Question

a stadium has 53,000 seats. seats sell for $42 in section A, $36 in section B, and $30 in section C. the number of seats in section A equals the total number of seats in sections B and C. supposed the stadium takes in $1,997,400 from each sold -out event. how many seats does each section hold? Section A holds 26500 seats, how many does section B hold of seats?

Answer 1

The number of seats that section B holds is: 14900

How to solve simultaneous equation word problems?

We are told that:

The stadium has 53,000 seats.

Seats sell for $42 in section A, $36 in section B, and $30 in section C.

the number of seats in section A equals the total number of seats in sections B and C.

The stadium takes in $1,997,400 from each sold -out event.

Thus, the simultaneous equations formed are:

A + B + C = 53000 ------(1)

A = B + C -------(2)

42A + 36B + 30C = 1997400 -----(3)

Plug in A for B + C in equation 1 to get:

A + A = 53000

2A = 53000

A = 53000/2

A = 26500

Thus:

B + C = 26500 ----(4)

Divide eq 3 by 6 to get:

7A + 6B + 5C = 332,900 ---(5)

Put 26500 for A in eq 5to get:

7(26500) + 6B + 5C = 332,900

185500 + 6B + 5C = 332900

6B + 5C = 332900 - 185500

6B + 5C = 147400 -----(6)

Solving eq 4 and 6 simultaneously gives:

B = 14900

C = 11600