The local theater has three types of seats for broadway plays: main floor, balcony, and mezzanine. main floor tickets are $50, balcony tickets are $46, and mezzanine tickets are $35. one particular night, sales totaled $57,644. there were 19 more main floor tickets sold than balcony and mezzanine tickets combined. the number of balcony tickets sold is 101 more than 3 times the number of mezzanine tickets sold. how many of each type of ticket were sold?

Lets suppose total numbers of main floor tickets : A

total balcony ticket : B

total mezzanine ticket : C

main floor tickets are $50, balcony tickets are $46, and mezzanine tickets are $35

50 A + 46 B + 35 C = 57644 Equation (1)

there were 19 more main floor tickets sold than balcony and mezzanine tickets combined, means

A= B + C + 19 Equation (2)

the number of balcony tickets sold is 101 more than 3 times the number of mezzanine tickets sold, means

B = 3 C + 101 Equation (3)

Putting the value of B from equation 3 in (1 ) & (2)

50 A + 46 (3 C + 101 ) + 35 C = 57644

50 A + 138 C + 4646 + 35 C = 57644

50 A + 173 C = 52998 (4)

A = 3 C + 101 + C + 19

A = 4 C + 120 (5)

Putting the value of A from equation (5) in equation (4)

50 (4 C + 120) + 173 C = 52998

200 C + 6000 + 173 C = 52998

373 C = 46998

C = 126

A = 4C + 120 = 4 * 126 + 120 = 624

A = 624

B = 3 C + 101 = 3 * 126 + 101 = 479

B = 479

Hence each tickets : main floor = 624, balcony = 479, mezzanine = 126 : Answer

Hope it will help :)

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