document.write( "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?
\n" ); document.write( "Enter the solution below \n" ); document.write( "
Algebra.Com's Answer #563597 by TimothyLamb(4379)\"\" \"About 
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x = number of tickets main
\n" ); document.write( "y = number of tickets balcony
\n" ); document.write( "z = number of tickets mezzanine
\n" ); document.write( "---
\n" ); document.write( "43x + 35y + 27z = 45839
\n" ); document.write( "x = y + z + 71
\n" ); document.write( "y = 3z + 303
\n" ); document.write( "---
\n" ); document.write( "put the system of linear equations into standard form
\n" ); document.write( "---
\n" ); document.write( "43x + 35y + 27z = 45839
\n" ); document.write( "x - y - z = 71
\n" ); document.write( "y - 3z = 303
\n" ); document.write( "---
\n" ); document.write( "copy and paste the above standard form linear equations in to this solver:
\n" ); document.write( "https://sooeet.com/math/system-of-linear-equations-solver.php
\n" ); document.write( "---
\n" ); document.write( "solution:
\n" ); document.write( "x = number of tickets main = 626
\n" ); document.write( "y = number of tickets balcony = 492
\n" ); document.write( "z = number of tickets mezzanine = 63
\n" ); document.write( "---
\n" ); document.write( "now by substitution:
\n" ); document.write( "---
\n" ); document.write( "y - 3z = 303
\n" ); document.write( "y = 303 + 3z
\n" ); document.write( "---
\n" ); document.write( "x - y - z = 71
\n" ); document.write( "x - (303 + 3z) - z = 71
\n" ); document.write( "x - 4z = 374
\n" ); document.write( "x = 374 + 4z
\n" ); document.write( "---
\n" ); document.write( "43x + 35y + 27z = 45839
\n" ); document.write( "43(374 + 4z) + 35(303 + 3z) + 27z = 45839
\n" ); document.write( "43*374 + 4*43z + 35*303 + 3*35z + 27z = 45839
\n" ); document.write( "(4*43 + 3*35 + 27)z = 45839 - 35*303 - 43*374
\n" ); document.write( "z = (45839 - 35*303 - 43*374) / (4*43 + 3*35 + 27)
\n" ); document.write( "z = 63
\n" ); document.write( "---
\n" ); document.write( "y = 303 + 3z
\n" ); document.write( "y = 303 + 3*63
\n" ); document.write( "y = 492
\n" ); document.write( "---
\n" ); document.write( "x = 374 + 4z
\n" ); document.write( "x = 374 + 4*63
\n" ); document.write( "x = 626
\n" ); document.write( "---
\n" ); document.write( "solution by substitution:
\n" ); document.write( "x = number of tickets main = 626
\n" ); document.write( "y = number of tickets balcony = 492
\n" ); document.write( "z = number of tickets mezzanine = 63
\n" ); document.write( "---
\n" ); document.write( "Solve and graph linear equations:
\n" ); document.write( "https://sooeet.com/math/linear-equation-solver.php
\n" ); document.write( "---
\n" ); document.write( "Solve quadratic equations, quadratic formula:
\n" ); document.write( "https://sooeet.com/math/quadratic-formula-solver.php
\n" ); document.write( "---
\n" ); document.write( "Solve systems of linear equations up to 6-equations 6-variables:
\n" ); document.write( "https://sooeet.com/math/system-of-linear-equations-solver.php \n" ); document.write( "
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