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Question 928372: The local theater has three types of seats for Broadway plays: main floor, balcony and mezzanine. Main floor tickets are $43, balcony tickets are $35, and mezzanine tickets are $27. On one particular night the sales totaled $45,839. Main floor sales were 71 more than the total of balcony and mezzanine sales. Balcony seats were 303 more than 3 times mezzanine sales. How many of each type of ticket were sold?
Enter the solution below
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! x = number of tickets main
y = number of tickets balcony
z = number of tickets mezzanine
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43x + 35y + 27z = 45839
x = y + z + 71
y = 3z + 303
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put the system of linear equations into standard form
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43x + 35y + 27z = 45839
x - y - z = 71
y - 3z = 303
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copy and paste the above standard form linear equations in to this solver:
https://sooeet.com/math/system-of-linear-equations-solver.php
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solution:
x = number of tickets main = 626
y = number of tickets balcony = 492
z = number of tickets mezzanine = 63
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now by substitution:
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y - 3z = 303
y = 303 + 3z
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x - y - z = 71
x - (303 + 3z) - z = 71
x - 4z = 374
x = 374 + 4z
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43x + 35y + 27z = 45839
43(374 + 4z) + 35(303 + 3z) + 27z = 45839
43*374 + 4*43z + 35*303 + 3*35z + 27z = 45839
(4*43 + 3*35 + 27)z = 45839 - 35*303 - 43*374
z = (45839 - 35*303 - 43*374) / (4*43 + 3*35 + 27)
z = 63
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y = 303 + 3z
y = 303 + 3*63
y = 492
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x = 374 + 4z
x = 374 + 4*63
x = 626
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solution by substitution:
x = number of tickets main = 626
y = number of tickets balcony = 492
z = number of tickets mezzanine = 63
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