Question

A total of 800 tickets were sold for a music concert. The cheap tickets cost SEK 90/each and the more expensive tickets SEK 120/each. Total ticket revenue was SEK 85,500. How many expensive tickets were sold?

Answer 1

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:

`\begin{gathered} \\ \begin{cases}\mathrm{c+e=800}{} \\ \mathrm{90c+120e=85,500}\end{cases} \end{gathered}`

Let's rewrite the first equation as:

`\boxed{\mathrm{c=800-e}}`

Now, let's replace the value of c in the second equation:

`\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=(13,500)/(30) \\ \\ \boxed{\mathrm{e=450}\text{ }\mathrm{expensive}\text{ }\mathrm{tickets}} \end{gathered}`

Now that we know the number of expensive tickets sold, let's find the number of cheap tickets using equation 1 again:

`\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}`

Answer:

There were sold:

• 350 cheap tickets.

,

• 450 expensive tickets.