use elimination to solve. For a production of sweeney Todd in Las Vegas, orchestra seats cost $42 and mezzanine seats cost $25. If a group of 14 people show up and spend a total of $486, how many of each kind of seat did they buy? please help!​

Accepted Solution

They bought 8 orchestra seats and 6 mezzanine seats.Step-by-step explanation:Cost of one orchestra seat = $42Cost of one mezzanine seat = $25No. of people = 14Amount spent = $486Let, x be the number of orchestra seatsy be the number of mezzanine seatsAccording to given statement;x+y=14     Eqn 142x+25y=486    Eqn 2Multiplying Eqn 1 by 25;[tex]25(x+y=14)\\25x+25y=350\ \ \ \ Eqn\ 3[/tex]Subtracting Eqn 3 from Eqn 2 to eliminate y;[tex](42x+25y)-(25x+25y)=486-350\\42x+25y-25x-25y=136\\17x=136[/tex]Dividing both sides by 17[tex]\frac{17x}{17}=\frac{136}{17}\\x=8[/tex]Putting x=8 in Eqn 1[tex]8+y=14\\y=14-8\\y=6[/tex]They bought 8 orchestra seats and 6 mezzanine seats.Keywords: linear equation, elimination methodLearn more about elimination method at:brainly.com/question/11258952brainly.com/question/11343416#LearnwithBrainly