Linear Systems: 3 Variables

Question

A stadium has 52,400 seats. Seats sell for $40 in section A, $20 in section B, and for $15 in section C. The number of seats in section A equals the sum of the number of seats in sections B and C. For each sold-out event, the stadium takes in $1,510,500. How many seats does each section hold?

Answer 1

A=B+C

40A+20B+15C=1510500

A+B+C=52,400

A-B-C= 0, add to get

2A =52,400

A =52,400/2 = 26,200 seats for A section

B+C = A = 26,200

B=26200-C

40(26,200) + 20(26200-C) +15C = 1,510,500

1,048,000 + 524,000-20C + 15C = 1,510,500

5C =1,572,000-1,510,500 = 61,500

C =61,500/5 = 12,300 seats for C section

B = 26,200-12,300 = 13,900 seats for B section