A stadium has 55,000 seats. Seats sell for $28 in Section A, $16 in Section B, and $12 in Section C. The number of seats in Section A equals the total number of seats in Sections B and C. Suppose the stadium takes in $1,158,000 from each sold-out event. How many seats does each section hold?

Question

Mathematics

Arianna

24 April, 20:43

A stadium has 55,000 seats. Seats sell for $28 in Section A, $16 in Section B, and $12 in Section C. The number of seats in Section A equals the total number of seats in Sections B and C. Suppose the stadium takes in $1,158,000 from each sold-out event. How many seats does each section hold?

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Answers (1)

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Rodgers · Answer 1

A=number of seats in section A

B=number of seats in section B

C=number of seats in section C

We can suggest this system of equations:

A+B+C=55,000

A=B+C ⇒A-B-C=0

28A+16B+12C=1,158,000

We solve this system of equations by Gauss Method.

1 1 1 55,000

1 - 1 - 1 0

28 16 12 1,158,000

1 1 1 55,000

0 - 2 - 2 - 55,000 (R₂-R₁)

0 12 16 382,000 (28R₁-R₂)

1 1 1 55,000

0 - 2 - 2 - 55,000

0 0 4 52,000 (6R₂+R₃)

Therefore:

4C=52,000

C=52,000/4

C=13,000

-2B-2 (13,000) = - 55,000

-2B-26,000=-55,000

-2B=-55,000+26,000

-2B=-29,000

B=-29,000 / - 2

B=14,500.

A + 14,500+13,000=55,000

A+27,500=55,000

A=55,000-27,500

A=27,500.

Answer: there are 27,500 seats in section A, 14,500 seats in section B and 13,000 seats in section C.