Question 1102773
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Let *[tex \Large x] represent the number of orchestra tickets and let *[tex \Large y] represent the number of balcony tickets.

The total number of tickets is 360, so *[tex \Large x\ +\ y\ =\ 360].

The total value of the orchestra tickets is *[tex \Large 45x] dollars and the total value of the balcony tickets is *[tex \Large 35y] dollars.  So the total box office take must be the sum of the value of the orchestra tickets and the value of the balcony tickets, to wit: *[tex \Large 45x\ +\ 35y\ =\ 15150]


You now have a 2 X 2 system of equations that can be solved by either substitution or elimination.


Alternatively, you could have recognized that if *[tex \Large x] is the number of orchestra tickets, then the number of balcony tickets must be *[tex \Large 360\ -\ x], and since orchestra tickets are worth $45 and balcony tickets are worth $35, the total value of all the tickets must be *[tex \Large 45x\ +\ 35(360\ -\ x)\ =\ 15150].


All that is necessary is to solve for *[tex \Large x] and then calculate *[tex \Large 360\ -\ x]


You might want to compare this alternative method to the substitution method of solving the 2X2 system.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
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