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

Answer:

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

Step-by-step 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 $x$:

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

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

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