Tickets to a movie cost $7.25 for adults and $5.50 for students

Question

A group of friends purchased 8 tickets for $52.75 . How many adult tickets and student tickets were purchased

Answer 1

Let \( x \) be the number of adult tickets and \( y \) be the number of student tickets. We have the following system of equations based on the problem:

1. The total number of tickets: \[ x + y = 8 \]

2. The total cost of the tickets: \[ 7.25x + 5.50y = 52.75 \]

Now we can solve this system of equations.

From the first equation, we can express \( y \) in terms of \( x \): \[ y = 8 - x \]

Now, we substitute this expression for \( y \) into the second equation: \[ 7.25x + 5.50(8 - x) = 52.75 \]

Expanding this, we have: \[ 7.25x + 44 - 5.50x = 52.75 \]

Combining like terms: \[ (7.25 - 5.50)x + 44 = 52.75 \] \[ 1.75x + 44 = 52.75 \]

Subtracting 44 from both sides: \[ 1.75x = 8.75 \]

Now, dividing both sides by 1.75: \[ x = \frac{8.75}{1.75} = 5 \]

Now that we have \( x \), we can find \( y \): \[ y = 8 - x = 8 - 5 = 3 \]

Thus, the number of adult tickets purchased is \( 5 \) and the number of student tickets purchased is \( 3 \).

Conclusion

5 adult tickets and 3 student tickets were purchased.