 y + 410 2 y = 787 2 y = 98 y = 49 x = 139.5 1.5 49 x = 66 z = 51.25 0.25 49 z = 39individual price of a mezzanine ticket=66$, a lower balcony ticket=49$, and a middle balcony ticket=39$

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