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

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) (Show Source): You can put this solution on YOUR website!
Let x be the amount of $56 tickets and y being the $38 tickets.

Solved by pluggable solver: System of Equations

We have the system of equations
. 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 Plug this value into either equation to find that .

Answer by MathTherapy(10552) (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 =
Substitute 200 for F in eq (i) to get the value of T, the number of $38 tickets sold.
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