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?

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Tolamaes04 · Accepted Answer

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  yAnother group spends $787 for 2 mezzanine tickets, 7 lower balcony tickets, and 8 middle balcony tickets  2  x  +  7  y  +  8  z  =  787A third group purchases 3 lower balcony tickets and 12 middle balcony tickets for $615.  3  x  +  12  z  =  615    ⇒  z  =            615      −      3      y        12      ⇒  z  =  51.25  −  0.25  yput   x  =  139.5  −  1.5  y  ,     z  =  51.25  −  0.25  y in   2  x  +  7  y  +  8  z  =  787  2  (  139.5  −  1.5  y  )  +  7  y  +  8  (  51.25  −  0.25  y  )  =  787    279  −  3  y  +  7  y  +  410  −  2  y  =  787    2  y  =  98    y  =  49    x  =  139.5  −  1.5  ⋅  49    x  =  66    z  =  51.25  −  0.25  ⋅  49    z  =  39individual price of a mezzanine ticket=66$, a lower balcony ticket=49$, and a middle balcony ticket=39$

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