A 6000-seat theater has tickets for sale at $28 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $189600?
Accepted Solution
A:
Answer:4200 tickets of [tex]\$28[/tex] and 1800 tickets of [tex]\$40[/tex] were soldStep-by-step explanation:Given:Tickets are sold at price [tex]\$28[/tex] and [tex]\$40[/tex].Let Number of tickets sold at price [tex]\$28[/tex] be [tex]x[/tex].Let Number of tickets sold at price [tex]\$40[/tex] be [tex]y[/tex].Theater has maximum capacity of 6000 seat.Hence,[tex]x+y=6000 \ \ \ \ equation \ 1[/tex]Total revenue to be generated is [tex]\$189600[/tex][tex]\therefore 28x + 40y= 189600 \ \ \ \ equation \ 2[/tex]Now Multiplying equation 1 by 40 we get,[tex]x+y=6000\\40x+40y=240000\ \ \ \ equation \ 3[/tex]Now Subtracting equation 2 by equation 3 we get,[tex](40x+40y=240000)- (28x + 40y= 189600)\\12x=50400\\\\x=\frac{50400}{12}=4200[/tex]Now substituting value of x in equation 1 we get,[tex]x+y=6000\\4200+y=6000\\y=6000-4200= 1200[/tex]Hence a total of 4200 tickets of [tex]\$28[/tex] and 1800 tickets of [tex]\$40[/tex] were sold