Respuesta :
Hello!
Let's write some important information contained in the exercise:
Were sold 800 tickets
• cheap + expensive = 800
The price of each ticket was:
• cheap: SEK 90
,• expensive: SEK 120
The total ticket revenue was SEK 85,500.
Note: let's use 'c' for cheap and 'e' for expensive.
Knowing it, we can write it as a linear system look:
[tex]\begin{gathered} \\ \begin{cases}\mathrm{c+e=800}{} \\ \mathrm{90c+120e=85,500}\end{cases} \end{gathered}[/tex]Let's rewrite the first equation as:
[tex]\boxed{\mathrm{c=800-e}}[/tex]Now, let's replace the value of c in the second equation:
[tex]\begin{gathered} \mathrm{90c+120e=85,500} \\ \mathrm{90}\cdot(\mathrm{800-e})\mathrm{+120e=85,500} \\ 72,000-90e+120e=85,500 \\ 72,000+30e=85,500 \\ 30e=85,500-72,000 \\ 30e=13,500 \\ \\ e=\frac{13,500}{30} \\ \\ \boxed{\mathrm{e=450}\text{ }\mathrm{expensive}\text{ }\mathrm{tickets}} \end{gathered}[/tex]Now that we know the number of expensive tickets sold, let's find the number of cheap tickets using equation 1 again:
[tex]\begin{gathered} \mathrm{c+e=800} \\ \mathrm{c+}450\mathrm{=800} \\ \mathrm{c=800-450} \\ \boxed{\mathrm{c=}3\mathrm{50}\text{ }\mathrm{cheap}\text{ }\mathrm{tickets}} \end{gathered}[/tex]Answer:
There were sold:
• 350 cheap tickets.
,• 450 expensive tickets.
