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

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): You can put this solution on YOUR website!
f for Main Floor
b for Balcony
m for Mezzanine
-

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(52776)   (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?
~~~~~~~~~~~~~~~~

            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.

------------------

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.

RELATED QUESTIONS
The local theater has three types of seats for Broadway plays: main floor, balcony, and... (answered by TimothyLamb)
The local theater has three types of seats for Broadway plays: main floor, balcony and... (answered by stanbon)
The local theater has three types of seats for Broadway plays: main floor, balcony, and... (answered by stanbon)
The local theater has three types of seats for Broadway plays: main floor, balcony, and... (answered by solver91311)
The local theater has three types of seats for Broadway plays: main floor, balcony, and... (answered by nijneweed,ikleyn)
The local theater has three types of seats for Broadway plays: main floor, balcony, and... (answered by greenestamps)
the local theater has three types of seats for broadway plays: main floor, balcony, and... (answered by Boreal)
The local theater has three types of seats for Broadway plays: main floor, balcony and... (answered by TimothyLamb)
Use a system of equations to solve the following problem The local theater has three... (answered by josgarithmetic,MathTherapy)