SOLUTION: The local theater has three types of seats for Broadway plays: main floor, balcony, and mezzanine. Main floor tickets are $59, balcony tickets are $49, and mezzanine tickets are

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Question 1167782: The local theater has three types of seats for Broadway plays: main floor, balcony, and mezzanine. Main floor tickets are $59, balcony tickets are $49, and mezzanine tickets are $34. One particular night, sales totaled $106,306. There were 254 more main floor tickets sold than balcony and mezzanine tickets combined. The number of balcony tickets sold is 444 more than 3 times the number of mezzanine tickets sold. How many of each type of ticket were sold?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
f for Main Floor
b for Balcony
m for Mezzanine
-
system%28f-b-m=254%2Cb=3m%2B44%29

f-%28b%29-m=254
f-3m-44-m=254
f-4m=254%2B244
f-4m=498
f=498-4m

Try to fill the table here using only one variable, m.
Then make expressions for the revenue of each seat type. 

                  $/seat              $
TYPE             PRICE     COUNT      REVENUE
Main Floor        59      498-4m     59(498-4m)
Balcony           49      3m+44      49(3m+44)
Mezzanine         34       m         34m
TOTALS                                 106306

You can find the equation to arrange and to solve.

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
The local theater has three types of seats for Broadway plays: main floor, balcony, and mezzanine.
Main floor tickets are $59, balcony tickets are $49, and mezzanine tickets are $34.
One particular night, sales totaled $106,306. There were 254 more main floor tickets sold than balcony and mezzanine tickets combined.
The number of balcony tickets sold is 444 more than 3 times the number of mezzanine tickets sold. How many of each type of ticket were sold?
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            You, probably, will be very surprised, but this problem can be  EASILY  solved

            using one single equation in one unknown,  as I show it below. 


Let x be the number of the mezzanine tickets.

Then, according to the condition, the number of the balcony tickets is (3x + 444),

and the number of the main floor tickets is the sum  (x + (3x + 444)) + 254 = 4x + 698.


Next, you write the total money equation


    59*(4x + 698) + 49*(3x + 444) + 34*x = 106306   dollars.


Now you simply this equation and find x


    (59*4*x + 49*3*3x + 34x) + (59*698 + 49*444) = 106306

    417x                     + 62938             = 106306

    417x                                         = 106306 - 62938 = 43368

       x                                     = 43368/142 = 104.


So, 104 mezzanine tickets were sold;  3*104 + 444 = 756 balcony tickets and 4*104 + 698 = 114 main floor tickets.


It is the ANSWER, so the problem is

Solved.

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This problem is intended for 6th grade students,  who learn solving word problems on a single unknown equations.

The major goal of this  (and similar problems)  is to teach these students to make their setup using only one unknown.
So I teach you accordingly in my post.

There are other ways to solve the problem, but they go OUT the major goal of such assignments.