math equation

Question

a stadium has 50,000 seats. Seats sell for $30in Section A, $24 in Section B, and $18 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 $1,285,800 from each sold-out event. How many seats does each section hold?

Answer 1

Let number of seats in section A = a

Let number of seats in section B = b

Let number of seats in section C = c

 

Set up a system of equations.

 

a + b + c = 50000                           eq1   ---->  total number of seats in stadium

30a + 24b + 18c = 1285800             eq2   ---->  total cost

a = b + c                                         eq3   ---->  seats comparable

 

We can use substitution/elimination method to solve for a, b, and c.

 

Substitute eq3 into eq1 and eq2.  This will get those equations in terms of only b and c.

 

b + c + b + c = 50000

2b + 2c = 50000                    eq1

 

30(b + c) + 24b + 18c = 1285800

54b + 48c = 1285800                            eq2 

 

 

Then multiply bolded eq1 by 27.   Keep bolded eq2.

 

54b + 54c = 1350000               eq1

54b + 48c = 1285800                eq2

 

 

Next, subtract bolded eq2 from bolded eq1 to eliminate the b terms.  You will get an equation that you solve for c.  Once you have your value of c, substitute it into bolded eq1 to solve for b.  After you have the values of b and c, substitute those into eq3 to solve for a.