There were 5 adult tickets and 3 student tickets.
Step-by-step explanation:
Step 1:
Assume the number of adult tickets purchased is x and the number of student tickets purchased is y.
From the given data, we can write the following equations;
[tex]7.25x+5.50y=52.75[/tex], take this as equation 1.
Since 8 tickets were purchased,
[tex]x+y=8[/tex], take this as equation 2.
Step 2:
We rearrange equation 2 so we can substitute in equation 1.
[tex]y=8-x[/tex], take this as equation 3.
By substituting equation 3 in equation 1, we get
[tex]7.25x+5.50(8-x)=52.75, 7.25x + 44-5.50x=52.75.[/tex]
[tex]1.75x= 8.75, x = \frac{8.75}{1.75}, x = 5.[/tex]
Step 3:
Substituting this value of x in any of the previous equations we will get y's value.
Here this value of y is substituted in equation 2.
[tex]x+y=8, 5+y=8, y = 8-5, y=3.[/tex]
So we have x = 5 and y = 3. So there were 5 adult tickets and 3 student tickets.
