Question 3 (Multiple Choice Worth 1 points) ( 05.03 MC ) Visitors to a carnival can buy an unlimited-ride pass for \( \$ 50 \) or an entrance-only pass for \( \$ 20 \). In one day, 282 passes were sold for a total of \( \$ 10,680 \). The following system of equations models this scenario: \( \begin{array}{l}50 x+20 y=10,680 \\ x+y=282\end{array} \) How many unlimited-ride passes were sold?

To find out how many unlimited-ride passes were sold, we need to solve the system of equations provided. Here, \( x \) represents the number of unlimited-ride passes sold, while \( y \) represents the entrance-only passes. 1. From the second equation \( x + y = 282 \), we can express \( y \) in terms of \( x \): \( y = 282 - x \). 2. Now, substitute \( y \) in the first equation: \( 50x + 20(282 - x) = 10,680 \). Simplifying this gives: \( 50x + 5640 - 20x = 10,680 \). Combining like terms results in: \( 30x + 5640 = 10,680 \). 3. Subtract 5640 from both sides: \( 30x = 10,680 - 5640 \), which simplifies to: \( 30x = 5040 \). 4. Finally, divide both sides by 30: \( x = \frac{5040}{30} = 168 \). Thus, **168** unlimited-ride passes were sold, and you can tell all the thrill-seekers had a blast! As for the entrance-only passes: Substituting \( x = 168 \) back into \( y = 282 - x \) gives: \( y = 282 - 168 = 114 \). So, 114 entrance-only passes were sold, making it a fun day at the carnival for everyone!