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 :)