Question

One evening 1600 concert tickets were sold for the Fairmont Summer Jazz Festival. Tickets cost $20 for covered pavilion seats and $15 for lawn seats. Total receipts were $26,000. How many tickets of each type were sold? How many pavilion seats were sold?

Answer 1

There were 400 pavilion tickets sold and 1,200 lawn tickets sold.

Explanation:

Let's call the pavilion seats sold `p` and the lawn seats sold `l`. We know there was a total of 1600 concert tickets sold. Therefore:

`p + l = 1600` If we solve for `p` we get `p + l - l = 1600 - 1`

`p = 1600 - l`

We also know pavilion tickets go for $20 and lawn tickets go for $15 and the total receipts were $26000. Therefore:

`20p + 15l = 26000`

Now substituting `1600 - l` from the first equation into the second equation for `p` and solving for `l` while keeping the equation balanced gives:

`20(1600 - l) + 15l = 26000`

`32000 - 20l + 15l = 26000`

`32000 - 5l = 26000`

`32000 - 5l + 5l - 26000 = 26000 + 5l - 26000`

`6000 = 5l`

`6000/5 = (5l)/5`

`1200 = l`

Substitute `1200` for `l` in the result of the first equation to solve for `p`:

`p = 1600 - 1200`

`p = 400`