Question

Determine the total number of adult and student tickets

Answer 1

There were 5 adult tickets and 3 student tickets.

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 = (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.