SOLUTION: A ballet company sells 540 tickets for its upcoming performance of Swan Lake. Tickets for the orchestra center and front balcony seats are $56. Tickets for the left and right orche

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Question 1135486: A ballet company sells 540 tickets for its upcoming performance of Swan Lake. Tickets for the orchestra center and front balcony seats are $56. Tickets for the left and right orchestra and balcony seats are $38. The company has sold $24,120 in tickets. How many $56 and $38 seats were sold?
Found 2 solutions by Shin123, MathTherapy:
Answer by Shin123(626) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the amount of $56 tickets and y being the $38 tickets.
system%28x%2By=540%2C56x%2B38y=24120%29
Solved by pluggable solver: System of Equations

We have the system of equations
system%281+x%2B1+y=540%2C56+x%2B38+y=24120%29. Solving the 2 equations for y gets you
y= -(1) x+(540)
y=-(1.47368421052632) x+(634.736842105263) So -(1) x+(540)=-(1.47368421052632) x+(634.736842105263). 0.473684210526316 x+ 540=634.736842105263 0.473684210526316 x=94.7368421052631 highlight%28x=200%29 Plug this value into either equation to find that highlight%28y=340%29.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
A ballet company sells 540 tickets for its upcoming performance of Swan Lake. Tickets for the orchestra center and front balcony seats are $56. Tickets for the left and right orchestra and balcony seats are $38. The company has sold $24,120 in tickets. How many $56 and $38 seats were sold?
PLUGGABLE SOLVER is usually one of the MOST INEFFICIENT "tools" to solve a system of equations. It also makes the simplest problem very COMPLEX, and so I would NEVER recommend using it.

Plus, look at the other person's response using this "TOOL." Can you really learn anything from it? I think NOT!!



Let the number of $56 tickets sold be F, and the number of $38 tickets, T

We then get: F + T = 540 ------- eq (i)

Also, 56F + 38T = 24,120 ------- eq (ii)

- 38F - 38T = - 20,520 --------- Multiplying eq (i) by - 38 ------ eq (iii)

18F = 3,600 ------ Adding eqs (iii) & (ii)

F, or number of $56 tickets sold = highlight_green%28matrix%281%2C3%2C+%223%2C600%22%2F18%2C+%22=%22%2C+200%29%29

Substitute 200 for F in eq (i) to get the value of T, the number of $38 tickets sold.