Question 1118783
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After reading the condition, you should notice momentarily that half of the orchestra seats costs 18400 - 15600 = 2800 dollars.


Hence, the half of the orchestra seats is {{{2800/40}}} = 70 seats, and the entire number of the orchestra seats is 2*70 = 140.


Thus you just can reduce the original problem to the simpler one:


     There are 700-140 = 560 seats; of them, main seats sell for $25 and balcony seats sell for $20.

     The revenue obtained for main seats and balcony seats is  18400 - 140*40 = 12800 dollars.



You can solve this problem as an two-unknown problem or even as an one-unknown problem, on your choice.


I prefer one-unknown, as it is shown below.


Let x be the number of main seats.

Then the number of balcony seats is  (560-x).


The money equation for this reduced problem is

25x + 20*(560-x) = 12800    dollars.


Simplify and solve for x:


25x + 20*560 - 20x = 12800

25x - 20x = 12800 - 20*560 = 1600

5x = 1600  ====>  x = {{{1600/5}}} = 320.


<U>Answer</U>.  140 orchestra seats, 320 main seats and  (560-320) = 240 balcony seats.
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Solved.