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(39616) (Show Source): Answer by ikleyn(52776) (Show Source):
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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.
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