Question

A concert hall has three sections: the main floor, the balcony, and the gallery. For a recent concert, 1020 tickets were sold. There were twice as many balcony tickets sold as gallery tickets, and 225 more main floor tickets than balcony tickets. If g represents the number of gallery tickets sold, which expressions represents this situation?

Answer 1

Answer:

D. Gallery: g

Balcony: 2g

Main Floor: 2g+225

Step-by-step explanation:

Gallery is g

Balcony had 2 times as many tickets than Gallery so 2•g (2•gallery)

Main floor had 225 more tickets than Balcony so Balcony’s equation plus 225 tickets. 2g + 225

Answer 2

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      $\Rightarrow$  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      $\Rightarrow$ 2.5b  = 795     $\Rightarrow$  b = 318

v) g  = 0.5 b  = 0.5 $\times$ 318 = 159

vi) m = b + 225 = 318 + 225 = 543