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shandrablue6896
14.07.2019 •
Mathematics
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?
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Ответ:
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 :)
Ответ:
See explanations below
Step-by-step explanation:
Given the equation 6x - 9 = 45
Step 1; Add 9 to both sides based on addition property of equality
6x - 9 + 9 = 45 + 9
6x = 54
Step 2: Divide both sides by 5 based on division property of equality
6x/6 = 54/6
Step 3: Simply the result (Simplification)
x = 9