There is a rack of 11 billiard balls. Balls numbered 1 through 8 are solid-colored. Balls numbered 9 through 11 contain stripes
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Answer:
Let the number of balcony seats be b
Let the number of gallery tickets be g
Let the number of main floor tickets be m
b + g + m = 1020
b = 2g
m = b + 225
The number of balcony tickets = 318
The number of gallery tickets = 159
The number of main floor tickets = 543
Step-by-step explanation:
Let the number of balcony seats be b
Let the number of gallery tickets be g
Let the number of main floor tickets be m
i) Therefore we can write b + g + m = 1020
ii) there were twice as many balcony tickets sold as gallery tickets
therefore b = 2g g = 0.5b
iii) there were 225 more main floor tickets than balcony tickets
therefore m = b + 225
iv) using equation ii) and equation iii) in equation i) we can write
b + g + m = b + 0.5b + b + 225 = 1020 2.5b = 795
b = 318
v) g = 0.5 b = 0.5 318 = 159
vi) m = b + 225 = 318 + 225 = 543