Question

the local community theater sold a total of 240 tickets for saturday nights performance. they sold 180 more full - price tickets than discount tickets. which system of equations can be used to model this situation?
$\

$$\begin{cases}f + d = 240\\\\f = 180\\end{cases}$$

$
$\

$$\begin{cases}f + d = 240\\\\f - d = 180\\end{cases}$$

$
$\

$$\begin{cases}f - d = 240\\\\f = 180 + d\\end{cases}$$

$
$\

$$\begin{cases}f - d = 240\\\\f = 180d\\end{cases}$$

$

Explanation:

Step1: Define Variables

Let \( f \) be the number of full - price tickets and \( d \) be the number of discount tickets.

Step2: Analyze Total Tickets

The total number of tickets sold is 240. Since the total number of tickets is the sum of full - price tickets and discount tickets, we have the equation \( f + d=240 \).

Step3: Analyze the Relationship between Full - price and Discount Tickets

They sold 180 more full - price tickets than discount tickets. This means that the number of full - price tickets minus the number of discount tickets is 180, so \( f - d = 180 \).

Answer:

\(

$$\begin{cases}f + d=240\\f - d = 180\end{cases}$$

\) (the second system of equations among the given options)