They bought 8 orchestra seats and 6 mezzanine seats.
Step-by-step explanation:
Cost of one orchestra seat = $42
Cost of one mezzanine seat = $25
No. of people = 14
Amount spent = $486
Let,
x be the number of orchestra seats
y be the number of mezzanine seats
According to given statement;
x+y=14 Eqn 1
42x+25y=486 Eqn 2
Multiplying 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 method
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