Question

The community theatre troupe was putting on a summer production of Shakespeare's A

Midsummer Night's Dream. Tickets for children ages 12 and under were $5.50 each, and tickets for
everyone ages 13 and up were $7.50 each. The theatre troupe sold 30 tickets in the first hour of sales,
for a total of $185. How many tickets for children 12 and under did they sell in that first hour?

Answer 1

`20` tickets at
`\$5.50` and
`10` tickets at
`\$7.50`.

Explanation:

Assume that
`x` of the tickets were sold at
`\$5.50`. The other
`(30 - x)` tickets would be sold at
`\$7.50`.

• Revenue from the sale of the
  `\$5.50` tickets would be
  `5.50\, x`.
• Revenue from the sale of the
  `\$7.50` tickets would be
  `7.50\, x`.

The total ticket sale revenue would be:
`5.50\, x + 7.50\, (30 - x)`.

It is given that the total ticket sale revenue is
`\$185`. In other words:

`5.50\, x + 7.50\, (30 - x) = 185`.

Rearrange and solve this equation for
`x`:

`(5.50 - 7.50)\, x = 185 - (7.50)\, (30)`.

`\begin{aligned}x &= (185 - (7.50)\, (30))/(5.50 - 7.50) \\ &= 20\end{aligned}`.

In other words,
`20` of the tickets were sold at
`\$5.50`. The other
`(30 - 20) = 10` tickets were sold at
`\$7.50`.