Question

Tickets for a concert cost $35 for balcony seats and $75 for floor seats. Tickets at the same venue for a theatrical production cost $25 for balcony seats and $60 for floor seats. If tickets for all the seats are sold, the venue generates $27,750 in revenue for a concert and $21,750 for a theatrical production. Which system of equations can be used to find the number of floor seats and balcony seats in the theater? 35 x 75 y = 21,750. 25 x 60 y = 27,750. 35 x 75 y = 27,750. 25 x 60 y = 21,750. 75 x 35 y = 27,750. 25 x 60 y = 21,750. 75 x 35 y = 21,750. 25 x 60 y = 27,750.

Answer 1

The capacity of seats at a venue has to be determined by putting the data in an equation.

Given:

Price of balcony seat for a concert is $35

Price of floor seat for a concert is $75

Price of balcony seat for a theatrical production is $25

Price of floor seat for a theatrical production is $60

Revenue of concert at full capacity is $27,750

Revenue of theatrical production at full capacity is $21,750

Equation

By putting the data of a concert and the data of a theatrical production in the equation to found that the equation as follows:

35 x 75 y = 27,750. 25 x 60 y = 21,750.

Elaborating further, the data given for the concert at full occupancy is balcony seat $35 and floor seat $75 which generates the revenue of $27,750, is matching completely with the first part of equation.

Similarly, the data given for a theatrical production at full occupancy is balcony seat $25 and floor seat $60 which generates the revenue of $21,750, is matching completely with the second part of equation.

Hence the system of equations which can be  used to find the number of floor seats and balcony seats of the venue is OPTION B is correct i.e. 35 x 75 y = 27,750. 25 x 60 y = 21,750.

Learn more about the equations here:

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Answer 2

Answer:

35b+75f=27750  

25b+60f=21750

Explanation:

I hope this can help you out!