The Fabulous Fox Theater in St. Louis, Missouri, offers several levels of seatin

Question

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?

Explanation / 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

4x+6y =558

=>x=(558-6y)4

=>x=139.5 -1.5y

Another group spends $787 for 2 mezzanine tickets, 7 lower balcony tickets, and 8 middle balcony tickets

2x+7y+8z=787

A third group purchases 3 lower balcony tickets and 12 middle balcony tickets for $615.

3y+12z=615

=>z =(615-3y)/12

=>z =51.25-0.25y

put x=139.5 -1.5y ,z =51.25-0.25y in 2x+7y+8z=787

2(139.5 -1.5y)+7y+8(51.25-0.25y)=787

279 -3y+7y+410-2y=787

2y=98

y=49

x=139.5 -1.5*49

x=66

z =51.25-0.25*49

z=39

individual price of a mezzanine ticket=66$, a lower balcony ticket=49$, and a middle balcony ticket=39$

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