A movie theater complex is being built to have 24 new theaters. A total of 5,550 seats will be in the entire complex. Small theaters will have 175 seats each and large theaters will have 325 seats each. Determine how many small and large theaters are being built in the complex.

Question

Mathematics

Guest

20 January, 06:08

A movie theater complex is being built to have 24 new theaters. A total of 5,550 seats will be in the entire complex. Small theaters will have 175 seats each and large theaters will have 325 seats each. Determine how many small and large theaters are being built in the complex.

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Answers (1)

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Pooky · Answer 1

The correct answer is that 15 small and 9 large theaters are being built in the complex.

Step-by-step explanation:

1. Let's review the information that was given to us to answer the question correctly:

Number of new theaters = 24

Number of new seats = 5,550

Number of seats of small theaters = 175

Number of seats of large theaters = 325

2. Determine how many small and large theaters are being built in the complex.

Number of small theaters = x

Number of large theaters = y

System of equations

x + y = 24

175x + 325y = 5,550

Solving for x

x + y = 24

x = 24 - y

Solving for y

175x + 325y = 5,550

175 (24 - y) + 325y = 5,550

4,200 - 175y + 325y = 5,550

150y = 5,550 - 4,200

150y = 1,350

y = 1,350/150

y = 9 ⇒ x = 15

The correct answer is that 15 small and 9 large theaters are being built in the complex.

Note: Same answer to question 14178551, answered by me today.