Question

A stadium has 51,000 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 $1,078,400 from each sold-out event. How many seats does each section hold?

Answer 1

A: 25,500

B: 14,600

C: 10,900

Explanation:

This is what we know:

a = b + c

a + b + c = 51,000 Substitute in a for b + c

a + a = 51000 Combine like terms.

2a = 51000 Divide both sides by 2

a = 25,500

28a + 16b + 12c = 1078400 Substitute in 25.600 for a

28(25500) + 16b + 12c = 1078400

714000 + 16b + 12c = 1078400 Subtract 714000 from both sides

16b + 12 c = 364400

25500 +b + c = 51000 Subtract 25500 from both sides

b + c + = 25500 Multiply this equation all the way through by -12 and add it to the bold equation above it.

-12b -12c = -306000

16b + 12c = 364400

4b = 58400 divide both sides by 4

b = 14600

a + b + c = 51000 Plug in what we know

25500 + 14600 + c = 51000

40100 + c = 51000 Subtract 40100 from both sides

c = 10900