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?
<pre>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)
<font color = red><font size = 4><b>Number of mezzanine tickets sold</font></font></b>, or {{{highlight_green(matrix(1,5, highlight(E), "=", "5,856"/61, "=", highlight(96)))}}}

With E known, you can compute the ticket-types below.
<font color = red><font size = 4><b>Number of balcony tickets sold: 2E + 270</font></font></b>.

<font color = red><font size = 4><b>Number of main floor tickets sold: 3E + 313</font></font></b>.</pre>