Question

Determine the total number of adult and student tickets

Answer 1

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;

$7.25x+5.50y=52.75$, take this as equation 1.

Since 8 tickets were purchased,

$x+y=8$, take this as equation 2.

Step 2:

We rearrange equation 2 so we can substitute in equation 1.

$y=8-x$, take this as equation 3.

By substituting equation 3 in equation 1, we get

$7.25x+5.50(8-x)=52.75, 7.25x + 44-5.50x=52.75.$

$1.75x= 8.75, x = \frac{8.75}{1.75}, x = 5.$

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.

$x+y=8, 5+y=8, y = 8-5, y=3.$

So we have x = 5 and y = 3. So there were 5 adult tickets and 3 student tickets.