Respuesta :
ANSWER
The number of tickets for sale at $24 should be 3,500.
The number of tickets for sale at $40 should be 2,500.
EXPLANATION
Let the number of tickets sold for $24 be x.
Let the number of tickets sold for $40 be y.
The total number of seats is 6000. This implies that:
[tex]x+y=6000[/tex]The total revenue that is to be generated is $184,000. This implies that:
[tex]24x+40y=184,000[/tex]Now, we have two simultaneous equations:
[tex]\begin{gathered} x+y=6000 \\ 24x+40y=184,000 \end{gathered}[/tex]From the first equation, make x subject of the formula:
[tex]x=6000-y[/tex]Substitute that into the second equation:
[tex]\begin{gathered} 24(6000-y)+40y=184,000 \\ 144,000-24y+40y=184,000 \\ \Rightarrow16y=184,000-144,000=40,000 \\ \Rightarrow y=\frac{40,000}{16} \\ y=2,500 \end{gathered}[/tex]Substitute the value of y into the equation for x:
[tex]\begin{gathered} x=6000-2500 \\ x=3,500 \end{gathered}[/tex]Therefore, the number of tickets for sale at $24 should be 3,500 and the number of tickets for sale at $40 should be 2,500.
