Question 1030371
The local theater has three types of seats for Broadway plays: main floor, balcony, and mezzanine. Main floor tickets are $54, balcony tickets are $46, and mezzanine tickets are $41. One particular night, sales totaled $106,263. There were 482 more main floor tickets sold than balcony and mezzanine tickets combined. The number of balcony tickets sold is 198 more than 3 times the number of mezzanine tickets sold. How many of each type of ticket were sold? 
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Equations:
54m + 46b + 41z = 106,263
m = b + z + 482
b = 3z + 198
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Substitute for "b" to get m = 4z + 680
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Substitute for m and b and solve for "z"::
54(4z+680) + 46(3z+198) + 41z = 106263
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216z + 36720 + 138z + 9108 + 41z = 106263
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395z + 45828 = 106263
395z = 60435
z = 153 (# of mezzanine sold)
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Solve for "b" and for "m" using z = 153
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Cheers,
Stan H.
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