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There were 8000 tickets sold for the Uaap championship. The tickets were 150 for the bleachers, 300 for the upper box and 500 for the lower box. The number of bleacher tickets sold was three times the number of th lower box tickets sold. If the total amount collected was 2150000, how many of each type of ticket were sold?

Sagot :

ANSWER:

The number of tickets sold per seat type:
Lower box = 1,000 tickets
Bleacher = 3,000 tickets
Upper box = 4,000 tickets

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SOLUTION:
Total: 8,000 tickets.
Number of tickets per seat type:
Lower box = x
Bleacher = 3x
Upper Box = y  or 8,000 - 4x

               x + 3x + y = 8,000
               4x + y = 8,000
               y = 8,000 - 4x

Ticket prices:
Lower box: 500 (x)  or 500x
Bleacher: 150 (3x) or 450x
Upper: 300 (8,000 - 4x) or 2,400,000-1,200x

Equation:

500x + 450x + 2,400,000 - 1200x = 2,150,00
950x - 1,200x = 2,150.000
- 250x = -250,000
-250x/-250 = -250,000/-250
x = 1,000

Substitute 1,000 to x in:
y = 8,000 - 4 (1,000)
y = 8,000 - 4,000
y = 4,000
 
Substitute values of x and y to number of tickets:
Lower box: x                       = 1,000 tickets
Bleacher: 3x = 3 (1,000)     = 3,000 tickets
Upper box: y                       = 4, 000 tickets

Ticket Prices:
Lower box: 500 (1,000)         =    500,000
Bleacher: 150 (3,000)           =    450,000
Upper box: 300 (4,000)        = 1,200,000
 
TOTAL TICKET SALES      =  2,150,000


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