Nash Frank

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?

Tolamaes04

Expert

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
$4x+6y=558\phantom{\rule{0ex}{0ex}}⇒x=\left(558-6y\right)4\phantom{\rule{0ex}{0ex}}⇒x=139.5-1.5y$
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.
$3x+12z=615\phantom{\rule{0ex}{0ex}}⇒z=\frac{615-3y}{12}\phantom{\rule{0ex}{0ex}}⇒z=51.25-0.25y$
put in $2x+7y+8z=787$
$2\left(139.5-1.5y\right)+7y+8\left(51.25-0.25y\right)=787\phantom{\rule{0ex}{0ex}}279-3y+7y+410-2y=787\phantom{\rule{0ex}{0ex}}2y=98\phantom{\rule{0ex}{0ex}}y=49\phantom{\rule{0ex}{0ex}}x=139.5-1.5\cdot 49\phantom{\rule{0ex}{0ex}}x=66\phantom{\rule{0ex}{0ex}}z=51.25-0.25\cdot 49\phantom{\rule{0ex}{0ex}}z=39$individual price of a mezzanine ticket=66$, a lower balcony ticket=49$, and a middle balcony ticket=39\$

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