SOLUTION: A stadium has 48,000 seats. Seats sell for $28 in section A, $16 section B, $12 section C. The numbers of seats in section A equals the total number of seats in section B and C. Su

Question 1101033: A stadium has 48,000 seats. Seats sell for $28 in section A, $16 section B, $12 section C. The numbers of seats in section A equals the total number of seats in section B and C. Suppose the stadium takes $1,016,800 from each sold-out event. How many seats does each section hold?
Answer by ikleyn(52785) (Show Source): You can put this solution on YOUR website!
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A stadium has 48,000 seats. Seats sell for $28 in section A, $16 section B, $12 section C.
The numbers of seats in section A equals the total number of seats in section B and C. Suppose the stadium takes $1,016,800
from each sold-out event. How many seats does each section hold?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Let x be the number of seats in section B, and y be the number of seats in section C.


Then the number of seats in section A is x+y, the sum of seats in sections B and C, according to the condition.


The condition says

seatsA + seatsB + seatsC = 48000,   or

(x+y)  + x      + y      = 48000,   which is the same as

2(x+y) = 48000,                     which implies

x + y =  = 24000.


Thus we found that the sum of seats in sections B and C is 24000,  

and, therefore, the number of seats in section A is 24000.


Thus we have now the problem  FOR TWO UNKNOWNS only, since we just excluded A.

Now our system of two equations is

  x +   y = 24000,                  (1)
16x + 12y = 1016800 - 28*24000.     (2)   


Equation (2) express the money payed for seats in sections B and C together.


Simplify (1),(2) step by step:

  x +   y = 24000,                  (3)
16x + 12y = 344800.                 (4)


Multiply eq(1) by 16 (both sides). Then subtract eq(2) from it:

16x + 16y = 384000,                 (3)
16x + 12y = 344800.                 (4)
-------------------------

====> 4y = 384000-344800 = 39200  ====>  y =  = 9800.


Then  x = 24000 - y = 24000 - 9800 = 14200.


Answer.  There are 24000 sears in section A,  14200 in section B  and  9800 in section C.

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