Question 1198707: Use a system of equations to solve the following problem
The local theater has three types of seats for Broadway plays: main , , and mezzanineMain floor tickets are $44 balcony tickets are $38, and mezzanine tickets are $36. One particular night, sales totaled $47,456There were 43 more main floor tickets sold than balcony and mezzanine tickets combined. The number of balcony tickets sold is 270 more than 2 times the number of mezzanine tickets soldHow many of each type of ticket were sold?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618)   (Show Source):
You can put this solution on YOUR website! This example or others like it were solved several times before on this site.
TYPE PRICE QUANTITY COSTS
Main 44 43+(270+2z+z)
Mezzanine 36 z
Balcony 38 270+2z
TOTALS 47456
A few small simplifications can be done. Form the cost equation in one single variable, z. Solve...
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
Use a system of equations to solve the following problem
The local theater has three types of seats for Broadway plays: main , , and mezzanineMain floor tickets are $44 balcony tickets are $38, and mezzanine tickets are $36. One particular night, sales totaled $47,456There were 43 more main floor tickets sold than balcony and mezzanine tickets combined. The number of balcony tickets sold is 270 more than 2 times the number of mezzanine tickets soldHow many of each type of ticket were sold?
Let number of main floor, balcony, and mezzanine tickets be M, B, and E, respectively
Then we get the following: M = B + E + 43 -- eq (i)
Also, B = 2E + 270 ---- eq (ii)
And, we get revenue equation as: 44M + 38B + 36E = 47,456 ------ eq (iii)
M = (2E + 270) + E + 43 ----- Substituting 2E + 270 for B in eq (i)
M = 3E + 313 ====> M - 3E = 313 ----- eq (iv)
4M + 38(2E + 270) + 36E = 47,456 ----- Substituting 2E + 270 for B in eq (iii)
44M + 76E + 38(270) + 36E = 47,456
44M + 112E = 37,196
4(11M + 28E) = 4(9,299)
11M + 28E = 9,299 ---- eq (v)
11M - 33E = 3,443----- Multiplying eq (iv) by 11 ---- eq (vi)
61E = 5,856 ---- Subtracting eq (vi) from eq (v)
Number of mezzanine tickets sold, or 
With E known, you can compute the ticket-types below.
Number of balcony tickets sold: 2E + 270.
Number of main floor tickets sold: 3E + 313.
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